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

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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). ARTICLE IN PRESS B. Kazeminejad et al. / Planetary and Space Science 55 (2007) 1845–1876 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 ARTICLE IN PRESS B. Kazeminejad et al. / Planetary and Space Science 55 (2007) 1845–1876 1853 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
Page 1 and 2: Planetary and Space Science 55 (200
Page 3 and 4: was separated from Cassini on the t
Page 5 and 6: EXPERIMENT PLATFORM FRONT SHIELD AF
Page 7: drive the mass from its displaced p
Page 11 and 12: Altitude [km] above Ref. Surface of
Page 13 and 14: Altitude [km] Altitude [km] 1200 10
Page 15 and 16: 4.2. Discussion of reconstruction r
Page 17 and 18: West Longitude [deg] Latitude [deg]
Page 19 and 20: 2 km. The scales of the surface fea
Page 21 and 22: Aerodynamic Deceleration [m/s 2 ] 6
Page 23 and 24: therefore be considered as approxim
Page 25 and 26: Table 4 (continued ) ARTICLE IN PRE
Page 31 and 32: leading truncation error term. Tech

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