Huygens' entry and descent through Titan's atmosphere ...

Planetary and Space Science 55 (2007) 1845–1876 

Huygens’ entry and descent through Titan’s atmosphere—Methodology 

and results of the trajectory reconstruction 

Abstract 

Bobby Kazeminejad a,b, , David H. Atkinson c , Miguel Pe´rez-Ayućar d , 

Jean-Pierre Lebreton d , Claudio Sollazzo e 

a Deutsches Zentrum für Luft- und Raumfahrt (DLR), German Space Operations Center (GSOC), D-82234 Wessling, Germany 

b Department for Extraterrestrial Physics, Space Research Institute, Austrian Academy of Sciences, A-8042 Graz, Austria 

c Department of Electrical and Computer Engineering, University of Idaho, Moscow, ID 83844-1023, USA 

d ESA Research and Scientific Support Department, ESTEC, 2200 AG Noordwijk, The Netherlands 

e European Space Operations Center (ESOC), Robert-Bosch-Strasse 5, D-64293 Darmstadt, Germany 

Accepted 13 April 2007 

Available online 27 April 2007 

The European Space Agency’s Huygens probe separated from the NASA Cassini spacecraft on 25 December 2004, after having been 

attached for a 7-year interplanetary journey and three orbits around Saturn. The probe reached the predefined NASA/ESA interface 

point on 14 January 2005 at 09:05:52.523 (UTC) and performed a successful entry and descent sequence. The probe softly impacted on 

Titan’s surface on the same day at 11:38:10.77 (UTC) with a speed of about 4.54 m/s. The probe entry and descent trajectory was 

reconstructed from the estimated initial state vector provided by the Cassini Navigation team, the probe housekeeping data, and 

measurements from the scientific payload. This paper presents the methodology and discuss the results of the reconstruction effort. 

Furthermore the probe roll rate was reconstructed prior to the main entry phase deceleration pulse and throughout the entire descent 

phase under the main and drogue parachute. 

r 2007 Elsevier Ltd. All rights reserved. 

Keywords: Cassini/Huygens mission; Entry and descent trajectory reconstruction 

1. Introduction 

1.1. The Huygens mission and objectives 

The Huygens probe was designed to study the atmosphere 

and the surface of Titan, the largest moon in the 

Saturnian system (Lebreton and Matson, 2002; Lebreton et 

al., 2005). The probe’s scientific objectives comprised the 

detailed in situ measurements of the physical properties, the 

chemical composition, and the dynamics of Titan’s atmosphere 

along the probe descent path, and to provide a local 

characterization of the surface at and close to the impact 

site. Huygens was provided by the European Space Agency 

Corresponding author. Deutsches Zentrum fu¨r Luft- und Raumfahrt 

(DLR), German Space Operations Center (GSOC), D-82234 Wessling, 

Germany. Tel.: +49 8153 282603; fax: +49 8153 281450. 

E-mail address: Bobby.Kazeminejad@dlr.de (B. Kazeminejad). 

0032-0633/$ - see front matter r 2007 Elsevier Ltd. All rights reserved. 

doi:10.1016/j.pss.2007.04.013 

ARTICLE IN PRESS 

www.elsevier.com/locate/pss 

(ESA) to the joint NASA/ESA/ASI (Italian Space Agency) 

Cassini/Huygens dual-craft spacecraft, which was launched 

from Cape Canaveral (Florida) aboard a Titan-4B Centaur 

rocket on 15 October 1997 (Matson et al., 2002). With a 

launch mass of 5650 kg, the spacecraft was too massive for 

a direct injection towards Saturn and therefore required 

gravity assists from three planets—Venus (April 1998 and 

June 1999), Earth (August 1999), and Jupiter (December 

2000). Along this trajectory, the flight time to Saturn was 

slightly less than 7 years. Cassini/Huygens successfully 

performed its Saturn Orbit Insertion (SOI) maneuver on 

1 July 2004. Following the discovery of an anomaly in the 

probe-to-orbiter telecommunication system in 2000 (Clausen 

et al., 2002), the Huygens nominal mission would have 

resulted in severe data loss during the relay link and an 

alternative scenario was adapted in 2001 (Strange et al., 

2002), which required the addition of one more orbit prior 

to the probe mission. In the modified mission the probe

1846 


B. Kazeminejad et al. / Planetary and Space Science 55 (2007) 1845–1876 

Fig. 1. Upper panel: view from the north onto Saturn’s equatorial plane with a grid given in units of Saturn radii, i.e., RS ¼ 60330 km. The first three 

Cassini orbits after Saturn Orbit Insertion (SOI) are shown together with Titan’s orbit (circle). The Huygens probe was released on the third Cassini orbit 

(Rev C) on 25 December 2004 at 02:00 UTC. Lower panel: Huygens’ and Cassini’s trajectories with respect to Titan. Cassini passed its periapsis at a 

distance of 60,000 km from Titan and a time difference of 2.1 h with respect to the probe reaching the NASA/ESA interface point on UTC 14 January, 

09:05:52.523. The DSN ground-station visibility is also shown (courtesy of NASA/ESA).

was separated from Cassini on the third orbit (designated 

as Tc) around Saturn instead of the first orbit as planned in 

the original baseline mission. The first three Cassini orbits 

after SOI are depicted in the upper panel of Fig. 1. 

Although minor DV penalties resulted from the new 

Huygens mission design, the first two targeted Titan flybys 

in the new reference trajectory (Ta on 26 October 2004 and 

Tb on 13 December 2004) were used for key remote sensing 

investigations of Titan’s atmosphere, resulting in an 

improved knowledge of Titan’s atmosphere and validation 

of the current (Voyager based) Titan atmosphere reference 

model. 

1.2. Probe separation and targeting 

The responsibilities for meeting the probe trajectory 

requirements were carefully shared between NASA and 

ESA. The Cassini Navigation team was responsible for 

delivering the probe to the NASA/ESA interface point, 

which is defined by a probe to Titan center distance of 

3845 km (or a reference altitude of 1270 km), at a flight 

path angle of 65 3 (99% confidence level) and angle of 

attack of ð0 5 Þ 3ðsÞ. The respective time at which the 

probe would reach this interface point is referred to as the 

interface epoch. 

The Huygens probe was released from the Cassini 

spacecraft on 25 December 2004 at 02:00 UTC (Lebreton 

et al., 2005). In preparation for the separation, the Cassini 

spacecraft had been set on a Titan-impact trajectory. The 

Huygens separation mechanism consisted of a three-point 

attachment system, which provided the probe with a 

counter-clockwise roll rate of 7.2 rpm. This assured the 

stability of the probe during its atmospheric entry phase. 

With three redundant timers being the only active devices, 

the probe coasted along a ballistic trajectory to Titan for 20 

days, 2 h, 41 min, and 18 s. The countdown timers were 

loaded prior to the orbiter/probe separation event and were 

programmed to end 4 h and 23 min prior to the predicted 

interface epoch. 

After probe separation Cassini performed an ‘‘Orbiter 

Deflection Maneuver’’ (ODM) and its ‘‘trajectory cleanup 

maneuver’’ on 28 December 2004 and 3 January 2005, 

respectively. The ODM was necessary to avoid hitting 

Titan and to ensure the correct Titan flyby geometry, which 

was required to achieve the best conditions for the orbiter/ 

probe telemetry relay link via the two redundant S-band 

RF channels. The probe and orbiter trajectories relative to 

Titan are depicted in the lower panel of Fig. 1. Cassini 

reached its periapse at a Titan distance of 60,000 km about 

2.1 h after the probe had reached the ESA/NASA interface 

point. From extensive preflight simulations (Kazeminejad 

et al., 2004) it was concluded that this delay time would 

provide the best relay link conditions and still ensure that 

all the probe engineering and science payload requirements 

were met. 

The Cassini Navigation team’s task was to predict the 

interface epoch as well as the six-dimensional probe and 


B. Kazeminejad et al. / Planetary and Space Science 55 (2007) 1845–1876 1847 

orbiter state vectors together with the corresponding 

uncertainties expressed in the form of a covariance matrix. 1 

This information was used by the Huygens project for two 

main purposes: (1) to predict the probe impact point, a 

fixed point on Titan’s surface at which to point the 

orbiter’s high gain antenna during the entire orbiter/ 

probe relay sequence, and (2) as the official starting point 

for the reconstruction of the Huygens entry and descent 

trajectory. 

The probe flight path angle and the angle of attack at the 

interface altitude were reconstructed from the probe 

separation dynamics on the Cassini spacecraft. Values of 

65:6 0:3 ð1sÞ and 1:4 (respectively) were provided by 

the Cassini Navigation team to the project (J. Jones, 

private communication). Both the flight path angle and 

angle of attack requirements were met. 

1.3. Probe system and entry, descent, and landing overview 

The Huygens probe system consisted of the aeroshell 

comprising the front-shield and the back cover, and the 

Descent Module, which was enclosed within the aeroshell. 

The probe is shown in its entry phase configuration in 

Fig. 2 and in an exploded view in Fig. 3. The 79 kg, 2.7 m 

diameter, 60 half-angle coni-spherical front shield was 

built out of tiles of AQ60 ablative material (a felt of 

phenolic resin reinforced by silica fibers) (Clausen et al., 

2002), which protected the probe from the heat-flux 

during its hypersonic and supersonic entry phase. The 

physical dimensions and mass distribution of the probe in 

entry configuration are given in the lower panel of Fig. 2. 

The probe entry, descent, and landing (EDL) sequence is 

shown schematically in Fig. 4. The descent phase started 

with the initiation of the parachute sequence at T 0 ( Mach 

1.5) under a 2.59 m disk gap band (DGB) pilot chute, 

followed by an 8.30 m DGB main parachute and a 3.03 m 

stabilizing chute. As the probe was required to rotate (spin) 

during its descent, a swivel was incorporated in the 

connecting riser of both the main and the stabilizer 

parachutes. 

For trajectory reconstruction purposes it is useful to 

divide the Huygens mission sequence into the following 

phases: 

the entry phase scheduled by the pre-T 0 timeline; 

the descent phase scheduled by the post-T 0 timeline. 

The pre-T 0 timeline had to ensure the correct activation of 

the parachute deployment sequence with the firing of the 

pilot chute at T 0. This required two important events 

during the entry phase: the probe onboard software 

(POSW) mission timer start at time S0 and the triggering 

of the parachute sequence arming timer at time T A. 

1 The 14 14-dimensional covariance matrix contained the uncertainties 

of the probe and orbiter state vectors as well as the uncertainties of 

Saturn’s and Titan’s gravitational constants.

1848 

Sealings at experiment / structure interface 

Top platform: Alu 

After cone / Fore dome : Alu 

Internal foam : 4570 mm 

Horizontal / Vertical 

struts : Titanlum 

Mechanism brackets : 

conductively decoupled from 

F.S. 

Boxes : Black paint ()except 

batteries) 

Batteries : 

Radlatively / conductively 

decoupled 

RHU's : main plat. : 27 

top plat. : 8 

Shoulder 

Radius 

Ixx = 127.97 kg m 2 

Iyy =75.85 kg m 2 

Izz = 71.9 kg m 2 

Ixy = 0.45 kg m 2 

Iyz = 0.338 kg m 2 

Ixz = -0.096 kg m 2 

X 0 



Max. Diameter: 2.7 m 

Nose Radius: 1.201 m 

Half cone angle: 60° 

Shoulder Radius: 0.0486 m 

Ref. Surface: 5.73 m2 

Entry mass: 320 kg 

Z 

Reference Point 

Half cone 

Angle 

Nose Radius 

Back Cover : 

. External MLl : 15 Layers 

. HTP / Prosial : 0.5 to 2.7 mm 

. Al structure : 0.8 to 1.6 mm 

Orbiter struts : Titanium 

SED + Ring : ML1 : 15 layers 

Labyrinth foils : 

Front shield - outside : 

. Rear side ext. ML1: 15/16 layers 

. HTP / Prosial : 2.1 mm 

. CFRP / Honeycomb structure 

. HTP / AQ60 : 18.2 mm 

. Front side ext. ML1: 15/16 layers 

Front shield - central part: 

. FFRP / Honeycomb structure 

. HTP / AQ60 : 17.4 mm 

. External ML1 : 15 layers 

Radiative window : 

white paint, 0.17 m2 

Maximum 

Diameter 

Fig. 2. The Huygens probe in its entry aeroshell configuration. The upper panel shows the location of the Descent Module inside the aeroshell, which 

consisted of the back cover and the front shield. The lower panel shows the definition of the vehicle body-fixed reference system and provides important 

probe dimensions and the components of the mass inertia tensor (Clausen et al., 2002; Tran and Lenoir, 2005).

EXPERIMENT PLATFORM 

FRONT SHIELD 

AFTER CONE 


FORE DOME 

TOP PLATFORM 

DESCENT 

MODULE 

SEPERATION / EJECTION DEVICE 

BACK COVER 

ENTRY 

ASSEMBLY 

Fig. 3. The Huygens probe system in exploded view (Clausen et al., 2002). The separation/ejection device remained attached to the orbiter and ensured the 

probe roll/spin after release from Cassini. The back cover and front shield were ejected during the mission. The Descent Module was one single unit, which 

consisted of four parts as shown and named in the figure. 

Nominal 

1270 km 

Interface 

Altitude 

Entry 

Start of 

Descent 

Phase 

T0 = 0 sec 

Mach 1.5 

h=159 km 

Fire PDD T0 = +1.4 sec 

2.59 m dia 

DGB Pilot 

Chute Inflation T0 = +2.5 sec 

Release Aft Cover 

Deploy 8.30 m dia 

DGB Main 

About 3 minutes: 

Depends on atmospheric conditions 

Source: Huygens User Manual Operations 

HUY AS/c. 100.OP0384 rev 04 15 Jane 97 

Table 1.9-7. 


T0=+4.9 sec 

Main chute Inflation 

T0=+32.5 sec 

Mach < 0.6 

Release 

Front 

Shield 

Huygens Instrument 

beginning activities 

T0 = +10 sec 

Huygens Probe Descent Events 

T0 = +2 min 23.675 sec 

Data Transmission 

Starts 

T0 = +15 min 

Release Main Chute 

Deploy 3.03 m dia 

Stabilizing Drogue 

T0 = +15 min 3.4 sec 

Stabilzer Inflation 

Fig. 4. The Huygens probe entry and descent mission sequence as defined in Collet (1997). The reconstruction effort provided timing and altitudes of the 

various events during the sequence, which are summarized in Table 1.

1850 

Both events were timed by the detection of specific 

deceleration limits, which are provided in Table 1. Itis 

important to note that the detection of S0 and T A required 

the enabling of the detection process first, triggered by the 

detection of defined thresholds on the rising edge of the 

deceleration profile, i.e., 50 and 80 m=s 2 for S0 and T A, 

respectively. The detection event itself was declared when 

the corresponding deceleration limits on the trailing edge 

of the profile were measured. The detailed descent phase 

timeline with corresponding altitudes is provided in 

Table 1. 

2. Reconstruction strategy and input data sets 

The Huygens entry and descent trajectory reconstruction 

is the responsibility of the Huygens Descent Trajectory 

Working Group (DTWG) with its organizational structure 

outlined in Atkinson et al. (2007). The reconstruction 

strategy adapted by the group can be summarized by the 

following three phases: 

1. The reconstruction of the probe entry phase from the 

interface point down to an altitude of 100 km. 

2. The reconstruction of the probe descent phase from the 

surface up to 145 km. 

3. The entry and descent trajectory merging process, which 

ensured a smooth merging of the entry and descent 

phase in terms of both altitude and descent speed. 

The methodology and results of each step will be discussed 

separately in the subsequent sections. In this section 

we concentrate on the input data sets relevant for each 

phase. 



Table 1 

Timing of important events in the probe mission timing sequence (Lebreton et al., 2005; Couzin, 2005; Kazeminejad et al., 2004) 

Phase Time w.r.t. T 0 Event SCET-UTC Reconstructed altitude (km) 

Entry phase T 0 4m 28:08 s NASA/ESA Interface 09:05:52.52 1247.7 

acc:450 m=s 2 (RE) S0-detect. enabled 

acc:480 m=s 2 (RE) T A-detect. enabled 

acc:o10 m=s 2 (TE) S0-detection 09:10:14.23 157.0 

acc:o9:484 m=s 2 (TE) T A-detection 09:10:15.73 156.6 

T 0 ¼ S0 þ 6:375 s PDD firing 09:10:20.60 155.0 

T 0 þ 1:47 s Pilot chute inflated 09:10:22.07 154.4 

Descent with main chute T 0 þ 2:50 s Back cover release 09:10:23.10 

and front shield T 0 þ 4:95 s Main parachute deployed 09:10:25.55 

T 0 þ 32:50 s Front shield jettison 09:10:53.10 149.5 

Descent with main chute T 0 þ 143:63 s Start data transmission 09:12:44.23 148 

T 0 þ 900 s Main parachute release 09:25:20.60 111 

Descent with stabilizing drogue T 0 þ 901:02 s Stabilizing drogue deployed 09:25:21.62 

T 0 þ 31 m 54:62 s RAU power on 09:42:15.22 62 

T 0 þ 2 h 27 m 50:4 s Surface impact 11:38:11.00 0 

acc: ¼ measured acceleration value; RE ¼ rising edge of the deceleration profile; TE ¼ trailing edge; T A ¼ triggering of the parachute sequence arming 

timer, S0 ¼ probe onboard software (POSW) mission timer start, T 0 ¼ starting time of the parachute deployment sequence (T 0 ¼ 158 965 885:184 ET 

seconds past the epoch J2000, which corresponds to UTC 2005-01-14T09:10:20.999), and SCET ¼ spacecraft event time. Note that RAU-1 and RAU-2 

altitude measurements are actually available from 42 to 38 km, respectively, even if the switch on time happened at an altitude of 62 km. 

2.1. Entry phase input data 

The entry phase reconstruction is based on the probe 

position and velocity vector at the interface epoch of 14 

January 2005 UTC-09:05:52.523 (both provided by the 

Cassini Navigation team) and the measurements of the 

probe accelerations. The Huygens probe was equipped with 

two sets of accelerometers, the engineering (housekeeping) 

accelerometers, which were responsible for the proper 

detection of deceleration thresholds for the arming and 

triggering of events in the parachute sequence, and the 

science accelerometers, which were part of the scientific 

payload. The engineering accelerometers consisted of the 

Central Accelerometer Sensor Unit (CASU) which comprised 

three redundant accelerometers mounted in the axial 

probe direction (probe X-axis) and the Radial Accelerometer 

Sensor Unit (RASU), which was designed to 

measure the probe spin during the descent phase. The 

science accelerometers were part of the Huygens Atmospheric 

Structure Instrument (HASI) and consisted of one 

servo and three piezo accelerometers (Fulchignoni et al., 

2005). The HASI servo accelerometer was mounted in the 

probe symmetry axis direction, and had a sampling rate of 

3.125 Hz during the entry phase and 4.167 and 1.754 Hz 

during the descent phase and at probe impact, respectively. 

The three HASI piezoresistive accelerometers had a lower 

sampling rate of 1.6129 Hz. One piezo sensor was mounted 

in the axial direction (X-axis) and the two other sensors 

were mounted in the two normal directions (probe Y- and 

Z-axes). To improve the measurement accuracy along the 

probe’s symmetry axis the servo accelerometer was located 

near the spacecraft center of mass and operated by sensing 

the displacement of a seismic mass. The current required to

drive the mass from its displaced position back to its null 

position is a direct measurement of acceleration. The 

piezoresistive accelerometers consisted of a suspended 

seismic mass supported by a cantilever whose displacement 

is determined by two strain-dependent resistances. 

The HASI servo and CASU measured axial deceleration 

profiles close to T 0 and the time of main chute release are 

shown, respectively, in Figs. 5 and 6. The CASU 

measurements were characterized by a lower sampling rate 

of only 1 Hz and a cut-off at 10 Earth-g, which represents 

the maximum measurement range of the sensor. The 

CASU is responsible for sensing certain deceleration limits, 

which initiated important events in the EDL sequence. 

Aerodynamic Deceleration [m/s 2 ] 


120 

100 

80 

60 

40 

20 

0 

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 

Time [min] past Interface Epoch UTC: 2005-01-14T09:05:52.523 

120 

110 

100 

90 

80 

70 

Arming 

POSW enables 

S0 

60 

2.9 3 3.1 3.2 3.3 3.4 3.5 3.6 3.7 


T0 


XSERVO 

CASU 

XSERVO 

CASU 

Fig. 5. HASI servo (solid line) and CASU (crosses) accelerometer 

measurements during the hypersonic and supersonic entry phase. The 

three horizontal (dashed) lines in the upper panel show the acceleration 

limits, which were sensed by the CASU for the proper initiation of the 

parachute sequence at T 0, i.e., the Probe Onboard Software (POSW) and 

arming timer detection limit at respectively 50 and 80 m=s 2 (both on the 

raising edge of the deceleration pulse), and the POSW mission timer start 

S0 at 10 m=s 2 (on the trailing edge of the deceleration pulse). The lower 

panel zooms into the region of peak deceleration and shows the design 

specific detection limit of the CASU at 10g E. 




35 

30 

25 

20 

15 

10 

BC 

XSERVO 

CASU 

5 

0 

Mortar 

T0 = s0 + 6.375 sec 

4.35 4.4 4.45 4.5 4.55 4.6 4.65 4.7 4.75 4.8 


1.6 

1.4 

1.2 

1 

0.8 

0.6 

0.4 

0.2 

0 

T0 + 900 sec = main chute release 

-0.2 

19 19.5 20 20.5 21 21.5 22 22.5 23 

Time [sec] past Interface Epoch UTC: 2005-01-14T09:05:52.523 

Fig. 6. The upper panel shows the HASI servo (solid line) and CASU 

(crosses) accelerometer measurements around the time of 

T 0 S0 þ 6:375 s. Note that T 0 could only be determined with an 

uncertainty of 0.6 s. The mortar firing and the back cover release are 

indicated with labels. The lower panel shows the HASI servo accelerometer 

measurements close to the time of main chute release and 

deployment of the drogue chute ðT 0 þ 15 minÞ. It can be seen that it took 

about 2.5 min for the drogue chute to attain terminal velocity. 

Those deceleration limits and the corresponding events are 

shown as horizontal lines in the upper panel of Fig. 5. T 0 

occurred in the time window of UTC 09:10:20.3– 

09:10:20.9. The mortar firing, back over release, as well 

as the subsequent deployment of the pilot and main chute 

can be clearly identified in the upper panel of Fig. 6. The 

main chute release occurred at about 19.5 min past 

interface epoch (see lower panel of Fig. 6) and was 

followed by the deployment of the stabilizing drogue chute. 

In addition to the measured probe accelerations, a 

prograde wind velocity of 90 m/s is assumed in the 

integration of the equations of motion (see Section 3) 

down to the altitude at which real drift or wind 

measurements were available. In the zonal direction the 

Doppler Wind Experiment (DWE) (Bird et al., 2005a)

1852 

provided drift measurements from T 0 þ 118 s. In the 

meridional directions the probe drift was derived from 

extrapolated data of the Descent Imager/Spectral Radiometer 

(DISR) Experiment (Tomasko et al., 2005). 

2.2. Descent phase input data 

The descent phase retrieval comprised the reconstruction 

of both the probe vertical trajectory (altitude and descent 

speed) as well as the wind-induced horizontal drift (zonal 

and meridional). The reconstruction of the horizontal 

motion caused by wind provided the estimated coordinates 

(i.e., longitude and latitude) of the probe landing site. 

The descent phase reconstruction is based on the 

following data sets: 

Atmospheric in situ measurements from the HASI 

pressure and temperature measurements corrected for 

dynamical effects by the instrument team 2 (Fulchignoni 

et al., 2005). 

Mole fraction measurements of Titan’s major constituents 

from the gas chromatograph and mass spectrometer 

(GCMS) (Niemann et al., 2005). 

Wind measurements as derived from the Doppler shift 

of the probe relay signal from the DWE (Bird et al., 

2005a). 

The exact time of probe surface impact measured by the 

impact penetrometer (ACC-I) of the Surface Science 

Package (SSP) (Zarnecki et al., 2005). 

Altitude and descent speed measurements provided by 

the SSP acoustic sonar (API-S) and the two Radar 

Altimeter Units (RAU) (Trautner, 2005). 

The instrument sensors are briefly described in the 

subsequent paragraphs. For a more detailed description 

the reader is referred to the referenced literature. 

The two HASI temperature sensors (TEM-1 and TEM- 

2) are dual element platinum resistance thermometers 

(Fulchignoni et al., 2005). Each unit comprised a platinum–rhodium 

truss cage frame exposing the two sensing 

elements to the atmospheric flow. The two redundant 

temperature sensor units (fine and coarse) were mounted 

together with the pressure sensor on a stub, which ensured 

that the sensors were appropriately located and oriented 

with respect to the flow. The TEM sensors could resolve 

0.02 K with an accuracy of 0.5 K. 

The HASI Pressure Profile Instrument (PPI) included 

sensors for measuring the atmospheric pressure during 

descent and on the surface. The transducers and the related 

electronics were located in the HASI Data Processing Unit 

(DPU). The atmospheric pressure is conveyed to the DPU 

through a Kiel-type pressure probe accommodated within 

2 Nota bene: the HASI TEM and PPI input data used for the 

reconstruction are consistent with the file HASI_L4_ATMO_PROFILE_ 

DESCEN.TAB in the ESA Planetary Science Archive (data set ID ¼ HP- 

SSA-HASI-2-3-4-MISSION-V1.1). 



a pitot tube, mounted on the same stub as the TEM 

sensors. The Kiel probe provided accurate measurements 

of the total pressure (static plus dynamic) for flow 

inclination angles up to 45 . The pressure transducers are 

silicon capacitive absolute pressure sensors known as 

Barocaps. The Barocap consists of a small sensor head 

with associated transducer electronics. The varying ambient 

pressure deflected a thin silicon diaphragm in the sensor 

head, causing a change in the separation of two capacitive 

plates. The variation in capacitance was then converted 

into an oscillation frequency in the PPI electronics. The 

PPI sensor had a sampling rate of 2/2.3 Hz and an accuracy 

of 1% of the measured value with a maximum measurement 

error limited to 1 hPa. 

The GCM measured the chemical composition of Titan’s 

atmosphere during the entire descent phase and determined 

the isotope ratios of the major gaseous constituents. The 

instrument consisted of a quadrupole mass filter with a 

secondary electron multiplier detection system and a gas 

sampling system providing continuous direct atmospheric 

composition measurements and batch sampling through 

three gas chromatographic columns. The mass spectrometer 

employed five ion sources sequentially feeding the 

mass analyzer. The GCMS measurements of N2 and CH4 

mole fractions were used to infer the mean molecular mass 

as a function of altitude during the entire descent phase. 

The SSP consisted of a collection of nine instrument 

subsystems, designed primarily to study Titan’s surface 

properties. However, two of the instruments were relevant 

for the trajectory reconstruction: (1) the SSP Acoustic 

Properties Instrument—Sonar (API-S) providing altitude 

and descent speed measurements in the range from 85 to 

13 m, and (2) the SSP internal ACC-I accelerometer 

providing the most accurate time of surface impact, 

UTC ¼ 11: 38: 10:77. 

The DWE measured the vertical profile of zonal (east/ 

west) winds in the atmosphere of Titan. Measurements 

were nominally scheduled to start once the orbiter/probe 

relay link was established and cover the entire descent 

phase down to the surface impact. The DWE is the only 

scientific payload which included hardware on both the 

probe and the orbiter. The orbiter-mounted hardware was 

part of the Probe Support Avionics in the orbiter-mounted 

Probe Support Equipment. The Doppler wind hardware 

comprised two ultrastable oscillators, the Transmitter 

Ultrastable Oscillator (TUSO) and the Receiver Ultrastable 

Oscillator (RUSO). The TUSO was the primary 

signal generator used to drive the probe relay link (PRL) of 

transmitter A. The 10 MHz output of the TUSO was 

upconverted to the PRL-A frequency of 2.040 GHz and 

was amplified for transmission through the probe transmitting 

antenna (PTA) to the Cassini orbiter high gain 

antenna. All timing and signal generator requirements for 

receiver A on the orbiter were controlled by the RUSO. 

Unfortunately due to a missing telecommand in the probe 

relay sequence, the RUSO was not switched on, leading to 

a full loss of the Channel A telemetry. The DWE data were

initially thought to be entirely lost, since DWE was the 

only instrument without Channel A/B redundancy. Fortunately 

extensive effort was invested prior to the mission 

to establish an Earth-based radio-dish network that was 

able to receive the Probe Channel A signal (Folkner et al., 

2004). Originally planned to complement the DWE science 

results, the ground-based observations turned out to be the 

only means by which the Channel A data were recorded, 

thereby saving the DWE wind retrieval (Bird et al., 2005b). 

One more independent direct measurement of probe 

altitude was made by the two radar altimeters, which 

provided measurements in the altitude range from 40 km 

down to 130 m. The altitude measurements of radar unit A 

(15.4–15.43 GHz) and B (15.8–15.83 GHz) required extensive 

postprocessing in order to correct for various 

systematic measurement errors (i.e., digital, altitude, and 

temperature errors). The data reduction was performed by 

a dedicated team at ESA/ESTEC and is described in more 

detail in Trautner (2005). The calibration provided a 

relative ð1sÞ error bar of 2.7%. 

It should be pointed out that neither the RAU nor the 

SSP API-S measurements were directly incorporated into 

the reconstruction algorithm but were primarily used for 

comparison and consistency checks. 

2.3. Entry and descent merging data 

The final step in the reconstruction effort is the 

estimation of initial state vector corrections. No additional 

instrument data sets were needed for this phase. The state 

vector corrections were based on a least-squares estimation 

algorithm that minimized the residuals in the reconstructed 

altitude and descent speed profiles. The residuals were 

calculated in the region where the reconstructed trajectories 

of the entry and descent phase overlapped each other 

(i.e., about 145–100 km altitude range). 

3. Entry phase reconstruction 

3.1. Methodology 

The entry phase trajectory is reconstructed by numerical 

integration of the equations of motion using an adaptive 

step size Runge–Kutta algorithm (Fehlberg, 1968). The 

equation of motions are traditionally formulated and 

integrated in a rotating (planet-fixed) coordinate system. 

For the Huygens reconstruction, the added complexity of 

including the Coriolis and centrifugal forces has been 

eliminated by integrating the equations of motion in the 

Titan-centered Earth Mean Equator and Equinox of J2000 

(EME2000) inertial frame. To express the reconstructed 

trajectory in body-fixed spherical coordinates (i.e., height 

above surface, longitude and latitude) a coordinate 

transformation based on the IAU rotational elements 

(i.e., Titan pole coordinates, prime meridian angle, and 

rotational period) according to Davies et al. (1995) and a 

planetary radius of 2575 km is performed after the 



trajectory is integrated. In an inertial frame the equation 

of motions can be written as 

d 2 r 

dt2 a ¼ ag þ aAd, (1) 

where r is the probe position vector and a the total probe 

acceleration, which is composed of the gravitational 

acceleration ag and the aerodynamic acceleration aAd. 

The gravitational acceleration ag is composed of contributions 

from the primary body mass M0 and a specified 

number of perturbing body masses Mj. It is important to 

keep in mind that ag could not be measured by onboard 

accelerometers and was therefore entirely modeled, based 

on the integrated probe position vector r according to 

ag ¼ 

r X2 

GM0 þ GMj 

3 jrj 

r 

rj3 pj jpjj3 " # 

þ =U, (2) 

j¼1 

pj jpj where p j is the position vector of jth perturbing body, G is 

the gravitational constant, and =U is the gradient of the 

disturbing function due to the dynamical flattening of 

Titan. For the reconstruction of the Huygens trajectory the 

masses of Saturn ðGM1 ¼ 37 940 515:88 km 3 =s 2 Þ, the Sun 

ðGM2 ¼ 132 712 440 017:987 km 3 =s 2 Þ, and Titan ðGM0 ¼ 

8978:14229785491 km 3 =s 2 Þ were taken into account. For 

Titan an axisymmetric gravity field up to J2 is modeled. 

The aerodynamic force acceleration vector aAd is derived 

from the data of the onboard accelerometers, which 

measured the linear accelerations of the spacecraft center 

of mass in the three orthogonal directions (i.e., axial and 

normal) of the spacecraft body frame. The correct 

transformation of the measurements from the spacecraft 

frame to the inertial frame of integration requires the 

knowledge of the orientation of the spacecraft with respect 

to the direction of the flow velocity. The flow velocity 

direction is reconstructed in the inertial frame of integration 

based on the assumption of a stiff planetary corotating 

atmosphere and a constant prograde zonal wind 

velocity vector. 

The separation angle of the probe axial body axis and 

the flow velocity vector is given by the angle of attack aðtÞ. 

In planetary entry probe missions the angle of attack is 

typically estimated from the ratio of measured normal to 

axial accelerations as those equal the ratio of the 

corresponding aerodynamic coefficients. The aerodynamic 

coefficients in return are determined from preflight wind 

tunnel tests and computational fluid dynamic simulations 

and provided as a function of a and Mach number Ma in 

the form of an aerodynamic database. Due to a sensitivity 

problem of the HASI piezoresistive accelerometers, the 

measurements along the normal axis turned out to be too 

inaccurate for the angle of attack to be determined from 

accelerometer ratios. A zero angle of attack therefore had 

to be assumed for the reconstruction of the entire entry 

trajectory. In this special case the aerodynamic drag aD 

equals the measured axial acceleration aA, and the

1854 

accelerometer measurements in the normal spacecraft 

directions were not used. 

Once the norm of the drag force is measured, the 

corresponding vector aAd is reconstructed based on 

the simple fact that the drag force vector always points in 

the opposite direction of the relative flow velocity vector 

vrel of the spacecraft with respect to the ambient atmosphere 

(expressed in the inertial frame of integration). The 

acceleration due to drag can therefore be written as 

aAd ¼ aD 

vrel 

j vrel j 

with vrel given by the relation 

vrel ¼ v ~op r vw, (4) 

where r and v are again the probe position and velocity 

vectors (in the inertial frame), ~op ¼ 4:560678 10 6 rad=s 

is the angular velocity vector of Titan, and vw the velocity 

vector of the atmospheric wind, which must also be 

expressed in the inertial frame of integration. The wind 

vector is first expressed in the equatorial coordinate 

system 3 according to 

8 9 

vw ¼ 

>< 

>: 

vzonrx=r 

þvzonry=r 

þvmer 

>= 

(3) 

, (5) 

>; 

where vzon is the zonal wind component (measured 

positively from west to east) and vmer the meridional wind 

component (measured positively from south to north). 

Once evaluated in the equatorial system a simple rotation is 

used for the transformation into the inertial system of 

integration (cf. Kazeminejad, 2005, p. 50). 


Table 2 

Initial state vector at the interface epoch 2005-01-14T09:05:52.523 SCET-UTC (158 965 616.707 ET seconds past J2000) 

Coordinate NAV 1s Adjusted Difference ðsÞ 

x 74.84856340 5.62 68.24626095 1.18 

y 3832.088332 32.10 3809.336798 0.71 

z 305.9503431 3.63 311.8217596 1.62 

vx 2.379991142 8:58E 04 2.379411383 0.68 

vy 5.537146584 3:23E 03 5.534426806 0.84 

vz 0.2269144660 4:46E 04 0.2273084312 0.88 

West lon. (deg) 185.53 0.13 185.43 0.79 

South lat. (deg) 8.50 0.12 8.61 0.96 

Altitude (km) 1270.01 30.73 1247.69 0.73 

Inertial velocity (km/s) 6.0312 6.0285 2:7E 03 

Inertial flight path angle (deg) 65.547 65.62 0.07 

Inertial azimuth angle (deg) 259.897 259.895 0.02 

The column labeled ‘‘NAV’’ lists the probe state vector as provided by the Cassini Navigation team (JPL-050214 DELIVERY) with corresponding 

uncertainties. The column labeled ‘‘Adjusted’’ shows the corrected state vector after the trajectory merging process has converged. The difference between 

the NAV vector and the adjusted one is provided in the last column in units of the NAV 1s uncertainty. Reference system for all vectors is the Titan 

centered EME2000 inertial system and units are in km and km/s. The inertial azimuth angle is measured positive from north to east. 

3 In the equatorial system the x-axis points to the intersection of the 

Earth mean equator of the epoch J2000 and the planet’s equator, the 

z-axis points to Titan’s north pole (and is parallel with its rotation axis), 

and the y-axis fills out an orthogonal right-handed system. 


3.2. Trajectory results 

The numerical integration is started at the interface point 

using the Cassini Navigation estimation of the probe state 

vector. To ensure a good match of the entry and descent 

phase, the interface state vector is adjusted in the trajectory 

merging process (see also Section 6 for details on merging 

of entry and descent phase). Both the Cassini Navigation 

solution and the adjusted state vectors are listed in Table 2. 

It is important to note that the direction of the relative 

velocity vector vrel is influenced by atmospheric winds 

according to Eq. (4). The DWE zonal wind measurements 

were limited to the descent phase, however. A parameter 

study shows that the assumption of a constant 90 m/s 

prograde zonal wind for altitudes above 143.9 km (for 

lower altitudes DWE measurements were available) 

achieves the best merging of entry and descent phase 

(Kazeminejad et al., 2005a). 

The entry phase reconstruction based on the HASI 

accelerometer data could only be achieved down to an 

altitude of 100 km. At lower altitudes the numerical 

integration of the equations of motion did not converge 

due to the built-up error introduced by the integration of 

accelerometer measurements, which were strongly perturbed 

by the pendulum motion introduced by the opening 

of the various parachutes. An additional systematic error is 

introduced by the fact that during the parachute sequence 

the accelerometers were no longer located at the center of 

gravity, as the jettison of the back cover and the release of 

the parachutes introduced a non-negligible change of mass 

distribution. 

The results of the entry phase trajectory reconstruction 

are depicted in Fig. 7. The upper panel shows the altitude 

profile with respect to the reference surface, which is 

considered to be at a radial distance of 2575 km from 

Titan’s center. The figure shows both the reconstructed 

profile (solid line) based on the flight data and the preflight

Altitude [km] above Ref. Surface of 2575.0 km 

Inertial Velocity [m/s] 

1200 

1000 

800 

600 

400 

200 

6000 

5000 

4000 

3000 

2000 

1000 

Huygens Probe Trajectory: Entry Phase 

0 

0 

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 

Time [min] 

past Interface Epoch UTC: 2005-01-14T09:05:52.523 

Huygens Probe Trajectory: Entry Phase 

Flight Data 

PREDICT 

0 

0 

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 

Time in [min] past Epoch: UTC: 2005-01-14T09:05:52.523 

Fig. 7. Reconstructed entry phase altitude (upper panel) and inertial 

velocity profile (lower panel) based on the HASI Servo accelerometer 

measurements. The dashed lines show the results of the preflight 

simulations. The dashed-dotted lines show the deceleration pulse with 

units provided on the right side ordinate ð1g E ¼ 9:806 m=s 2 ). 

simulation trajectory as described by Kazeminejad et al. 

(2004) (dashed line). It is important to point out that the 

preflight simulation is based on the initial conditions as 

estimated by the Cassini Navigation team (i.e., an altitude 

of exactly 1270 km at interface epoch). The reconstructed 

profile (labeled ‘‘Flight Data’’) used the modified initial 

state vector based on the correction that is provided by the 

entry and descent phase merging algorithm. The altitude 

difference between the two state vectors is about 22 km, 

which corresponds to approximately 0:72s of the specified 

radial error. A summary of important probe events and 

their corresponding reconstructed altitudes can be found in 

Table 1. 

The lower panel of Fig. 7 shows the norm of the inertial 

velocity vector for both the reconstructed profile (solid) 

and the preflight simulation (dashed). Although the actual 

velocity at the interface altitude is very close to the preflight 

prediction, the two profiles start to diverge slightly once the 

probe enters the entry deceleration pulse. This is due to the 



14 

12 

10 

8 

6 

4 

2 

14 

12 

10 

8 

6 

4 

2 

Acceleration [g E] 

Acceleration [g E] 

altitude difference of 22 km: as the actual probe initial 

position at interface is lower than the predicted one (and 

the one used in the preflight simulation), the probe 

encountered denser atmospheric layers during the main 

deceleration pulse, which is also depicted in the plot. This 

implied a faster velocity decrease and explains the 

difference between the two velocity profiles. The two 

vertical dashed lines mark the T 0 event at about 155 km 

altitude as well as the start of the probe relay transmission 

at about 143 km. 

3.3. Drag coefficient and aerodynamic regime 

The reconstruction of the various aerodynamic regimes 

throughout the entry phase is an important aspect of any 

planetary probe trajectory estimation effort, requiring the 

knowledge of the atmospheric structure, i.e., the density 

rðzÞ, pressure pðzÞ, and temperature TðzÞ profiles as a 

function of altitude z. The reconstruction of the atmospheric 

structure in return requires the knowledge of the 

aerodynamic flight regimes as the drag coefficient CD 

changes throughout the various regimes and their transitions. 

An iterative reconstruction strategy is therefore 

necessary. 

Once the probe position and velocity are reconstructed 

from the numerical integration of the measured aerodynamic 

deceleration (see Section 3.1), the atmospheric 

density is inferred from 

r ¼ 2mðtÞ jaAdj 

CDA v2 , (6) 

rel 

where mðtÞ and A are, respectively, the probe mass and the 

cross-section area. The probe mass was not constant during 

the entry phase due to the ablation process of heat shield 

material, which is expressed by the time dependence of m in 

Eq. (6). As the Huygens heat shield was not equipped with 

any thermal protection system recession sensors, the 

ablation process could only be modeled taking into 

account the integrated mass loss estimated from preflight 

simulations. The time-dependent mass loss is simulated 

according to the relation (Gaborit, 2004) 

mðtÞ ¼m0 expf0:5sðjvrelj 2 

jvmaxj 2 Þg (7) 

with s ¼ 4:18 10 10 m 2 s2 and the initial mass 

m0 ¼ 320 kg. The flow velocity vmax (relative probe velocity 

with respect to the atmosphere) at the time of the start of 

the ablation process and is assumed to be the maximum 

probe velocity during the entry phase. The value of s is 

adjusted to fit the estimated integrated ablation mass of 

9.7 kg. The drag coefficient CD is also time dependent and 

is interpolated from the preflight aerodynamic database 

(Tran and Lenoir, 2005), which provides the Huygens entry 

module axial and normal coefficients for free molecular 

flow (Kn410), transitional flow (0:001pKnp10), and 

continuum flow (Kno0:001), as a function of angle-ofattack 

a (assumed as zero as explained in Section 3.1) and 

Knudsen number Kn or Mach number Ma. The Knudsen

1856 

number is obtained from 

Kn ¼ 1:2533 ffiffi p Ma 

g , (8) 

Re 

where Re is the dimensionless Reynolds number and g the 

ratio of specific heats. The Reynolds number is derived 

from 

Re ¼ jvreljrDspc 

, (9) 

mvisc where Dspc is the diameter of the probe front shield (i.e., 

2.7 m) and m visc is the dynamic viscosity, calculated (in units 

of kg/m/s) according to 

mvisc ¼ 1:458 10 6 T 1:5 

. 

T þ 110:4 

(10) 

In Eq. (10) T is the atmospheric temperature in units 

of Kelvin which is derived from the ideal gas law 



1400 

1200 

1000 

800 

600 

400 

200 

1400 

1200 

1000 

800 

600 

400 

200 

CFR TFR FMFR 

10-6 10-5 10-4 10-3 10-2 10-1 100 101 102 103 0 

Knudsen Number 

FMFR 

TFR 

CFR 

0 

0.8 1 1.2 1.4 1.6 1.8 2 2.2 

Drag Coefficient 

Fig. 8. Upper panel: reconstructed Knudsen number profile showing the 

various flow regimes; lower panel: interpolated drag coefficient during 

entry phase; the various flight regimes are separated by dashed lines; 

FMFR ¼ free molecular flow regime, TFR ¼ transitional flow regime, 

CFR ¼ continuum flow regime. 



according to 

TðzÞ ¼ pðzÞmðzÞ 

(11) 

rðzÞRuniv 

which is a valid approximation in the upper parts of the 

atmosphere due to the low density. The altitude-dependent 

molecular weight mðzÞ was not measured during the entry 

phase as the GCMS measurements were only performed 

during the descent phase under the parachute. Profiles 

consistent with the mean molecular weight profile derived 

from measurements of the Ion Neutral Mass Spectrometer 

on the Cassini spacecraft during its close Ta encounter with 

Titan on 26 October 2004 (Yelle et al., 2006) are therefore 

used. The pressure profile pðzÞ is determined from the 

density profile from the integration of the equation of 

hydrostatic equilibrium according to 

pðzÞ ¼ rðz0ÞgðzÞ d 

1 Z z 

ln r rgðzÞ dz. (12) 

dz 

z 0 

The initial value of p at z0 is estimated from the density and 

density scale height at this level. This boundary terms 

assumes that variations in TðzÞ and mðzÞ are small 

compared to variations in rðzÞ (Magalha˜es et al., 1999). 

The local acceleration of gravity gðzÞ is calculated using the 

reconstructed height profile. 

The Mach number Ma in Eq. (8) is derived from the 

ratio of the relative probe velocity and the speed of sound 

cs, given by 

cs ¼ 

sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 

, (13) 

gRunivT 

m 

where g is again the ratio of specific heats. 

The reconstructed Knudsen number is depicted in the 

upper panel of Fig. 8 and shows that the probe faced free 

molecular flow conditions down to an altitude of about 

Probe Mass [kg] 

320 

315 

310 

305 

300 

295 

290 

Entry Mass 

285 

0 

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 

Time in [min] past Epoch: UTC: 2005-01-14T09:05:52.523 

Fig. 9. Modeled mass loss due to heat-shield ablation used during the 

reconstruction of the atmospheric density according to Eq. (6). Also 

shown by the dashed–dotted line is the deceleration pulse measured by the 

HASI Servo accelerometer with respective units provided on the right side 

ordinate ð1g E ¼ 9:806 m=s 2 ). 

z 0 

14 

12 

10 

8 

6 

4 

2 

Acceleration [g E]

Altitude [km] 

Altitude [km] 

1200 

1000 

800 

600 

400 

200 

1200 

1000 

800 

600 

400 

200 

10 -16 10 -14 10 -12 10 -10 10 -8 10 -6 

Y97 min 

Y97 rec 

Y97 max 

DTWG 

Density [g/cm 3 ] 

930 km before entering the transitional flow regime 

(typically characterized by the condition 10 3 oKno10). 

The interpolated drag coefficient profile is shown in the 

lower panel of Fig. 8 and according to the transitions in the 

flow regimes, appropriate changes in the drag coefficient 

can be seen. 

The simulated mass ablation process is shown in Fig. 9. 

It can be seen that as expected the main mass ablation 

occurred during the main deceleration pulse, which is also 

shown in the same plot. 

The reconstructed density and temperature profiles are 

shown in Fig. 10 (labeled as ‘‘DTWG’’) and compared to 

the Y97 recommended and extreme profiles (Yelle et al., 

1997). It can be seen that Titan’s upper atmospheric density 

profile is higher than the ‘‘recommended’’ engineering 

profile from the Y97 model. The sudden jump in both the 


Y97 min 

Y97 rec 

Y97 max 

DTWG 

110 120 130 140 150 160 170 180 190 200 210 

Temperature [K] 

Fig. 10. Reconstructed density (upper panel) and temperature (lower 

panel) profile of Titan’s atmosphere (labeled ‘‘DTWG’’) compared the 

three model profiles from Yelle et al. (1997) (labeled ‘‘Y97’’). The sudden 

jump in both the reconstructed temperature and density at about 155 km 

stem from the perturbation caused by the initiation of the parachute 

sequence (i.e., T 0). 



1400 

1200 

1000 

800 

600 

400 

200 

reconstructed temperature and density profiles at an 

altitude of about 155 km stem from the perturbations 

caused by the initiation of the parachute sequence at T 0. 

The reconstructed Mach number profile is depicted in 

Fig. 11 as a line and compared to the preflight simulation 

(dashed line). The horizontal line shows the T 0 event at an 

altitude of 155 km and a Mach number of 1.5. The 

reconstructed Ma profile clearly reflects some oscillations, 

which stem from both temperature variations in Titan’s 

upper atmosphere (see lower panel of Fig. 10) and very low 

magnitude oscillations in the measured accelerations. 

Neither of these effects were taken into account in the 

preflight simulations, which explains the smooth simulated 

profile. 

4. Probe vertical motion during the descent phase 


The descent phase altitude and descent speed reconstruction 

is performed in an upward direction, starting from the 

time of probe impact as measured by the SSP impact 

penetrometer. Conversion of the HASI atmospheric 

pressure P and temperature T measurements into altitude 

z and descent speed _z is based on the assumption of 

hydrostatic equilibrium and the equation of state for a real 

gas. The descent velocity can be expressed as 

_z ¼ dz 

dt ¼ 

T0-Event 

Flight Data 

PREDICT 

0 

0 5 10 15 

Mach Nr. 

20 25 

Fig. 11. Mach number profile during entry phase based on the 

reconstructed atmospheric temperature (solid line) and the preflight 

simulation (dashed line). The horizontal line shows the T 0 epoch. 

1 RunivTz 

gðzÞ mðzÞ 

1 

P 

dP 

, (14) 

dt 

where dP is the incremental change in atmospheric 

pressure, which is related to the corresponding incremental 

change in altitude dz. The local acceleration of gravity g is 

recalculated at each step according to g ¼ GM0=z 2 where z 

is approximated by the previous reconstruction step zi 1.

1858 

Runiv is the universal gas constant (8314.3 J/kmol/K). The 

mean molecular mass profile mðzÞ (in kg/kmol) is inferred 

from the measured mole fractions of nitrogen f N2 and 

methane f CH4 (GCMS) according to 

m ¼ f N2mN2 þ f CH4mCH4 , (15) 

where mN2 and mCH4 are the molecular masses of N2 and 

CH4, respectively. In Eq. (14) the compressibility factor z 

takes into account the deviation of the gas behavior from 

an ideal gas due to particle interaction (van der Waals 

forces) and the effect of a finite molecular volume. In the 

altitude ranges from the surface up to about 70 km, Titan’s 

atmosphere is characterized by a combination of relatively 

high densities (on the order of magnitude of 

10 4 –10 2 g=cm3 ) and low temperatures (100–93 K) which 

are both drivers for a deviation of the atmosphere from an 

ideal gas behavior. For the computation of the compressibility 

we restricted ourselves to the second virial 

coefficient B2 and its relations to z as provided by Dymond 

and Smith (1992) 

z ¼ 1 þ B2 r 

. (16) 

m 

For a gas mixture of N2 and CH4 the temperaturedependent 

second virial coefficient is derived from 

B2ðTÞ ¼f 2 

N 2 B2;N 2 ðTÞþf N2 f CH4 B2;CH 4 2N 2 ðTÞ 

þ f 2 

CH 4 B2;CH 4 ðTÞ, ð17Þ 

where B2;N 2 , B2;CH 4 , and B2;CH 4 2N 2 are the temperaturedependent 

virial coefficients for the various pure gas and 

interaction components, which are evaluated using polynomial 

fits of laboratory measurements data as tabulated 

by Dymond and Smith (1992). Based on the measured 

mole fractions from the GCMS measurements and the 

derived virial coefficients from Eq. (17), values of the 

compressibility z are obtained in the range from very close 

to 1 (i.e., almost ideal gas behavior) at altitudes above 

70 km, decreasing continuously down to values of 0.965 

(i.e., a deviation of 3.5% from the ideal gas law) near the 

surface. 

Multiplying Eq. (14) by dt and integrating both sides 

yields 

Dz ¼ðzi zi 1Þ ¼ 1 

g 

Runiv T i 1=2z 

m 

ln Pi 

Pi 1 

. (18) 

The temperature T is considered to be constant 

throughout the altitude interval Dz and is approximated 

by the mean value of two consecutive measurements, i.e., 

T i 1=2 ¼ 1 

2 ðT i þ T i 1Þ. Starting from the initial value z0 at 

Titan’s surface the final altitude is derived by simple 

addition of the subsequently derived altitude intervals Dz 

zi ¼ z0 þ X 

Dzi 1. (19) 

i 

Note that the minus sign in Eq. (18) ensures that for a 

reconstruction starting from the surface in an upward 

direction the pressure gradient has to be negative (i.e., 



PioPi 1) and Dz therefore positive. Assuming a constant 

descent velocity for the descent interval Dz the descent 

velocity is approximated by 

_z 

Dz 

. (20) 

Dt 

It should also be noted that the altitude profile 

reconstructed from Eq. (19) provides the radial probe 

distance from the probe impact point neglecting Titan’s 

flattening. However, the integration of the equations of 

motion during the entry phase reconstruction [see Eq. (2)] 

provides the distance of the probe to Titan’s center. To 

obtain the altitude relative to the surface requires the 

assumption of Titan’s radius (2575 km). 

Altitude [km] above Impact Point 


180 

160 

140 

120 

100 

80 

60 

40 

20 

DTWG 

+1 α 

-1 α 

PREDICT 

Drogue Impact 

0 

20 40 60 80 100 120 140 

Time [min] past Interface Epoch: UTC: 2005 01 14T09:05:52.523 

0.18 

0.16 

0.14 

0.12 

0.1 

0.08 

0.06 

0.04 

0.02 

Flight 

RAU 1 

RAU 2 

SSP APIS 

0 

151.7 151.8 151.9 152 152.1 152.2 152.3 152.4 

Time [min] past Interface Epoch: UTC: 2005 01 14T09:05:52.523 

Fig. 12. Upper panel: reconstructed descent phase altitude profile based 

on the HASI P and T, GCMS mole fraction, and SSP impact epoch 

measurements (solid line, labeled ‘‘DTWG’’) compared to the preflight 

trajectory simulation (Pérez-Ayúcar et al., 2004; Kazeminejad et al., 2004) 

(dashed line, labeled ‘‘PREDICT’’). The lower panel shows the final 

portion of the reconstructed altitude profile prior to impact, compared to 

the RAU 1 and 2 measurements as well as to the SSP API-S (acoustic 

sounder) measurements (solid line with triangles).

4.2. Discussion of reconstruction results 

The reconstructed altitude descent profile is depicted in 

Fig. 12. The upper panel provides an overview of the entire 

descent phase altitude range from about 155 km down to 

the surface. The reconstructed profile (solid thick line, 

labeled ‘‘DTWG’’) with its 1s uncertainty envelope (solid 

dashed line) is compared to the preflight simulation 

(dashed thin line). It can be readily seen that the simulated 

descent trajectory predicted that the probe impact would 

have occurred about 14 min earlier. In large part, this 

difference can be attributed to the uncertainties in the main 

and drogue chute aerodynamic database. The lower panel 

shows a zoom of the very last portion of the descent phase 

to surface impact. In the final descent portion the SSP 

Descent Velocity [m/s] 

Descent Velocity [m/s] 

80 

70 

60 

50 

40 

30 

20 

T0 Drogue 

DESCENT 

ENTRY 

PREDICT 

5 10 15 20 25 30 35 40 

Time [min] past Interface Epoch: UTC: 2005-01-14T09:05:52.523 

25 

20 

15 

10 

5 

Drogue Impact 

0 

40 60 80 100 120 140 



DESCENT 

PREDICT 

SSP APIS 

Fig. 13. Huygens descent speed profile during the first portion (upper 

panel) and final portion (lower part) of the descent phase. In the upper 

panel the dashed-dotted line (labeled ‘‘ENTRY’’) shows the descent speed 

derived from the entry phase (accelerometer based) reconstruction. The 

solid line (labeled ‘‘DESCENT’’) shows the descent speed profile derived 

from the reconstructed descent phase (atmosphere based) altitude profile 

as shown in the upper panel of Fig. 12. The triangle in the lower panel 

represents the descent speed derived from measurements of the SSP 

acoustic sounder sensor. 


acoustic sounder instrument (SSP-APIS) provided altitude 

measurements, which are represented as triangles. The 

good agreement between the SSP-APIS data and the 

reconstructed altitude profile (solid line) can be clearly 

seen. In the same panel the very last measurements of 

the two RAU before they saturated can also be seen. The 

difference between the RAU measurements and the 

reconstructed altitude profile is discussed in Section 4.3. 

The reconstructed descent speed profile is shown in 

Fig. 13. The upper panel zooms into the time of main chute 

release shown by the vertical dashed line labeled ‘‘Drogue’’. 

The solid line (labeled ‘‘DESCENT’’) is the reconstructed 

descent speed profile based on Eq. (14) and the dashed line 

(labeled ‘‘PREDICT’’) represents the results of the preflight 

simulation. It can be seen that under the main 

parachute the actual descent speed was about 5 m/s lower 

than predicted. This is also very likely the cause for the 

longer flight time in the actual mission. Also shown in the 

same panel is the descent speed profile from the entry phase 

reconstruction (dashed-dotted line, labeled ‘‘ENTRY’’). It 

can be seen that although the descent phase velocity shows 

some oscillations during the main chute phase, the overall 

trend agrees well with the smooth velocity profile from the 

entry phase reconstruction. 

The lower panel of Fig. 13 depicts the descent speed 

profiles during the drogue chute phase down to probe 

surface impact. The descent speed reconstruction predicts a 

probe impact speed of 4:54 m=s, consistent with the speed 

derived from the altitude measurements of the SSP-APIS 

sensor (shown as a single triangle). 

4.3. Comparison to RAU measurements 

The residual between the reconstructed descent trajectory 

and the RAU measurements are shown in Fig. 14. 

The 1s error of the reconstructed altitude profile is 

evaluated and is shown as a dashed line in the same figure. 

Altitude Residual [m] 

3500 

3000 

2500 

2000 

1500 

1000 

500 

RES-RAU1 

RES-RAU2 

DTWG 1-α 

0 

60 70 80 90 100 110 120 130 140 150 


Fig. 14. Residuals of the RAU 1 and 2 measured altitude profiles and the 

reconstructed descent trajectory. The 1s error of the reconstructed 

trajectory is also shown as dashed line.

1860 

The altitude error, sðDziÞ, derived from the sum of the 

errors at each altitude interval sðDziÞ in Eq. (19), is 

calculated at each time interval ti based on the law of error 

propagation. According to Eq. (18) the 1s uncertainties of 

the temperature measurements (i.e., 0:25 and 1 K in the 

measurement ranges from 60 to 110 K and 110 to 330 K, 

respectively), the pressure measurements (i.e., 1% of the 

measurement value), the mean molecular mass (1% of the 

inferred value), and the gravitational acceleration sðgÞ are 

assumed. For the evaluation of sðgÞ an error of Titan’s GM 

of 0:2818 km 3 =s 2 and Titan’s radius of 0.5 km are used 

(Cassini Navigation team, private communication). Note 

that the errors in the compressibility factor z, the universal 

gas constant, and the ratio of specific heats are neglected. 

One can see a steady increase of the RAU residuals from 

a few meters close to the surface up to more than 3.5 km at 

an altitude of 60 km. Above 1 km altitude the error bar of 

the reconstructed trajectory is smaller than the residuals. 

The altitude discrepancy between the RAU measurements 

and the reconstructed trajectory has not yet been fully 

explained. The following facts, however, speak for a higher 

confidence in the DTWG model. The DTWG-reconstructed 

trajectory 

provides a much better fit in the merging process with 

the entry phase reconstruction; 

is consistent with the descent altitude as well as derived 

impact speed of the SSP acoustic sounder instrument 

(see lower panel of Fig. 12); 

is consistent with DWE and DISR data. If the RAU 

profiles are correct, then the DWE and DISR measurements 

would not be consistent with each other; 

is confirmed by independent reconstruction efforts 

(Striepe et al., 2007) 

5. Probe horizontal motion and impact coordinates 


The exploration of Titan’s atmospheric dynamics is one 

of the main goals of the Huygens mission, and is the 

primary goal of the Huygens DWE (Bird et al., 2005a). The 

strength and direction of atmospheric winds are not only of 

scientific interest, however, but also played an important 

role in the preflight mission analysis activities, which 

required an accurate prediction of the estimated probe 

impact coordinates for the pointing of the Cassini high gain 

antenna (Kazeminejad, 2002; Kazeminejad et al., 2002, 

2005b). Once the parachute sequence began, atmospheric 

winds caused a drift in both the zonal and meridional 

directions. Two sources of wind drift measurements are 

currently available: (1) the DWE zonal wind measurements 

and (2) the image derived zonal and meridional drifts from 

the Descent Imager and Radial Spectrometer (DISR) 

instrument (Tomasko et al., 2002). Note that both the 

DWE and the DISR derived drift measurements required 

as an input the vertical probe descent profile (i.e., altitude 



and descent speed), which was provided to the instrument 

teams by the DTWG. The probe horizontal motion 

reconstruction was therefore carried out in an iterative 

process between the DTWG, DWE, and DISR teams. 

In the body-fixed Titan system the Huygens velocity 

vector can be decomposed into radial, zonal, and 

meridional components according to 

8 9 

>< 

vr >= 

v ¼ vzon , (21) 

>: >; 

vmer 

where prograde zonal is considered as the motion from 

west to east and positive meridional from south to north. 

From the kinematic equations for a spherical coordinate 

system the change in longitude and latitude caused by 

zonal and meridional drift (in radians/second) can be 

derived from 

dl 

dt ¼ 

vzonðtÞ 

RðtÞ cos jðtÞ , 

dj 

dt 

vmerðtÞ 

¼ , (22) 

RðtÞ 

where RðtÞ is the instantaneous distance of the probe from 

the center of Titan and is given by R ¼ RP þ zi where RP is 

the planetary radius of 2575.0 km, l is the probe longitude, 

and j is the planetocentric latitude. The independent 

reconstruction of the probe vertical trajectory was previously 

outlined and yields the altitude profile zi. It can be 

seen that Eq. (22) is a system of two coupled first order 

differential equations which can be solved by numerical 

integration since all time-dependent variables are known at 

each integration step. It should also be noted that the 

coupling in Eq. (22) vanishes for small latitude ranges and 

could therefore also be solved with reasonable accuracy if 

no meridional drift measurements were available, and the 

latitude was assumed constant over the integration time 

span. 

Table 3 

Initial conditions for the numerical integration of Eq. (22) 

Parameter Value Comment 

Epoch T 0 þ 118:0s ¼ interface epoch þ 6:44 min 

Altitude (km) 144.2 w.r.t. surface impact point 

West lon. (deg) 195.94 – 

South lat. (deg) 10.33 – 

Integration step (s) 0.5 – 

Impact coordinates 

(w.r.t. reference surface 

RT ¼ 2575 km) 

West lon. (deg) 192.32 0:24 ð1sÞ 

South lat. (deg) 10.25 0:17 ð1sÞ 

The resulting surface impact coordinates are provided at the end of the 

table.

West Longitude [deg] 

Latitude [deg] 

196.5 

196 

195.5 

195 

194.5 

194 

193.5 

193 

192.5 

192 

191.5 

T0 Drogue Impact 

191 

0 50 100 150 

Time [min] 

past Interface Epoch: UTC: 2005-01-14T09:05:52.523 

-10.2 

-10.22 

-10.24 

-10.26 

-10.28 

-10.3 

-10.32 

T0 

Drogue 

0 50 100 150 

Time [min] 


5.2. Discussion of reconstruction results 

The integration of the horizontal probe drift starts at 

T 0 þ 118:0s (¼interface epoch þ6:44 min corresponding 

to an altitude of 144:2 km). The corresponding initial 

conditions are summarized in Table 3. Further inputs to 

the drift integration are the previously reconstructed 

vertical descent altitude profile, the zonal wind speed as 

provided by DWE, and the meridional drift derived from 

236 images of the DISR instrument containing significant 

surface detail (Karkoschka et al., 2007). Note that even if 

the DISR image-based drift trajectory is only well 

constrained below altitudes of 30 km the DISR team is 

able to extend their reconstruction up to an altitude of 

144 km. 


DESCENT 

ENTRY 

DESCENT 

ENTRY 

Impact 

Fig. 15. Upper panel: reconstructed longitude drift from the entry phase 

reconstruction (dashed line), which is based on the numerical integration 

of the equations of motion, compared to the descent phase reconstruction 

of the horizontal wind drift integration (solid line). Lower panel: same as 

upper panel but for the latitude drift of the probe. The reconstructed 

probe impact coordinates are 192:32 W and 10:25 S. 


Resdiual in Longitude (DISR - DTWG) [deg] 

Resdiual in Latitude (DISR - DTWG) [deg] 

-0.01 

-0.012 

-0.014 

-0.016 

-0.018 

-0.02 

-0.022 

-0.024 

T0 Drogue 

-0.026 

0 20 40 60 80 100 120 140 160 

Time [min] 


7.6 

7.4 

7.2 

7 

6.8 

6.6 

x 10-4 

Impact 

T0 Drogue Impact 

6.4 

0 20 40 60 80 100 120 140 160 

Time [min] 


Fig. 16. Residuals between DISR and DTWG longitude (upper panel) 

and latitude (lower panel) probe drift during descent phase. 

The results of the horizontal drift integration are 

depicted in Fig. 15 as a solid line (labeled ‘‘DESCENT’’). 

The horizontal motion from the accelerometer based entry 

phase reconstruction are also shown as dashed lines 

(labeled ‘‘ENTRY’’). The smooth transition between entry 

and descent phase reconstruction can be seen in the 

overlapping region. 

The residuals to the DISR based reconstruction results 

are shown in Fig. 16 and stay below 0:026 in longitude and 

7:6 10 4 deg in latitude. 

The surface impact coordinates are estimated to be 

192:32 0:24 W longitude and 10:25 0:17 S latitude. 

The upper panel of Fig. 17 shows the coordinates of the 

probe interface point (marked as a triangle) and the surface 

impact location (marked as a cross) overlayed on a Titan 

surface image. The map has been assembled from images 

obtained from the Cassini Imaging Science System in the 

near-infrared (centered at 938 nm) as the Cassini orbiter

1862 

approached the Saturn system and during the closer flybys 

in July, October and December (CICLOPS 4 

image 


Fig. 17. Upper panel: interface (triangle) and impact (cross) coordinates of Huygens overlayed on a Titan surface map, which was assembled from images 

taken by the Cassini Imaging Science Subsystem (PIA06201) using a near-infrared filter centered at 938 nm (Credit: NASA/JPL/Space Science Institute). 

The map reveals complex patterns of bright and dark material on Titan’s surface (Porco et al., 2005). The lower panel shows a zoom of the interface and 

impact region with the 1, 2, and 3s dispersion ellipses of the interface state vector and the predicted impact coordinates. 

4 

Cassini Imaging Central Laboratory for Operations:http://ciclops.org/ 

index.php. 


designation: PIA06201). Due to Titan’s thick and hazy 

atmosphere the size of surface features that can be resolved 

is a few to five times larger than the actual image pixel 

scale. The pixel scale of the individual images in the map is 

specified by the instrument team to be in a range from 88 to

2 km. The scales of the surface features that can be resolved 

range from 180 to 10 km. The lower panel of Fig. 17 zooms 

into the region around the probe interface and impact 

coordinates. The reconstructed interface and impact 

coordinates are shown together with the coordinates from 

the preflight estimations (represented by the center points 

of dispersion ellipses). The 1, 2, and 3s dispersion ellipses 

are also shown. 

6. Merging of entry and descent phase 

The reconstruction of the entry phase trajectory requires 

as an essential input the probe state vector at the interface 

epoch, which is provided together with the estimated 

uncertainties in Table 2. It is interesting to observe that the 

Huygens state vector uncertainties are significantly larger 

compared to typical values for Mars entry probes such as 

Viking or Mars Pathfinder. Due to Pathfinder’s direct entry 

from interplanetary orbit, the entry state had a radial 

uncertainty of only about 1.7 km ð1sÞ (Magalha˜es et al., 

1999). After separation from the Cassini spacecraft the 

Huygens probe coasted for 20 days with no direct earthbased 

tracking information. Prior to the mission it was 

already clear that this would increase the delivery 

uncertainties at the interface epoch. A probe imaging 

activity was therefore introduced between the period of 

probe separation and ODM. Using optical navigation 

images of the probe taken from the Cassini orbiter, the 



Huygens state vector uncertainties at the interface point 

were reduced to about 30 km, as compared to a radial 

uncertainty of about 70 km without images. 

The initial state vector uncertainties introduced the 

following problems in the reconstruction effort: 

(1) The initial state vector introduced a systematic error in 

the position vector, resulting in an incorrect modeling 

of the gravitational forces with respect to the measured 

accelerometer values. In other words, the equations of 

motion were filled with inconsistent data, which 

introduced an error in the reconstructed state vector. 

The errors at each integration step summed up and 

finally led to a largely erroneous solution. 

(2) As a result of (1) the integrated trajectory diverged 

significantly from the descent phase trajectory in the 

regions of overlap. 

A strategy to merge the entry and descent phase was 

therefore developed, which is schematically shown in 

Fig. 18. The entry and descent phase trajectory portions 

provided profiles of altitude and descent speed which, for 

each phase, is based on independent sets of input data and 

independent reconstruction techniques. This is indicated by 

the vertical bold dashed line in Fig. 18. On the left side the 

entry phase reconstruction is shown, based on the 

numerical integration of the probe accelerometer data. 

An important input is the initial state vector and 

Fig. 18. Computational flow of the entry and descent trajectory merging process. The entry phase (left side of the bold vertical dashed line) and the descent 

phase are both independently reconstructed from different sets of input data. In the overlapping region (altitude region of 1452100 km) residuals in both 

altitude and descent speed were computed, which served as input into the least-squares fitting algorithm. The proposed corrections of the initial state 

vector were fed into the subsequent iteration until the loop converged. Note that the state vector corrections were constrained by the covariance of the a 

priori epoch state vector (cf. Table 2), which was taken into account in the least-squares estimation process.

1864 

covariance matrix shown on the top of the figure. The right 

side represents the reconstruction of the descent phase 

trajectory, which is based on atmospheric in situ measurements 

as outlined in the previous sections. Both trajectories 

overlap in the time interval from about 6.3 to 22 min past 

interface epoch. This corresponds to an altitude range of 

about 145–100 km. In this ‘‘overlap region’’ residuals . in 

altitude and descent speed are calculated and used as input 

in a weighted least-squares estimation algorithm. The task 

of the statistical estimation algorithm is to calculate initial 

state vector corrections, which ensures a smooth transition 

between the entry and descent phase trajectory portions in 

terms of both altitude and descent speed. 

Note that the residuals in the horizontal components 

(i.e., meridional and zonal probe drift) are not considered 

in the estimation algorithm. When the DTWG trajectory 

retrieval algorithm design was designed, reliable measurements 

of meridional motion were not expected. The 

inclusion of horizontal residuals into the estimation 

algorithm is subject to future analysis. 

As only corrections within the specified uncertainty 

range should be considered it is necessary to provide the 

least-squares algorithm with the capability to take into 

account the a priori covariance matrix P apr 

0 

of the initial 

(modeled) state vector ~x apr 

0 . Introducing the information 

matrix K as the inverse of the covariance matrix, the 

following solution x lsq 

0 of the weighted least-squares 

estimation (with a priori knowledge) is used (e.g., 

Montenbruck and Gill, 2000) 

Dx lsq 

0 ¼ðKþ HTWHÞ 1 ðKDx apr 

0 þ HTW.Þ, (23) 

where H is the Jacobian containing the partial derivatives 

of h with respect to the initial state vector x0 at the initial 

(i.e., interface) epoch t0, and h is the vector 

h ¼ zðx0Þ 

( ) 

(24) 

_zðx0Þ 

which consists of the altitude and descent speed derived 

from the integrated probe initial state vector. The weighting 

matrix W is a diagonal matrix and contains the variances 

of the residuals, which are derived from the uncertainties of 

z and _z as shown in Fig. 14. Furthermore it is worth noting 

that the assumption of independent measurements z and _z 

(i.e., diagonal matrix W) provides the best convergence of 

the estimation algorithm, even if both observables result 

from an integration of initial conditions and are therefore 

not fully independent quantities. 

Table 2 lists the probe state vector and uncertainties as 

provided by the Cassini Navigation team as well as the 

adjusted state vector, which result from the converging of 

the trajectory merging algorithm. The last column of this 

table shows the deviation of the corrected state vector 

expressed in units of the state vector uncertainties from the 

second column. 

The overlapping portion of the entry and descent phase 

altitude and descent speed profiles are shown in Fig. 19. It 




Altitude Residual: Entry - Descent [m] 

180 

170 

160 

150 

140 

130 

120 

110 

100 

90 

80 

5 10 15 20 25 30 

Time [min] 


200 

100 

0 

-100 

-200 

-300 

-400 

-500 

can be seen that the modifications of the initial state vector 

ensures a smooth transition between the two phases. The 

difference between the two reconstructed altitude profiles 

are less than 0.6 km (in the overlapping region of ca. 

147–100 km), which is shown in the residual plot in the 

lower panel of the same figure. 

7. Vehicle roll rate 

T0 Drogue 

7.1. Vehicle roll during entry 

ENTRY 

DESCENT 

-600 

6 8 10 12 14 

Time [min] 

16 18 20 22 


Fig. 19. Comparison of reconstructed altitude profiles from the entry 

phase reconstruction (dashed thick line) and the descent phase reconstruction 

(solid line). The lower panel shows the corresponding altitude 

residuals in the overlapping altitude region. 

The Huygens probe postseparation axial and lateral 

velocity as well as the roll rate 5 were reconstructed from the 

Cassini bounce back reaction and the measurements of the 

5 

Note that in various Huygens papers the probe roll rate is also referred 

to as probe ‘‘spin’’.


6 

5.5 

5 

4.5 

4 

3.5 

3 

2.5 

2 

1.5 

x 10 -4 

magnetometer instrument subsystem aboard Cassini (Project 

Team, 2005). The roll rate reconstruction yielded a 

counter-clockwise (viewed from the back of the probe into 

the velocity direction) rotation of 7.5 rpm. This initial 

rotation is a typical means to achieve a certain attitude 

control for planetary entry probes and to ensure stability 

during the coast phase and furthermore null out any lift 

and side forces during the atmospheric entry (Lorenz, 

2006). The misalignment between the vehicle’s body axis 

(defined by the aeroshell symmetry axis) and the principal 

axis (defined by the aeroshell mass distribution) can be seen 

in the non-zero products of inertia, which are listed in the 

lower panel of Fig. 2. The resulting deviation moments as 

well as external torques caused a probe nutation motion, 

which can be clearly seen in the HASI servo accelerometer 

measurements taken prior to the start of the deceleration 

pulse as shown in Fig. 20. From the periodic oscillations a 

coning frequency of f coning ¼ 0:0889 Hz can be derived. 

Keeping in mind that due to the axis definition the 

maximum moment of inertia is along the probe X-axis 

the vehicle roll rate can be derived using the relation 

(Spencer et al., 2005) 

oconing ¼ 1 

-4.5 -4 -3.5 -3 -2.5 -2 -1.5 -1 -0.5 0 0.5 

I xx 

1 

2 ðI zz þ I yyÞ oroll. (25) 

Substituting the moment of inertia ratio and the measured 

coning frequency f coning ¼ 0:0889 Hz yields a vehicle roll 

rate of oroll ¼ 7:28 rpm. Note that this value is very close to 

the results of the preflight simulation, which predicted a 

value in the range of 7.281–7.298 rpm (Ortiz, 2004). A 

comparison with the reconstructed value of 7.5 rpm, 

however, suggests that a roll damping of about 0.22 rpm 


XSERVO 

CASU 


Fig. 20. HASI servo accelerometer measurements prior to the deceleration 

pulse. Due to the high sensitivity of the accelerometer the probe 

coning motion can be seen. One can clearly see a constant coning 

frequency of 0.0889 Hz, which allows to calculate the vehicle roll rate 

during that time. 


took place. The very low atmospheric density above 

1250 km suggests that atmospheric roll damping effects 

(i.e., viscous roll damping due to energy dissipation within 

the boundary layer) could not have been strong enough to 

explain the observed change. One possible effect, which 

could partially cause a change in roll rate are solar pressure 

torques. A quantitative estimation of this torque throughout 

the entire coast phase would, however, require a 

detailed analysis, which is beyond the scope of this work 

and will be subject to future analysis. 

7.2. Vehicle roll during descent 

The vehicle roll rate during the probe descent phase is 

reconstructed based on two data sets: (1) the RASU 

measurements and (2) the telemetry data of the Automatic 

Gain Control (AGC) unit, part of the Huygens receiver 

onboard Cassini. Note that this paper is restricted to a brief 

overview of descent phase roll rate reconstruction effort. 

For a more extensive and detailed description on this topic 

the reader is referred to Pérez-Ayućar et al. (2005c). 

The RASU is a suite of two highly sensitive accelerometers 

sharing a common design with the CASU but 

mounted offset from the probe symmetry axis and tuned to 

measure a much smaller range of accelerations (0–120 mg). 

The RASU was sampled at 4 Hz and had an accuracy of 

0.47 mg. Raw measurements were used by the onboard 

processor to compute a near real time roll rate estimation 

that was distributed to the instruments in the Data Descent 

Broadcast (DDB). 6 A DDB independent roll rate reconstruction 

based on the reduction of the raw RASU 

measurements as shown in Fig. 21 is presented here. The 

raw data are treated with a median smoothing algorithm, 

which filters out the measurement noise created by the 

recording of attitude disturbance accelerations. Assuming 

that the disturbed radial acceleration component is equally 

distributed around the ideal centrifugal component, a 

smoothed windowed median filter provides a good estimation 

of the actual instantaneous radial acceleration. It is 

important to note that the RASU was designed to provide 

only positive acceleration measurements. From the 

smoothed radial accelerations the vehicle roll rate is then 

derived according to 

rffiffiffiffiffiffi 

oroll ðrpmÞ ¼ 2p D 

, (26) 

60 acf 

where D is the radial distance of the RASU with respect to 

the vehicle center of mass and acf is the centrifugal 

acceleration. For RASU-B, D ¼ 412 mm under the main 

chute (i.e., front shield and DISR cover jettisoned) and 

D ¼ 411 mm under the stabilizer chute. 

6 A subset of housekeeping data were broadcasted every 2 s to all the 

instruments for their real time use during descent. This data set is referred 

to as DDB and comprised the mission time, altitude and the real-time 

derived roll rate. It was used by the instruments to optimize their 

measurement cycles.

1866 

Radial Acceleration (g) 

0.008 

0.007 

0.006 

0.005 

0.004 

0.003 

0.002 

0.001 

0 

-0.001 

RASU analysis around the spin reversal 

RASU_raw 

MEDIAN (50 percentile), 100 samples 

200 300 400 500 600 700 800 900 1000 

Time after T0 (sec) 

Fig. 21. RASU raw measurements around the time of roll rate inversion. 

Note the design related data cut-off at 0g. It can be seen that the spurious 

contributions from attitude related accelerations that were filtered out 

applying a windowed median filter. From the smoothed signal the roll rate 

was derived knowing the radial distance of RASU to the center of mass 

(Pérez-Ayúcar et al., 2005b, c). 

The second method is based on the AGC telemetry 

parameter, which is the control word of the second 

coherent AGC loop in the digital part of the receiver and 

was reported at 8 Hz. The AGC value can be interpreted as 

a power measurement of the received probe radiofrequency 

signal once it arrives at the probe receiver onboard Cassini. 

Extensive effort was invested into the detailed reconstruction 

of the chain B signal strength (Pe´rez-Ayućar et al., 

2005b). The analysis of the AGC data provides the 

absolute azimuth of the probe orientation (w.r.t. to the 

instantaneous position of Cassini in the sky) as a function 

of time. The PTAs emitted not ideally but with an 

azimuthal asymmetry (Clausen et al., 2002). This implies 

that the probe roll rate was modulated onto the received 

power at Cassini as can be seen in Fig. 22. The period of 

the power oscillations (which are directly measured by the 

AGC) allow the roll rate to be inferred. As the PTA gain 

pattern was measured prior to launch on a representative 

mock-up, the comparison allowed the estimation of the 

absolute orbiter azimuth in a probe spacecraft-fixed frame. 

Furthermore, the roll rate direction could be analyzed and 

showed an unexpected reversal during the descent at about 

T 0 þ 10 min. In other words, the probe rotated in a 

counter-clockwise direction (viewed in the velocity direction) 

for the early part of the descent (consistent with the 

roll direction at separation from Cassini), and in a 

clockwise direction for the remaining part of the descent. 

This inversion of the probe rotation was not foreseen in the 

nominal mission sequence and remains to be explained. 

A consolidated Huygens roll rate is reconstructed based 

on a combination of both methods and is depicted in 

Fig. 23. The AGC derived profile (black solid line) is used 

whenever possible. 7 The RASU-smoothed profile is used 

during the roll rate inversion where the probe stopped its 

7 The constant quantification step in the RASU telemetry implied a 

variable step when expressed in (rpm), which increased in proportion to 

the roll rate. Many of the near surface measurements, therefore, were in 



EsNo [dB] 

Huygens link. EsNo reconstructed [dB] 

15.5 

15 

14.5 

14 

13.5 

13 

12.5 

12 

11.5 

Cycle 1 Cycle 2 Cycle 3 

1 1.1 1.2 1.3 

Time [min] 

1.4 1.5 1.6 

Fig. 22. Signal-to-noise ratio ES=N0 (in dB) of the received Huygens relay 

link signal measured aboard Cassini at 1 min in the mission. The observed 

periodic variations are due to the scanning of the asymmetric transmitting 

antenna gain pattern caused by the probe rotation. The measurement of 

this periodicity allowed to infer the roll rate. Furthermore, the absolute 

phase within the cycle (azimuth) and rotation sense were retrieved from 

comparison to the preflight measured PTA pattern profile (Pérez-Ayúcar 

et al., 2005c). 

Spin (rpm) 

8 

6 

Hugens In-Flight SPIN RATE profile 

derived from engineering sensors 

AGC 

4 

2 

0 

-2 

-4 

-6 

RASU Median 

-8 

-10 

AGC smoothed 

09:10:00 09:40:00 10:10:00 10:40:00 11:10:00 11:40:00 

Time (SCET UTC) 

Fig. 23. Reconstructed roll rate profile based on the combination of the 

AGC and RASU analyses. Note that the RASU median method is used 

around the inversion of the rotation and the AGC method is used 

otherwise (smoothed around the roll rate peak) (Pérez-Ayúcar et al., 

2005c). 

rotation, which precluded the identification of the AGC 

cycle as the link repetition pattern was not present. The 

AGC profile is smoothed during the roll rate peak, where 

the fast rotation ð 10 rpmÞ combined with strong attitude 

disturbances in this interval results in noisy data. 

An integration of the probe roll rate during the entire 

descent yields 24 rotations in a clockwise direction and 330 

rotations in a counter-clockwise rotation. It should be 

pointed out that these numbers stem from a pure counting 

of the roll cycles in the AGC telemetry, which as mentioned 

above was not clearly visible during the portion of roll rate 

inversion. The number of rotations provided here should 

(footnote continued) 

the level of the quantification step, which implied a less reliable roll rate 

reconstruction compared to the method based on the AGC measurements.

therefore be considered as approximate values, and might 

differ from values derived by different reconstruction 

efforts. 

8. Concluding remarks 

The Huygens probe mission provided data of high 

quality that allowed an accurate reconstruction of the 

vehicle’s entry and descent trajectory as well as its roll rate 

profile prior to atmospheric entry and throughout the 

entire descent phase. 

Within the framework of the Huygens DTWG, an 

algorithm was developed and implemented to reconstruct 

the trajectory based on all available probe measurements. 

The DTWG tool was extensively tested prior to the mission 

using simulated probe data (Pe´rez-Ayućar et al., 2004, 

2005a) and was successfully applied to the actual flight 

data. The reconstructed altitude and descent speed profiles 

during both the hypersonic and supersonic entry phases as 

well as the subsonic descent phase under the main and 

drogue parachutes are presented and discussed. As the 

entry and descent phase reconstruction are both based on a 

different set of input data as well as a different reconstruction 

methodology, a key part of the effort is to obtain a 

smooth and accurate transition between the two phases. 

This is achieved through the implementation of a weighted 

least-squares estimation algorithm, which is equipped with 

the capability to take into account the initial state vector 

covariance matrix. 

The probe horizontal motion was reconstructed based 

on DWE measurements of Titan’s zonal winds as well as a 

DISR image based meridional drift motion (converted into 

a meridional wind measurement). The currently best 

estimated impact coordinates are provided. It is important 

to note that an independent Huygens impact coordinate 

estimation was accomplished by Lunine et al. (2007) 

comparing the T8 Radar image with the DISR image 

observations. The resulting coordinates for the Huygens 

landing site (i.e., 192:4 W longitude and 10:2 S latitude) 

are in good agreement with those derived from the DTWG 

reconstruction effort (i.e., 192:32 W, and 10:25 S, see 

Table 3). 

Table 4 

Reconstruction results of the Huygens entry phase trajectory 



Finally, results of the probe roll rate for both the entry 

and the descent phase are presented. The entry phase roll 

rate reconstruction used the very sensitive measurements of 

the axial probe acceleration and suggests a roll rate 

damping of about 0.22 rpm if compared to the separation 

value, which was derived from the orbiter bounce back 

reaction and the measurements of the magnetometer 

instrument subsystem. During the descent phase the probe 

rotation reversed its direction, which was not foreseen in 

the nominal probe design and remains to be explained. 

Acknowledgments 

B. Kazeminejad and D. Atkinson would like to thank the 

European Space Agency’s Research and Scientific Support 

Department (RSSD) for funding this work. The reconstruction 

of the Huygens entry and descent trajectory would not 

have been possible without the science instrument data and 

the excellent cooperation of the Principal Investigators and 

their teams in the framework of the Huygens Descent 

Trajectory Working Group, with special thanks to the 

Huygens Atmospheric Structure Instrument (M. Fulchignoni, 

F. Ferri, V. Gaborit), the Gas Chromatograph and Mass 

Spectrometer (H. Niemann), the Surface Science Package 

(J. Zarnecki, R. Lorenz, B. Hathi, M. Leese, N. Ghafoor), the 

Descent Imager and Spectral Radiometer (M. Tomasko, 

B. Rizk, C. See), and the Doppler Wind Experiment 

(M. Bird, R. Dutta-Roy). Furthermore we would like to 

acknowledge the excellent work and cooperation of the 

Project Scientist Team at RSSD (O. Witasse), the Radar 

Altimeter Unit team at ESTEC (R. Trautner and 

H. Svedhem), the Huygens ground-segment operations team 

at the European Space Operations Center (D. Salt), the 

Cassini Navigation team at the NASA Jet Propulsion 

Laboratory (J. Jones, D. Roth, and N. Strange), and the 

Huygens engineering team at the Prime Contractor Alcatel 

Cannes (P. Couzin and A.-M. Schipper). We thank the 

Huygens interdisciplinary scientists for all their valuable 

advise and support (J. Lunine, F. Raulin, T. Owen, and 

D. Gautier). Finally we would like to thank two reviewers for 

very helpful comments. 

Time (s) Alt. (km) W-Lon. (deg) Lat. (deg) Inert. vel. (m/s) 

268.48 1247.68717 185.4293 8.6080 6028.52782 

268.00 1245.06813 185.4472 8.6111 6028.79502 

258.00 1190.21259 185.8271 8.6774 6034.46986 

248.00 1135.46325 186.2184 8.7452 6040.29500 

238.00 1080.82583 186.6214 8.8146 6046.27551 

228.00 1026.30644 187.0366 8.8856 6052.41629 

218.00 971.91160 187.4648 8.9584 6058.72174 

208.00 917.64825 187.9063 9.0329 6065.19350 

198.00 863.52387 188.3619 9.1093 6071.82522 

188.00 809.54657 188.8321 9.1875 6078.60549 

178.00 755.72526 189.3177 9.2675 6085.47602

1868 

Table 4 (continued ) 




168.00 702.07031 189.8193 9.3496 6092.32182 

158.00 648.59409 190.3377 9.4336 6098.87387 

148.00 595.31406 190.8736 9.5196 6104.38206 

138.00 542.25802 191.4276 9.6077 6107.08085 

128.00 489.47983 192.0002 9.6977 6101.92483 

118.00 437.12368 192.5906 9.7896 6071.26950 

108.00 385.55358 193.1953 9.8826 5976.65772 

98.00 335.63113 193.8034 9.9750 5732.95878 

88.00 289.18462 194.3898 10.0633 5186.11580 

78.00 249.26093 194.9087 10.1407 4225.74208 

68.00 218.63782 195.3134 10.2010 3044.80861 

58.00 197.41950 195.5930 10.2430 2025.44689 

48.00 183.25367 195.7749 10.2708 1344.79256 

38.00 173.55652 195.8932 10.2895 922.36406 

28.00 166.63883 195.9713 10.3025 658.03774 

18.00 161.48662 196.0234 10.3118 488.69147 

8.00 157.47556 196.0583 10.3186 379.62061 

0.00 155.84331 196.0701 10.3213 343.20156 

2.00 154.21106 196.0818 10.3239 306.78250 

12.00 151.91058 196.0914 10.3271 170.39866 

22.00 150.50190 196.0886 10.3286 125.68778 

32.00 149.44468 196.0805 10.3293 111.54127 

42.00 148.58999 196.0692 10.3296 105.29901 

52.00 147.86893 196.0556 10.3296 104.38452 

62.00 147.22535 196.0406 10.3293 105.08875 

72.00 146.63031 196.0245 10.3289 106.28355 

82.00 146.06611 196.0077 10.3284 107.52382 

92.00 145.52221 195.9903 10.3278 108.68106 

102.00 144.99121 195.9725 10.3272 109.71034 

112.00 144.46867 195.9544 10.3265 110.54808 

122.00 143.95323 195.9360 10.3257 111.63279 

132.00 143.44217 195.9171 10.3250 113.63344 

142.00 142.93314 195.8977 10.3242 115.51311 

152.00 142.42634 195.8779 10.3234 117.29837 

162.00 141.92213 195.8576 10.3226 118.84766 

172.00 141.41979 195.8370 10.3217 120.41787 

182.00 140.91968 195.8160 10.3209 121.65504 

192.00 140.42232 195.7947 10.3200 122.40360 

202.00 139.92845 195.7732 10.3191 123.05037 

212.00 139.43813 195.7516 10.3183 123.69067 

222.00 138.95005 195.7298 10.3174 123.93127 

232.00 138.46513 195.7079 10.3165 124.08700 

242.00 137.98264 195.6860 10.3156 124.28340 

252.00 137.50210 195.6640 10.3147 124.42473 

262.00 137.02429 195.6419 10.3139 124.55550 

272.00 136.54896 195.6198 10.3130 124.67807 

282.00 136.07625 195.5977 10.3121 124.79741 

292.00 135.60580 195.5754 10.3112 124.91695 

302.00 135.13889 195.5532 10.3103 124.93866 

312.00 134.67502 195.5309 10.3094 124.85725 

322.00 134.21316 195.5086 10.3085 124.82197 

332.00 133.75339 195.4863 10.3076 124.52935 

342.00 133.29561 195.4641 10.3067 124.34790 

352.00 132.84014 195.4418 10.3058 124.02195 

362.00 132.38771 195.4197 10.3050 123.80382 

372.00 131.93894 195.3975 10.3041 123.12606 

382.00 131.49454 195.3756 10.3032 121.99366 

392.00 131.05416 195.3538 10.3023 121.03047 

402.00 130.61642 195.3323 10.3015 119.77141 

412.00 130.18277 195.3111 10.3006 118.61212 

422.00 129.75291 195.2900 10.2997 117.93929 

432.00 129.32558 195.2690 10.2989 117.55718 

442.00 128.90143 195.2480 10.2980 117.41745 

452.00 128.47953 195.2270 10.2972 117.50997





462.00 128.05919 195.2060 10.2963 117.69112 

472.00 127.64069 195.1849 10.2955 118.03577 

482.00 127.22209 195.1637 10.2946 118.47314 

492.00 126.80415 195.1424 10.2938 118.75435 

502.00 126.38916 195.1210 10.2929 118.84079 

512.00 125.97849 195.0996 10.2920 119.09928 

522.00 125.57045 195.0780 10.2912 119.84699 

532.00 125.16402 195.0563 10.2903 120.66595 

542.00 124.75881 195.0343 10.2894 121.15358 

552.00 124.35545 195.0123 10.2885 121.40883 

562.00 123.95250 194.9901 10.2876 121.81255 

572.00 123.54994 194.9679 10.2867 122.39091 

582.00 123.14896 194.9455 10.2858 123.02038 

592.00 122.74998 194.9230 10.2849 123.49260 

602.00 122.35247 194.9003 10.2840 123.79206 

612.00 121.95619 194.8776 10.2831 123.87992 

622.00 121.56376 194.8549 10.2822 123.76539 

632.00 121.17567 194.8321 10.2813 123.68782 

642.00 120.78531 194.8094 10.2803 123.72291 

652.00 120.39437 194.7867 10.2794 123.51119 

662.00 120.00565 194.7640 10.2785 123.17146 

672.00 119.62011 194.7415 10.2776 122.10742 

682.00 119.23779 194.7192 10.2767 120.59806 

692.00 118.85930 194.6973 10.2759 119.00004 

702.00 118.48585 194.6757 10.2750 117.51557 

712.00 118.11447 194.6544 10.2741 116.06698 

722.00 117.74397 194.6334 10.2733 114.24369 

732.00 117.37379 194.6128 10.2725 112.63288 

742.00 117.00410 194.5926 10.2717 111.29819 

752.00 116.63603 194.5726 10.2709 110.29640 

762.00 116.26917 194.5529 10.2701 108.85752 

772.00 115.90371 194.5335 10.2693 107.27244 

782.00 115.53933 194.5145 10.2686 105.67123 

792.00 115.17613 194.4959 10.2678 104.02272 

802.00 114.81433 194.4776 10.2671 102.36216 

812.00 114.45490 194.4596 10.2664 100.56993 

822.00 114.09780 194.4421 10.2657 98.91472 

832.00 113.74265 194.4249 10.2650 97.15893 

842.00 113.38959 194.4082 10.2644 95.44570 

852.00 113.03879 194.3918 10.2637 93.41516 

862.00 112.69176 194.3759 10.2631 91.55983 

872.00 112.34730 194.3603 10.2625 89.65349 

882.00 112.00406 194.3452 10.2619 87.83838 

892.00 111.66189 194.3304 10.2613 87.07423 

902.00 111.31635 194.3156 10.2607 88.76411 

912.00 110.89697 194.3008 10.2601 93.12664 

922.00 110.39080 194.2859 10.2595 96.95070 

932.00 109.81353 194.2712 10.2590 100.09297 

942.00 109.17955 194.2567 10.2584 102.58854 

952.00 108.50169 194.2423 10.2578 104.49571 

962.00 107.79035 194.2281 10.2572 105.86773 

972.00 107.05467 194.2141 10.2567 106.69727 

982.00 106.30241 194.2002 10.2561 107.13677 

992.00 105.54030 194.1864 10.2556 107.09867 

1002.00 104.77430 194.1728 10.2550 106.82460 

1012.00 104.00714 194.1594 10.2545 106.48605 

1022.00 103.23967 194.1460 10.2539 106.05737 

1032.00 102.47457 194.1327 10.2534 105.54946 

1042.00 101.71243 194.1195 10.2529 105.08021 

1052.00 100.95477 194.1064 10.2523 104.56702 

1062.00 100.20367 194.0933 10.2518 103.85669 

1065.52 99.94100 194.0887 10.2516 103.57336 

The time in the first column is provided in seconds w.r.t. the T 0 epoch (i.e., UTC 2005-01-14T09:10:21). Electronic file: data set ID HP-SSA-DTWG-6- 

TRAJECTORY-V1.0 in ESA/PSA (http://www.rssd.esa.int/PSA) and/or NASA/PDS (http://pds.nasa.gov).

1870 

Table 5 

Reconstruction results of the Huygens descent phase trajectory 



Time (s) Alt. (km) W-Lon. (deg) Lat. (deg) Descent vel. (m/s) 

80.00 145.87476 – – 47.72245 

110.00 144.52357 – – 57.11407 

140.00 142.91573 195.8968 10.3241 54.87502 

170.00 141.35614 195.8313 10.3214 51.32799 

200.00 139.80623 195.7648 10.3187 44.42313 

230.00 138.38087 195.6983 10.3160 47.74028 

260.00 136.94104 195.6317 10.3133 47.71498 

290.00 135.52327 195.5647 10.3106 45.90862 

320.00 134.15854 195.4977 10.3079 50.89922 

350.00 132.74061 195.4314 10.3052 49.25310 

380.00 131.39365 195.3664 10.3026 47.07743 

410.00 130.00043 195.3041 10.3000 38.93603 

440.00 128.75582 195.2419 10.2975 43.34490 

470.00 127.48616 195.1783 10.2949 41.82604 

500.00 126.24237 195.1137 10.2923 41.41616 

530.00 124.96740 195.0476 10.2896 38.84863 

560.00 123.81111 194.9806 10.2868 42.53136 

590.00 122.61026 194.9122 10.2841 39.84609 

620.00 121.40258 194.8437 10.2813 39.15200 

650.00 120.27764 194.7757 10.2786 39.83928 

680.00 119.04807 194.7098 10.2759 35.70091 

710.00 117.97591 194.6476 10.2734 36.99364 

740.00 116.87547 194.5889 10.2710 35.79069 

770.00 115.80822 194.5322 10.2687 38.60423 

800.00 114.71735 194.4792 10.2666 36.25165 

830.00 113.69115 194.4296 10.2647 36.02049 

860.00 112.61983 194.3837 10.2629 34.71465 

890.00 111.63740 194.3410 10.2611 37.52017 

920.00 110.47704 194.2968 10.2594 48.58070 

950.00 108.82954 194.2575 10.2578 64.27305 

980.00 106.77638 194.2189 10.2562 72.54918 

1010.00 104.60788 194.1807 10.2546 74.65025 

1040.00 102.39860 194.1426 10.2531 72.69762 

1070.00 100.23049 194.1042 10.2515 70.21827 

1100.00 98.15865 194.0672 10.2501 68.07214 

1130.00 96.14679 194.0319 10.2486 65.43539 

1160.00 94.18976 193.9985 10.2473 60.95764 

1190.00 92.32958 193.9670 10.2460 61.07398 

1220.00 90.49113 193.9374 10.2448 61.50024 

1250.00 88.71312 193.9107 10.2437 57.38240 

1280.00 87.02618 193.8879 10.2428 54.71855 

1310.00 85.38884 193.8688 10.2420 54.23154 

1340.00 83.77634 193.8526 10.2413 50.50905 

1370.00 82.24631 193.8391 10.2408 51.03189 

1400.00 80.72989 193.8278 10.2403 49.29909 

1430.00 79.28134 193.8185 10.2399 47.38661 

1460.00 77.85498 193.8120 10.2397 43.98281 

1490.00 76.52925 193.8080 10.2395 44.22941 

1520.00 75.21004 193.8048 10.2394 42.75959 

1550.00 73.92475 193.8022 10.2393 41.36608 

1580.00 72.68666 193.7993 10.2392 40.64489 

1610.00 71.48417 193.7960 10.2391 39.52488 

1640.00 70.31695 193.7907 10.2389 36.46398 

1670.00 69.22079 193.7807 10.2385 35.21222 

1700.00 68.17721 193.7667 10.2380 35.09248 

1730.00 67.13577 193.7487 10.2374 32.79244 

1760.00 66.15953 193.7270 10.2366 31.58246 

1790.00 65.22248 193.7037 10.2358 30.97945 

1820.00 64.30098 193.6804 10.2350 29.45250 

1850.00 63.42644 193.6570 10.2342 27.86615 

1880.00 62.59061 193.6333 10.2334 27.14875 

1910.00 61.78045 193.6094 10.2326 26.04254 

1940.00 61.00566 193.5851 10.2318 25.41181





1970.00 60.24619 193.5604 10.2310 24.92400 

2000.00 59.50755 193.5356 10.2302 24.13121 

2030.00 58.78500 193.5107 10.2295 23.71148 

2060.00 58.08608 193.4862 10.2287 22.82059 

2090.00 57.40252 193.4623 10.2280 22.45346 

2120.00 56.73364 193.4388 10.2274 21.99634 

2150.00 56.08086 193.4160 10.2268 21.21908 

2180.00 55.44537 193.3937 10.2262 21.17531 

2210.00 54.81988 193.3717 10.2256 20.48474 

2240.00 54.21296 193.3499 10.2251 19.96695 

2270.00 53.61327 193.3283 10.2246 19.65318 

2300.00 53.02909 193.3069 10.2241 19.35205 

2330.00 52.45149 193.2861 10.2237 18.66908 

2360.00 51.89047 193.2657 10.2233 18.63099 

2390.00 51.33548 193.2459 10.2229 18.44712 

2420.00 50.79148 193.2268 10.2226 18.03302 

2450.00 50.25502 193.2083 10.2223 17.59354 

2480.00 49.73077 193.1901 10.2221 17.38721 

2510.00 49.21431 193.1721 10.2219 17.11882 

2540.00 48.70133 193.1547 10.2217 16.90256 

2570.00 48.19809 193.1374 10.2215 16.55894 

2600.00 47.70370 193.1203 10.2214 16.23464 

2630.00 47.21874 193.1035 10.2212 16.04345 

2660.00 46.73926 193.0869 10.2212 15.74911 

2690.00 46.26903 193.0705 10.2211 15.66185 

2720.00 45.80596 193.0543 10.2211 15.39215 

2750.00 45.34982 193.0384 10.2210 14.81501 

2780.00 44.90296 193.0229 10.2211 14.78191 

2810.00 44.45695 193.0079 10.2211 14.66499 

2840.00 44.02059 192.9930 10.2212 14.29095 

2870.00 43.58729 192.9788 10.2213 13.91472 

2900.00 43.16531 192.9647 10.2214 14.08899 

2930.00 42.74780 192.9511 10.2215 13.80853 

2960.00 42.33378 192.9377 10.2216 13.63424 

2990.00 41.92727 192.9247 10.2217 13.39720 

3020.00 41.52289 192.9118 10.2219 13.46047 

3050.00 41.12275 192.8991 10.2220 13.06836 

3080.00 40.72892 192.8870 10.2222 13.01831 

3110.00 40.33726 192.8750 10.2224 12.82131 

3140.00 39.95498 192.8630 10.2226 12.53171 

3170.00 39.57570 192.8512 10.2228 12.56885 

3200.00 39.19890 192.8395 10.2230 12.08444 

3230.00 38.83024 192.8284 10.2232 12.34752 

3260.00 38.46049 192.8177 10.2234 12.07361 

3290.00 38.09916 192.8069 10.2236 12.00704 

3320.00 37.74171 192.7964 10.2239 11.88009 

3350.00 37.38751 192.7863 10.2241 11.87816 

3380.00 37.03540 192.7763 10.2244 11.64400 

3410.00 36.68745 192.7665 10.2247 11.27836 

3440.00 36.34534 192.7569 10.2249 11.29146 

3470.00 36.00640 192.7472 10.2252 11.46998 

3500.00 35.66806 192.7377 10.2255 10.99143 

3530.00 35.33837 192.7286 10.2258 11.04983 

3560.00 35.00906 192.7197 10.2261 11.00241 

3590.00 34.68567 192.7111 10.2264 10.87971 

3620.00 34.36342 192.7027 10.2268 10.63601 

3650.00 34.04731 192.6944 10.2271 10.56734 

3680.00 33.73278 192.6861 10.2274 10.47486 

3710.00 33.41629 192.6781 10.2278 10.41691 

3740.00 33.10468 192.6704 10.2281 10.17070 

3770.00 32.80043 192.6627 10.2285 9.99349 

3800.00 32.49640 192.6552 10.2289 9.99756 

3830.00 32.19712 192.6478 10.2292 10.19483 

3860.00 31.89378 192.6406 10.2296 9.80949

1872 





3890.00 31.60117 192.6335 10.2300 9.77012 

3920.00 31.30772 192.6267 10.2304 9.62563 

3950.00 31.01774 192.6201 10.2308 9.59657 

3980.00 30.73069 192.6137 10.2312 9.45977 

4010.00 30.44770 192.6073 10.2316 9.54650 

4040.00 30.16480 192.6009 10.2320 9.58685 

4070.00 29.88047 192.5947 10.2324 9.26908 

4100.00 29.60427 192.5886 10.2328 9.31846 

4130.00 29.32385 192.5827 10.2332 9.02446 

4160.00 29.05134 192.5768 10.2337 9.03679 

4190.00 28.78176 192.5710 10.2341 9.11907 

4220.00 28.51070 192.5656 10.2346 8.97521 

4250.00 28.24303 192.5602 10.2350 8.94630 

4280.00 27.97742 192.5550 10.2355 8.82621 

4310.00 27.71046 192.5498 10.2359 8.47264 

4340.00 27.45383 192.5447 10.2364 8.75837 

4370.00 27.19483 192.5399 10.2368 8.31297 

4400.00 26.93818 192.5351 10.2373 8.67838 

4430.00 26.67860 192.5305 10.2378 8.48575 

4460.00 26.42177 192.5259 10.2383 8.45700 

4490.00 26.16782 192.5215 10.2388 8.28864 

4520.00 25.92020 192.5170 10.2393 8.46008 

4550.00 25.66730 192.5125 10.2397 8.28350 

4580.00 25.42022 192.5082 10.2402 8.10115 

4610.00 25.17661 192.5040 10.2407 8.40709 

4640.00 24.93158 192.4998 10.2412 8.10988 

4670.00 24.68948 192.4957 10.2417 7.97632 

4700.00 24.45091 192.4917 10.2422 8.20620 

4730.00 24.20804 192.4874 10.2427 7.91554 

4760.00 23.96923 192.4831 10.2432 8.18937 

4790.00 23.72901 192.4789 10.2437 7.66383 

4820.00 23.49539 192.4748 10.2442 7.63835 

4850.00 23.26515 192.4709 10.2447 7.84179 

4880.00 23.03252 192.4673 10.2452 7.69834 

4910.00 22.80277 192.4638 10.2458 7.69531 

4940.00 22.57279 192.4602 10.2463 7.53131 

4970.00 22.34773 192.4565 10.2468 7.65652 

5000.00 22.12231 192.4529 10.2473 7.65650 

5030.00 21.89548 192.4495 10.2478 7.50630 

5060.00 21.66886 192.4462 10.2482 7.37011 

5090.00 21.44670 192.4430 10.2487 7.37023 

5120.00 21.22637 192.4401 10.2492 7.26847 

5150.00 21.00496 192.4373 10.2496 7.21700 

5180.00 20.78735 192.4345 10.2500 7.43009 

5210.00 20.56620 192.4317 10.2504 7.01251 

5240.00 20.35609 192.4289 10.2508 7.18236 

5270.00 20.14176 192.4262 10.2512 7.32178 

5300.00 19.92763 192.4234 10.2516 7.31090 

5330.00 19.71252 192.4208 10.2519 7.20721 

5360.00 19.50051 192.4184 10.2522 6.96025 

5390.00 19.29087 192.4160 10.2526 6.88923 

5420.00 19.08324 192.4136 10.2529 6.78754 

5450.00 18.87799 192.4112 10.2532 6.88907 

5480.00 18.66875 192.4088 10.2535 7.17022 

5510.00 18.45898 192.4063 10.2537 6.79053 

5540.00 18.25652 192.4035 10.2540 6.85018 

5570.00 18.05106 192.4009 10.2542 6.87907 

5600.00 17.84819 192.3983 10.2544 6.90496 

5630.00 17.64364 192.3959 10.2546 6.63270 

5660.00 17.44048 192.3936 10.2548 6.46137 

5690.00 17.24356 192.3914 10.2549 6.75616 

5720.00 17.04449 192.3891 10.2551 6.73136 

5750.00 16.84637 192.3869 10.2552 6.59969 

5780.00 16.64915 192.3848 10.2554 6.66226





5810.00 16.45249 192.3827 10.2555 6.64656 

5840.00 16.25390 192.3805 10.2556 6.41873 

5870.00 16.05687 192.3784 10.2557 6.37687 

5900.00 15.86405 192.3762 10.2557 6.34228 

5930.00 15.67053 192.3741 10.2558 6.31724 

5960.00 15.47819 192.3722 10.2558 6.32238 

5990.00 15.28763 192.3703 10.2559 6.31600 

6020.00 15.09818 192.3684 10.2559 6.26524 

6050.00 14.91027 192.3665 10.2559 6.20508 

6080.00 14.72204 192.3646 10.2558 6.39566 

6110.00 14.53208 192.3627 10.2558 6.22452 

6140.00 14.34459 192.3609 10.2558 6.13328 

6170.00 14.16054 192.3591 10.2557 6.22246 

6200.00 13.97506 192.3572 10.2556 6.11483 

6230.00 13.79165 192.3554 10.2555 5.96117 

6260.00 13.61107 192.3536 10.2555 5.95625 

6290.00 13.42998 192.3520 10.2554 6.07882 

6320.00 13.24867 192.3505 10.2554 6.07399 

6350.00 13.06694 192.3490 10.2553 5.95507 

6380.00 12.88948 192.3475 10.2552 6.01335 

6410.00 12.70875 192.3460 10.2552 5.99633 

6440.00 12.52827 192.3446 10.2551 5.80720 

6470.00 12.35343 192.3433 10.2551 5.62885 

6500.00 12.17976 192.3417 10.2550 5.80418 

6530.00 12.00493 192.3402 10.2550 5.87927 

6560.00 11.82998 192.3386 10.2549 6.00904 

6590.00 11.65297 192.3371 10.2549 5.76657 

6620.00 11.47852 192.3357 10.2548 5.66962 

6650.00 11.30651 192.3343 10.2548 5.90213 

6680.00 11.13280 192.3329 10.2547 5.72767 

6710.00 10.96121 192.3316 10.2547 5.63692 

6740.00 10.79072 192.3303 10.2547 5.65145 

6770.00 10.61991 192.3290 10.2546 5.68541 

6800.00 10.45021 192.3278 10.2546 5.69116 

6830.00 10.28027 192.3266 10.2546 5.60234 

6860.00 10.11481 192.3255 10.2545 5.66801 

6890.00 9.94503 192.3243 10.2545 5.48754 

6920.00 9.77828 192.3233 10.2545 5.62022 

6950.00 9.60928 192.3222 10.2544 5.61004 

6980.00 9.44107 192.3213 10.2544 5.58076 

7010.00 9.27438 192.3203 10.2544 5.39540 

7040.00 9.11060 192.3194 10.2544 5.48073 

7070.00 8.94772 192.3185 10.2544 5.53363 

7100.00 8.78081 192.3177 10.2543 5.50701 

7130.00 8.61879 192.3169 10.2543 5.53871 

7160.00 8.45441 192.3161 10.2543 5.28141 

7190.00 8.29471 192.3154 10.2543 5.42047 

7220.00 8.13382 192.3147 10.2543 5.50383 

7250.00 7.97073 192.3140 10.2543 5.32723 

7280.00 7.81012 192.3134 10.2542 5.43944 

7310.00 7.64879 192.3128 10.2542 5.28827 

7340.00 7.48805 192.3123 10.2542 5.31183 

7370.00 7.32822 192.3118 10.2542 5.29823 

7400.00 7.17028 192.3114 10.2542 5.28338 

7430.00 7.01096 192.3109 10.2542 5.25953 

7460.00 6.85392 192.3106 10.2542 5.26468 

7490.00 6.69586 192.3102 10.2542 5.19608 

7520.00 6.53899 192.3099 10.2542 5.13401 

7550.00 6.38325 192.3096 10.2542 5.08317 

7580.00 6.22799 192.3094 10.2542 5.17979 

7610.00 6.07224 192.3092 10.2542 5.06590 

7640.00 5.91801 192.3091 10.2542 5.08304 

7670.00 5.76400 192.3090 10.2541 5.19385 

7700.00 5.61008 192.3089 10.2541 5.10108

1874 


Appendix A 

Entry and descent phase trajectories are shown in 

Tables 4 and 5. 

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7760.00 5.30694 192.3088 10.2539 5.11553 

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8690.00 0.82179 192.3260 10.2493 4.61699 

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8810.00 0.27110 192.3252 10.2504 4.46494 

8840.00 0.13441 192.3250 10.2506 4.48282 

8869.77 0.00000 192.3247 10.2507 4.54741 

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