Accepted Manuscript - Cnr

Accepted Manuscript
Drag and Energy Accommodation Coefficients During Sunspot Maximum
C. Pardini, L. Anselmo, K. Moe, M.M. Moe
PII: S0273-1177(09)00618-8
DOI: 10.1016/j.asr.2009.08.034
Reference: JASR 9965
To appear in: Advances in Space Research
Received Date: 30 January 2009
Revised Date: 22 May 2009
Accepted Date: 27 August 2009
Please cite this article as: Pardini, C., Anselmo, L., Moe, K., Moe, M.M., Drag and Energy Accommodation
Coefficients During Sunspot Maximum, Advances in Space Research (2009), doi: 10.1016/j.asr.2009.08.034
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Drag and Energy Accommodation Coefficients During Sunspot Maximum
C. Pardini a , L. Anselmo a , K. Moe b and M. M. Moe b
a Space Flight Dynamics Laboratory, ISTI/CNR, Via G. Moruzzi 1, 56124 Pisa, Italy
b Space Environment Technologies, 23 Purple Sage, Irvine, CA 92603, United States
a E-mail: Carmen.Pardini@isti.cnr.it; Luciano.Anselmo@isti.cnr.it
b E-mail : kmmoe2@att.net
Abstract
Conditions appropriate to gas-surface interactions on satellite surfaces in orbit have not been
successfully duplicated in the laboratory. However, measurements by pressure gauges and mass
spectrometers in orbit have revealed enough of the basic physical chemistry that realistic theoretical
models of the gas-surface interaction can now be used to calculate physical drag coefficients. The
dependence of these drag coefficients on conditions in space can be inferred by comparing the
physical drag coefficient of a satellite with a drag coefficient fitted to its observed orbital decay.
This study takes advantage of recent data on spheres and attitude-stabilized satellites to compare
physical drag coefficients with the histories of the orbital decay of several satellites during the
recent sunspot maximum. The orbital decay was obtained by fitting, in a least squares sense, the
semi-major axis decay inferred from the historical two-line elements acquired by the US Space
Surveillance Network. All the principal orbital perturbations were included, namely geopotential
harmonics up to the 16 th degree and order, third body attraction of the Moon and the Sun, direct
solar radiation pressure (with eclipses), and aerodynamic drag, using the Jacchia-Bowman 2006
(JB2006) model to describe the atmospheric density. After adjusting for density model bias, a
comparison of the fitted drag coefficient with the physical drag coefficient has yielded values for
the energy accommodation coefficient as well as for the physical drag coefficient as a function of
altitude during solar maximum conditions. The results are consistent with the altitude and solar
cycle variation of atomic oxygen, which is known to be adsorbed on satellite surfaces, affecting
both the energy accommodation and angular distribution of the reemitted molecules.
1. Introduction
Both accelerometer measurements and orbital decay studies show that satellite drag
coefficient calculations need improving, especially between 300 and 800 km altitude, where many
important satellites fly. Better drag coefficients are needed for improving lifetime predictions of
satellites and for refining thermospheric density models. Atmospheric densities derived from
accelerometer measurements and orbital decay depend on the drag coefficient, CD, assigned to the
satellite, because satellites rarely incorporate a method of measuring it. Consequently, the accuracy
of the inferred densities can be no better than the accuracy of the assumed value of CD. In the past,

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the use of inaccurate drag coefficients has introduced biases in thermospheric density models
(Chao, et al., 1997; Moe, et al., 2004).
The relationship between the magnitude of the drag force F and atmospheric density ρ is
F = M a = ½ ρ CD A Vi 2 (1)
in which Vi is the speed of the satellite relative to the atmosphere, M is the mass of the satellite, and
A is a reference area, usually taken to be the cross sectional area of the satellite normal to the
incident airstream. The product A Vi 2 is usually well known (except during large geomagnetic
storms). The drag force F is measured either by an accelerometer or by the observed orbital decay.
Therefore, it is the product ρ CD which is determined by the observations.
In practice, three types of satellite drag coefficients have been used: fixed drag coefficients,
fitted drag coefficients, and physical drag coefficients. Fixed drag coefficients simplify the
processes of constructing and using atmospheric density models. Fitted drag coefficients are of
great value in constructing orbits with the aid of an atmospheric model. Physical drag coefficients
are related directly to the drag force, and require a realistic model of the molecular collisions and
adsorptive processes at the satellite surface. They are required for determining absolute atmospheric
densities.
Early in the space age, scientists used a variety of fixed drag coefficients, mostly in the range
of 2.0 to 2.3 (Wolverton, 1963). Outstanding theoretical work was done by Schaaf and Chambré
(1958), Schamberg (1959a and b), and Sentman (1961a and b), but it received little attention from
thermospheric workers at that time. Studies by Izakov (1965) and Cook (1965 and 1966), based on
laboratory measurements, led to the widespread use of a fixed drag coefficient of 2.2 by the
international space community. This had the advantage that there was one less variable when
reducing data or comparing data sets. (The equations for drag and accommodation coefficients
given by Cook are still sometimes used. They agree with idealized laboratory measurements on
clean surfaces, but do not represent the conditions encountered by satellite surfaces in orbit.)
Classified flights of long cylindrical reconnaissance satellites, beginning in 1960, showed that long
cylinders had drag coefficients between 3 and 4, which confirmed the calculations of Sentman
(1961a), but this information was not declassified until 1971 (DeVries, 1971).
Satellite and rocket measurements by pressure (density) gauges (Carter, et al, 1969) and mass
spectrometers (Hedin, et al, 1973; Offermann and Grossmann, 1973) revealed that satellite surfaces
are contaminated by adsorbed molecules. Moe et al. (1972) showed that adsorption on the walls of
Carter’s pressure gauge could be modeled by assuming heterogeneous adsorption, using the
Langmuir isotherm. Hedin, et al., (1973) modeled the adsorption of atomic oxygen in the mass
spectrometer on OGO 6 using the Langmuir isotherm. These modeling studies confirmed that
satellite surfaces are contaminated with adsorbed gases, and emphasized the importance of correctly
representing the energy accommodation and angular distributions of atmospheric molecules
reemitted from satellite surfaces (Moe, et al., 1995, 1998).
In the 1970s, energy accommodation coefficients were measured in low-earth orbit at times of
low and moderate solar activity by paddlewheel satellites (Beletsky, 1970; Imbro, et al. 1975), and
by the ratio of lift to drag on the S3-1 satellite (Ching, et al., 1977). These accommodation
coefficients were 0.99 to 1.00 near 200 km, and about 0.88 near 320 km. Angular distributions of
reemitted molecules have been measured near 180 km by Beletsky (1970), near 225 km by Gregory
and Peters (1987), and near 700 km, by Moe and Bowman (2005). Near 200 km the angular
distribution was about 98% diffuse, while near 700 km it appeared to be nearly diffuse during two
sunspot cycles. These orbital measurements have made it possible to calculate the drag coefficients
of satellites in low Earth orbit up to 300 km with considerable confidence at times of low to
moderate solar activity (Moe, et al., 1995; Moe and Moe, 2005). Above 300 km, and during high

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solar activity, the uncertainty in these calculations increases rapidly because physical drag
coefficient measurements are so rare. The precise fitted drag coefficients (Willis, et al, 2005) at 800
to 1300 km could help fill this void, and make possible the improvement of thermospheric models
at these high altitudes and during geomagnetic storms. Near sunspot maximum, when the
concentration of atomic oxygen is high, the accommodation coefficients are expected to be higher
and less variable, causing drag coefficients to be lower than at solar minimum (Moe and Moe,
1995). In relation to this, see Figure 7 in Bowman and Moe (2005). The present paper improves the
accommodation coefficients at sunspot maximum given in Moe et al. (1995). A review of sunspot
cycles has recently been published by Vacquero (2007).
In addition to the solar cycle variation of accommodation coefficients, there is the possibility
of a longer-term secular variation: Several recent studies (Marcos et al. 2005; Qian, et al., 2008;
Emmert et al., 2008) have reported a long-term secular decrease in thermospheric temperature and
density caused by the secular increase in atmospheric carbon dioxide. In all of these studies it was
assumed that the drag coefficients of satellites are independent of altitude, solar activity, atomic
oxygen concentration, and other parameters. Since drag coefficients vary with all of these
parameters, it would be of value to investigate the effect of varying drag coefficients on the reported
results. In particular, a secular reduction in atomic oxygen will reduce the accommodation
coefficients and increase the drag coefficients of satellites. The trend in accommodation and drag
coefficients could be measured by flying some paddlewheel satellites, as was done early in the
space age (Reiter and Moe, 1969). Such satellites, measuring both spin and orbital decay, are
capable of determining absolute thermospheric densities as well as drag and accommodation
coefficients. Lacking the advantages of a paddlewheel design, we can try to use satellites of
different shapes to infer the behavior of drag and energy accommodation coefficients. In the present
study, we have taken advantage of the increasing data available to compare theoretical
determinations of satellite drag coefficients with a history of satellite orbital decay during sunspot
maximum. In particular, we have extended earlier research (Bowman and Moe, 2005; Moe and
Bowman, 2005) to altitudes above 500 km, to the maximum of solar cycle 23, and to non-spherical
satellites.
2. Accommodation coefficient
The parameters used in drag coefficient models are the angular distribution of the molecules
reemitted from the satellite surface and the energy accommodation coefficient , defined as
= (Ei – Er)/(Ei – Ew). (2)
Here Ei is the kinetic energy of the incident molecules, Er is the kinetic energy of the reemitted
molecules, and Ew is the energy the reemitted molecules would have if they had adjusted completely
to the surface (or wall) temperature before reemission. In other words, the accommodation
coefficient indicates how closely the kinetic energy of the incoming molecule has adjusted to the
thermal energy of the surface before it is reemitted. If the adjustment is complete, then = 1.00.
This is called complete accommodation. It is important to know the accommodation coefficient,
because CD could be 1.8, or 2.4, or some other value, depending on the accommodation coefficient
and angular distribution. The theoretical determination of drag coefficients requires that we
calculate the momentum transferred to the satellite by the impact of the molecules striking the
surface. That momentum transfer cannot be calculated unless we know the angular distribution and

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energy loss of the molecules. The energy accommodation coefficient gives us the vital information
about energy loss.
The value of the accommodation coefficient for a particular satellite is dependent on the
stream velocity, Vi , the masses of the incident molecules, and the condition of the surface. Surface
conditions are influenced by a number of parameters. The most important is satellite altitude, which
largely determines the number of oxygen atoms striking the surface and then being adsorbed.
Atomic oxygen binds strongly to many surfaces and changes surface properties (Riley and Giese,
1970; Wood, 1971). It is now well known that satellite surfaces at altitudes of 150-300 km are
contaminated with adsorbed atomic oxygen and its reaction products. The higher the altitude, the
lower the surface fraction covered with adsorbed atoms and molecules. If the incoming molecules
struck a clean surface, they would be reemitted near the specular angle with a partial loss of incident
kinetic energy. But when the surface is contaminated by adsorbed molecules, the incident molecules
lose a large amount of kinetic energy and are reemitted in a diffuse distribution. Adsorbed
molecules then increase energy accommodation and broaden the angular distribution of reflected
molecules. The equation for the drag coefficient of a flat plate, based ultimately on Sentman’s
(1961b) analysis, is given in terms of accommodation coefficients by Moe, et al., (2004). It can be
calculated for other convex shapes by integration.
The brief review of satellite measurements in the introduction has revealed that, in low Earth
orbit near 200 km, is between 1.00 and 0.99 (Moe and Bowman, 2005), and that the angular
distribution of reemitted molecules is diffuse. Sentman’s analysis of gas-surface interactions
(Sentman, 1961b) is then appropriate for calculating the physical drag coefficients of satellites in
the neighborhood of 200 km, because it assumes diffuse reemission. At higher altitudes the
accommodation coefficient decreases, suggesting a lower surface contamination and a quasispecular
reemission of some of the incident molecules. At altitudes near 300 km at solar minimum,
has fallen by about 10%, to the vicinity of 0.9. In this case, Schamberg’s model of drag
coefficients (Schamberg, 1959a and b) could be appropriate for calculating the contribution of the
quasi-specular component, particularly at times of low solar activity. However, an earlier study
(Moe and Bowman, 2005) demonstrated that even at 700 km altitude, the orbital decay of three
Calspheres with different surface materials over a period of 19 years was independent of the surface
material. This suggests that even at 700 km the surfaces are contaminated and the reemission is
mostly diffuse. The present study is made for solar maximum when the most atomic oxygen is
adsorbed on satellite surfaces, so more diffuse reemission is to be expected. Therefore the use of
Sentman’s analysis is justified in the present investigation.
3. Drag and energy accommodation coefficients at sunspot maximum
Ten satellites were involved in this study, including several processed by Bowman and Moe
(2005). Their perigee altitudes were between 200 and 630 km, and their orbital decay was analyzed
during the sunspot maxima of solar cycles 22 and 23. Spherical smooth objects (5 Taifun Yug
satellites and 3 Calspheres) were considered, together with one Surrey satellite (Clementine) and the
Student Nitric Oxide Explorer (SNOE), a small student satellite project of the University of
Colorado. Both Clementine and SNOE had simple shapes and were attitude stabilized in order to
have constant orientation with respect to the airstream. Clementine also slowly rotated about the
vertical axis to prevent overheating. SNOE is pictured in Figure 1, and Clementine in Figure 2.
Table 1 lists the satellites analyzed by Bowman and Moe that decayed during the maximum of
solar cycle 22. Table 2 includes the additional satellites considered in this study during the sunspot

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maximum of solar cycle 23. The time span covered by our analysis is specified, together with the
perigee/apogee altitude and the orbital inclination of each satellite at the beginning of the time span.
Drag coefficients for the various shapes of the bodies in the study (see Tables 1 and 2) were
calculated using a range of energy accommodation coefficients. This was carried out by applying
Sentman’s analysis of the interaction of incoming particles with a satellite surface to determine the
component of the force along the satellite's direction of motion. Sentman’s assumption of diffuse
reemission of the particles is appropriate as discussed in Section 2. In addition to the
accommodation coefficient, , the input quantities used for calculating the drag coefficients
included satellite speed and the temperature and mean molecular mass of the ambient atmosphere,
together with the parameters related to the shape of the satellite. For each satellite, a series of drag
coefficient values was obtained as a function of . The drag coefficients so determined are named
“physical drag coefficients”, to distinguish them from drag coefficients determined by fitting the
orbital decay to a particular density model.
The “fitted drag coefficients” were computed by an analysis of the orbital decay of satellites.
In some cases the drag coefficients so obtained were updated, when more recent information
regarding the dimensions of the satellite became available. The fitted drag coefficients were then
adjusted upward by a certain amount (dependent on altitude) to account for the known biases in the
atmospheric density model used at sunspot maximum. The modified fitted drag coefficients are
called “observed drag coefficients”.
After having found the physical drag coefficient that matched the observed drag coefficient,
the corresponding energy accommodation coefficient was identified.
3.1 Fitted drag coefficients
For each satellite, the fitted drag coefficient was obtained by fitting, in a least squares sense,
the semi-major axis decay inferred from the historical two-line elements (TLEs) provided by the US
Space Surveillance Network (Hoots and Roehrich, 1980) . The inverse ballistic coefficient of the
satellite is defined as
B = CD A/M (3)
where CD, A and M are, respectively, the satellite drag coefficient, cross-sectional area and mass.
In orbit fitting, B was adjusted to force the atmospheric density model to agree with the air drag
revealed by the tracking data, i.e. the historical TLE record. Having fixed the area-to-mass ratio
A/M, the only solve-for parameter of the fit, in the least squares sense, was the satellite drag
coefficient CD. The semi-major axis root mean square (rms) residuals (R) were computed according
to the relationship (Pardini and Anselmo, 2008)
N
a a
i _ obs
i _ com
2
i 1
R (4)
N
where ai_obs and ai_com are, respectively, the observed and the computed semi-major axis at the
same epoch and N is the number of observations available, i.e. the number of TLEs used in the

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fitting.
The software code CDFIT, specifically developed at ISTI/CNR and adopting the same force
model as the orbit propagator SATRAP (Pardini and Anselmo, 1994), was used to fit the semimajor
axis decay. All the main orbital perturbations were considered, namely geopotential
harmonics up to the 16 th degree and order (EGM96 model, Lemoine et al., 1998), third body
attraction of the Moon and the Sun, direct solar radiation pressure with eclipses, and aerodynamic
drag.
The recent Jacchia-Bowman 2006 (JB2006) model (Bowman et al., 2008) was used to
describe the atmospheric density. (Several other empirical density models, such as NRLMSISE-00
(Picone et al, 2002), DTM-2000 (Bruinsma et al., 2003), GOST-2004 (Volkov, 2004) are widely
used, but we chose JB2006 because its biases had been measured.) The JB2006 indices (Tobiska et
al., 2008) were those released by Space Environment Technologies (SET, 2008) on 13 June 2007
(release v3.8). Figure 3 shows the 81-day centered smoothed values of the v3.8 JB2006 solar
indices F10.7 (F81c), S10.7 (S81c) and M10.7 (M81c) during the sunspot maximum of solar cycle 23 (1
October 1999 – 31 December 2002).
3.1.1 Impact of mismodeled radiation pressure and other minor perturbations on fitted drag
coefficients
For satellites above 500 km, a mismodeling of radiation pressure, namely direct solar
radiation pressure, Earth-reflected radiation and Earth-emitted infrared radiation, might critically
affect the accuracy of the fitted drag coefficients. To assess the impact of such possible
miscalculations on our fitted drag coefficients and considering that they were determined from
semi-major axis decay, the orbit evolution of two satellites (one in the neighborhood of 500 km,
SNOE, and the other near 650 km, Clementine), was analyzed by disregarding or including the
various perturbations caused by radiation pressure. The special perturbations trajectory propagator
SATORB (Beutler, 2005) was used to carry out this analysis.
The orbit of SNOE (initial perigee/apogee altitude = 515/570 km, inclination = 97.7, A/M =
0.007 m 2 /kg) was propagated for 60 days (i.e. two times the typical length of the arcs used to obtain
fitted drag coefficients), including 16 16 geopotential, luni-solar attraction and air drag, plus
various combinations of smaller perturbations. The overall mean semi-major axis decay, due
basically to air drag, was about 6 km. The total exclusion of direct solar radiation pressure resulted
in an average mean semi-major axis error of 0.729 m. The average mean semi-major axis error
introduced by disregarding the Earth’s albedo was 0.066 m. It was also found that the
corresponding mean errors were 0.019 m for neglecting the Earth’s tides and 0.001 m for neglecting
the relativistic effects.
The orbit evolution of Clementine (initial perigee/apogee altitude = 643/663 km, inclination =
98.1, A/M = 0.011 m 2 /kg) was simulated for 3 years (i.e. the length of the greatest arc used in this
case to obtain the fitted drag coefficient), again with 16 16 geopotential, luni-solar attraction, air
drag in conditions of high solar activity, and various combinations of radiation pressure and smaller
perturbations. The overall mean semi-major axis decay, due basically to air drag, was about 47 km.
The total exclusion of direct solar radiation pressure resulted in an average mean semi-major axis
error of 16.440 m. A mismodeling of direct solar radiation pressure by 20% resulted in an average
mean semi-major axis error of 3.037 m. The average mean semi-major axis error introduced by
disregarding the Earth’s albedo was 1.406 m. It was also found that the corresponding mean errors
were 0.054 m for neglecting the Earth’s tides and 0.010 m for neglecting the relativistic effects.

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In conclusion, the effects on the mean semi-major axis of Earth’s albedo (reflected and
thermal emitted radiation) and other smaller perturbations were less than those due to direct solar
radiation pressure mismodeling. In addition, even direct solar radiation pressure with eclipses
(included in the force model used for drag coefficient fits) had a very small influence on mean
semi-major axis evolution and dispersion in the altitude regimes considered.
As a further test, fitted drag coefficients were computed with CDFIT for the Optical
Calibration Sphere (OCS) satellite (initial perigee/apogee altitude = 748/803 km, inclination =
100.2), varying solar radiation pressure by as much as 100%. However, even for this large area-tomass
ratio satellite (A/M = 0.543 m 2 /kg), the maximum difference of the drag coefficient estimate
was 0.5% or less. Finally, a mismodeling of direct solar radiation pressure by 20% had no
detectable effect (i.e. 0.01) on the CD estimation for the satellites Clementine and UOSAT-2
(initial perigee/apogee altitude = 648/663 km, inclination = 97.9, A/M = 0.007 m 2 /kg).
3.2 SNOE drag and energy accommodation coefficients
SNOE had a cylinder-like shape with a hexagonal cross section. It was attitude stabilized, so
that it maintained a constant aspect relative to the incident velocity vector, a feature that facilitated
the computation of its drag coefficient as a function of . After its first year, the attitude sometimes
deviated from the nominal by ten degrees. SNOE was in a nearly circular orbit with a perigee
altitude of 515 km at the beginning of our analysis (Figure 4). Its semi-major axis was observed to
decay by about 38 km per year from 1 October 1999 to 31 December 2002 (Figure 4). In the same
time interval, 40 values of the SNOE fitted drag coefficients were obtained: the first 39 over 30-day
intervals, the last over a 15-day interval. Figure 5 shows the fitted CD values, together with the
corresponding inverse ballistic coefficient (B) and semi-major axis root mean square (rms)
residuals, defined according to Eqs. 3 and 4, respectively. A cross-sectional area of 1 m 2 and a mass
of 115.5 kg were assumed in order to estimate the fitted drag coefficients. The average fitted CD
was found to be 1.810. The standard deviation of an individual measurement (), defined according
to
N
n1
2
xn x
N 1
where xn represents the n th measurement and x is the arithmetic mean of all N measurements, was
0.184. If each of the 40 monthly measurements were statistically independent, the standard
deviation of the average, i.e. / N , with N = 40, would be 0.029. However, there are about four
positive peaks in the 40 month record. This implies that the 40 monthly samples are not
independent. We infer that the autocorrelation function has eight zeros (Rice, 1954); in other
words, there are only eight independent samples. Therefore, / N
is 0.065.
Two adjustments were then made to calculate the observed drag coefficient of SNOE. First,
the average area facing the air stream, according to the exact dimensions of SNOE, was 0.8377 m 2 ,
compared to the approximate value of 1 m 2 . The average drag coefficient (fitted to JB2006) then
became 2.16. This value was later increased by 15% to correct for the bias in the JB2006 density
model at an altitude of around 500 km (see Table 3 for the biases of the modified Jacchia 1970
(5)

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model (J70 MOD), obtained by Bowman and Moe (2005), and the biases of JB2006 obtained by us
with Bowman’s help). The resulting observed drag coefficient of SNOE was therefore 2.485.
A comparison of this result with the calculated dependence of the SNOE physical drag
coefficient on the energy accommodation coefficient revealed an agreement for = 0.95. This high
accommodation coefficient does not fit smoothly in the sequence, perhaps because the satellite
orientation sometimes deviated by ten degrees from the nominal. at sunspot minimum from Moe
et al. (1995) is given in Table 6 for comparison. Near 200 km, is 1.00 at sunspot maximum and
0.99 at sunspot minimum; but at sunspot maximum, decreases more slowly as the altitude
increases above 200 km. This is physically reasonable, because during sunspot maximum the
increased solar UV radiation dissociates more molecular oxygen, and increased UV heating causes
the resulting atomic oxygen to rise to higher altitudes, increasing the energy accommodation.
3.3 Clementine drag and energy accommodation coefficients
Clementine was a gravity-gradient stabilized rectangular box (0.60 x 0.35 x 0.35 m 3 ), with
four solar panels (0.53 x 0.35 m 2 ) tilted backward at 45° (relative to the normal to the box surface),
plus a 6 meter long rod for gravity-gradient stabilization. The long axis of the spacecraft pointed
within 1° of the nadir direction. The vehicle slowly rotated about its long axis to prevent any
overheating of the instruments within the satellite. With an initial perigee altitude in the vicinity of
650 km (Figure 6), the satellite did not experience a strong drag perturbation. The observed mean
semi-major axis decay was about 11 km per year over the time span covered by our analysis, i.e.
from 3 December 1999 to 31 December 2002 (Figure 6). The effects of air drag on semi-major axis
then became significant only over a relatively long period, due to the secular nature of the induced
decay. In this case one-month arcs were too short to obtain sufficiently good fits of the drag
coefficient. Therefore, CD was estimated over orbital arcs of 180, 360 and 1080 days, over the time
interval of 8 December 1999 to 21 November 2002. The average fitted drag coefficients were 2.63
(over 6 180-day arcs), 2.65 (over 3 360-day arcs) and 2.64 (over a 1080-day arc) for an assumed
reference area of 0.48 m 2 and a mass of 50 kg. However, the actual cross-sectional area of the
satellite encountered by the airstream was computed to be 0.568 m 2 . This value included the
projected area of the central box, the solar panels and the long rod. By then applying the ratio
0.48/0.568 to adjust the reference area and the correction for the bias in the JB2006 model (15% at
630 km; see Table 3), the resulting observed drag coefficients were 2.56, 2.58 and 2.57,
respectively.
The physical drag coefficient was calculated by determining the momentum transfer to the
satellite caused by the incident air molecules and the molecules reemitted from the surface in a
diffuse angular distribution, with energy loss given by the energy accommodation coefficient. Since
the surfaces were rotating flat plates, the resultant drag force was determined by averaging over the
angles of rotation. The other input parameters used included a satellite velocity of 7,540 m/s, an
ambient atmospheric temperature of 1,260 K, and a mean molecular mass of 12 amu. The results of
the calculations are given in Table 4 as a function of a range of accommodation coefficients.
The next step was to compare the physical drag coefficients in Table 4 with the observed drag
coefficients derived from fitting the orbit, i.e. with CD = 2.56, 2.58 and 2.57. By means of the linear
interpolation in Table 4, Clementine’s average observed CD of 2.57 corresponds with an
accommodation coefficient of 0.875.

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3.4 Cosmos 2265 and Cosmos 2332 drag and energy accommodation coefficients
Both Cosmos 2265 and Cosmos 2332 were spheres with a smooth surface. Their crosssectional
area and mass were assumed to be 3.142 m 2 and 750 kg, respectively. They had an
elliptical orbit with initial perigee altitude in the neighborhood of 279 km for Cosmos 2265 (Figure
7) and 286 km for Cosmos 2332 (Figure 8). Their orbit inclination was around 83.
For Cosmos 2265, the observed semi-major axis decay was nearly 109 km per year and fitted
drag coefficients were obtained over 30-day intervals, from 1 October 1999 to 14 January 2003.
Figure 9 shows the fitted CD values of Cosmos 2265, together with the corresponding inverse
ballistic coefficient (B) and semi-major axis root mean square (rms) residuals. The average fitted
drag coefficient of Cosmos 2265 was 1.869. Its standard deviation was 0.152, and the standard
deviation of the mean of the 40 measurements would have been 0.024 if all 40 measurements had
been independent. Because only eight of the measurements were independent, the standard
deviation of the mean was 0.054.
For Cosmos 2332, the observed semi-major axis decay was nearly 89 km per year and fitted
drag coefficients were obtained over 30-day intervals, from 1 October 1999 to 14 January 2003.
Figure 10 shows the fitted CD values of Cosmos 2332, together with the corresponding inverse
ballistic coefficient (B) and semi-major axis root mean square (rms) residuals. The average fitted
drag coefficient of Cosmos 2332 was 1.920. Its standard deviation was 0.247, and the standard
deviation of the mean of the 40 measurements would have been 0.039 if they all were independent;
but it was 0.087 because there were only eight independent measurements.
The fitted drag coefficients of the two smooth Taifun-1 Yug spheres (Table 2) were below
2.0. This confirmed that the JB2006 density model was biased at sunspot maximum. Therefore, by
applying the correction for the bias in the density model (Table 3) at an average altitude of 275 km,
the observed drag coefficients were 2.08 and 2.14 for Cosmos 2265 and Cosmos 2332, respectively.
The corresponding accommodation coefficients were 1.00 and 0.993.
3.5 Overall results
Similar calculations were performed for the other satellites processed by Bowman and Moe,
(2005). Bowman and Moe used the modified Jacchia 1970 thermospheric model, for which the
biases also are given in Table 3. The drag and accommodation coefficients at sunspot maximum
derived in the present study are collected in Table 5. For comparison, the accommodation
coefficients at sunspot minimum from Moe, et al. (1995) are tabulated in Table 6. At both sunspot
maximum and minimum, energy accommodation was complete near 200 km, and decreased as the
altitude increased. But accommodation decreased faster at solar minimum. This was expected,
because atomic oxygen controls accommodation coefficients, and there is less atomic oxygen and a
lower temperature at solar minimum.
The relationships of the various drag coefficients and accommodation coefficients in Table 5
(for sunspot maximum) and Table 6 (for sunspot minimum) give an idea of the accuracy: Perhaps
3% for the drag coefficients of spheres and a higher uncertainty for more complicated shapes. An
independent estimate of the accuracy of drag coefficient calculations can be ascertained by
considering the following: A similar Sentman-based analysis of the completely independent US Air
Force data base of accelerometer measurements from three compact Atmosphere Explorer satellites

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and three long cylindrical satellites reduced the average discrepancy between measurements and
models at 200 km from 9% to 3% (Moe et al., 1998). We attribute this 3% to errors in calculating
the average drag coefficients of spheres and cylinders at 200 km.
As Table 5 and Table 6 show, the relationship between accommodation coefficients and
drag coefficients is nonlinear. It also is different for different shapes. Relationships for several
simple shapes were given in Geophysical Monograph 87 (Moe et al., 1995). One purpose of the
present paper is to improve the accommodations coefficients given in that earlier work.
4. Lessons learned from the analysis of the orbital decay of other satellites
Many other satellites were processed in this study, in order to improve the reliability of the
results obtained. The information from a number of objects was incomplete or had internal
inconsistencies that prevented us from keeping them in the final collection of satellites.
Nonetheless, meaningful lessons were learned from their orbital decay analyses. Here are two
examples:
The orbital decay of seven Taifun-1 Vektor satellites, with solar cells on their spherical
surfaces, was analyzed with the aim of reducing the uncertainty in the drag and accommodation
coefficients in the vicinity of 400 km (close to the perigee altitude of these satellites). Fitted drag
coefficients were calculated over 150-day intervals, between 1 October 1999 and 14 January 2003
(i.e. at sunspot maximum of solar cycle 23). The mean fitted drag coefficient for the seven Vektors,
at an average altitude near 400 km, was 2.591, with a standard deviation of the mean of the seven
measurements of 0.023. These data provided a quantitative indication of the increased drag
coefficients of “nearly spherical” satellites, which is attributed to various deviations from sphericity.
Previous studies have already shown this effect (Bowman and Moe, 2005; Moe and Bowman,
2005), but not with such precision. A recent study by Pilinski (2009), using precise engineering
drawings of Starshines 1 and 2, demonstrated that the actual shapes and cross sectional areas were
different from those publicized: The satellites had retained their attachment rings in orbit.
Some anomalies observed in the fitted drag coefficients of the Optical Calibration Sphere,
OCS, led to additional investigations. It was learned that the satellite, launched in a small canister
and expanded in orbit into a sphere with a diameter of 3.5 m, remained attached to the canister
(Guidamean, 2009). This would explain the OCS drag coefficient, which appeared to be different
from that of a smooth sphere, and to lie between the drag coefficients of smooth spheres and
modified spheres such as the Starshines and the Taifun-1 Vektors. It now appears that the attached
canister increased the average area and changed the shape, so that the drag coefficient was not
actually measured. These new results confirm that satellite dimensions in orbit often are
misreported, and place in doubt the drag coefficients derived for all of the modified spherical
satellites.
5. Conclusions and future work
A detailed analysis of ten satellites with smooth surfaces in low Earth orbit has revealed that:

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Energy accommodation coefficients are higher at sunspot maximum than at minimum, and
decrease more slowly with increasing altitude. These results are consistent with the larger
amount of atomic oxygen that is adsorbed on satellite surfaces at solar maximum;
Consequently, incident molecules rebound with less energy, so satellite drag coefficients
are generally lower at solar maximum than at minimum;
When spherical satellites are modified by attaching solar cells and other objects, the area
and shape are changed and often misreported, making it difficult to calculate an accurate
drag coefficient.
Knowledge of drag coefficients can be improved by further measurements of accommodation
coefficients using additional non-spherical, attitude-controlled satellites with perigee altitudes above
300 km. The effects of high orbital eccentricities, e.g. geosynchronous transfer orbits, on
accommodation coefficients should also be studied. Furthermore, the reported thermospheric
cooling by carbon dioxide, with its secular density decrease, implies a secular change in drag and
accommodation coefficients. This effect should be investigated. Paddlewheel satellites, similar to
those by means of which the first orbital measurements of energy accommodation were made, could
also be used for these purposes.
Acknowledgments
The results described in this paper were presented at the 37 th COSPAR Scientific Assembly,
held in Montréal, Canada, in July 2008. Anselmo and Pardini contributed to the study within the
framework of the ASI/CISAS Contract No. I/046/07/0.
We would like to thank Stan Solomon and Scott Bailey for information on the SNOE satellite;
Alex da Silva Curiel for information on the Surrey satellites, Clementine, UoSat 2, and Tzinghua-1;
Martin Sweeting and Audrey Nice for providing us with the drawing of Clementine; Koorosh
Guidamean for information on the Optical Calibration Sphere; the US Space Surveillance Network
for making available the TLEs of the satellites; and Space Environment Technologies, for providing
the historical solar indices used in the JB2006 model.
The editor, Pascal Willis, and the reviewers, including Bruce Bowman, made many valuable
suggestions for improving this paper.
References
Beletsky, V. V. An estimate of the character of the interaction between the airstream and a satellite,
Kosmicheskie Issledovaniya 8 (2), 206-217 (in Russian), 1970.
Beutler, G. Methods of Celestial Mechanics, Part. II: Application to Planetary System,
Geodynamics and Satellite Geodesy, Astronomy and Astrophysics Library, Springer-Verlag,
Berlin and Heidelberg, Germany, 2005.
Bowman, B. R., Moe, K. Drag coefficient variability at 175-500 km from the orbit decay analyses
of spheres, Paper AAS 05-257, Presented at the 2005 AAS/AIAA Astrodynamics Conference,
South Lake Tahoe, California, USA, 2005.
Bowman, B. R., Tobiska, W. K., Marcos, F. A., Vallares, C. The JB2006 empirical thermospheric
density model, Journal of Atmospheric and Solar-Terrestrial Physics 70 (5), 774-793, 2008.

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
ACCEPTED MANUSCRIPT
Bruinsma, S., Thuillier, G., Barlier, F. The DTM-2000 empirical thermospheric model with new
assimilation and constraints at lower boundary, accuracy and properties. J. Atmos Solar
Terrestr. Phys. 65, 1053-1070, 2003.
Carter, V. L., Ching, B. K., Elliott, D. D. Atmospheric density above 158 kilometers, J. Geophys.
Res. 74, 5083-5091, 1969.
Chao, C. C., Gunning, G. R., Moe, K., Chastain, S. H., Settecerri, T. J. An evaluation of Jacchia 71
and MSIS90 atmosphere models with NASA ODERACS decay data, J. Astronautical Sciences
45, 131-141, 1997.
Ching, B. K., Hickman, D. R., Straus, J. M. Effects of atmospheric winds and aerodynamic lift on
the inclination of the orbit of the S3-1 Satellite. J. Geophys. Res. 82, 1474-1480, 1977.
Cook, G. E. Satellite drag coefficients, Planetary and Space Science 13, 929-946, 1965.
Cook, G. E. Drag coefficients of spherical satellites, Annales of Geophysique 22, 53-64, 1966.
DeVries, L. L. Private communication, 1971.
Emmert, J. T., Picone, J. M., Meier, R. R. Thermospheric global average density trends, 1967-2007,
derived from orbits of 5000 near-earth objects, Geophys. Res. Lett., 35 L05101,
doi:10.1029/2007GL032809, 2008.
Gregory, J. C., Peters, P. N. A measurement of the angular distribution of 5 eV atomic oxygen
scattered off a solid surface in Earth orbit. Proceedings of the 15th International Symposium on
Rarefied Gas Dynamics, Vol. 2, B. G. Teubner, Stuttgart, Germany, pp. 644-654, 1987.
Guidamean, Koorosh, Personal communication, 2009.
Hedin, A. E., Hinton, B. B., Schmitt, G. A. Role of gas-surface interactions in the reduction of
OGO 6 neutral particle mass spectrometer data, J. Geophys. Res. 78, 4651-4668. 1973.
Hoots, F.R., Roehrich, R.L. Models for Propagation of NORAD Elements Sets, Spacecraft Report
No. 3, Project Spacetrack, Aerospace Defence Command, United States Air Force, Colorado
Springs, Colorado, USA, December 1980.
Imbro, D.R., Moe, M. M., Moe, K. On fundamental problems in the deduction of atmospheric
densities from satellite drag, J. Geophys. Res. 80, 3077-3086, 1975.
Izakov, M. N. Some problems of investigating the structure of the upper atmosphere and
constructing its models, Space Res. V., 1191, 1965.
Lemoine, F. G., Kenyon, S. C., Factor, J. K., et al. The development of the joint NASA GSFC and
NIMA geopotential model EGM96, NASA/TP-1998-206861, NASA Goddard Space Flight
Center, Greenbelt, MD, USA, July 1998.
Marcos, F. A., Wise, J. O., Kendra, M. J., Grossbard, N. J.,Bowman, B. R. Detection of a long-term
decrease in thermospheric neutral density, Geophys. Res. Let. 32, L04103,
doi:1029/2004GL021269, 2005.
Moe, K., Moe, M. M., Yelaca, N. W. Effect of surface heterogeneity on the adsorptive behavior of
orbiting pressure gages, J. Geophys. Res. 77, 4242-4247, 1972.
Moe, M. M., Wallace, S. D., Moe, K. Recommended drag coefficient for aeronomic satellites, The
Upper Mesosphere and Lower Thermosphere: A Review of Experiment and Theory,
Geophysical Monograph 87, 349-356, 1995.
Moe, K., Moe, M. M., Wallace, S. D. Improved satellite drag coefficient calculations from orbital
measurements of energy accommodation, Journal of Spacecraft and Rockets 35 (3), 266-272,
1998.
Moe, K., Moe, M. M., Rice, C. J. Simultaneous analysis of multi-instrument satellite measurements
of atmospheric density, J. Spacecraft and Rockets 41, 849-853, 2004.
Moe, K., Bowman, B. R. The effects of surface composition and treatment on drag coefficients of
spherical satellites, Paper AAS 05-258, Presented at the 2005 AAS/AIAA Astrodynamics
Conference, South Lake Tahoe, California, USA, 2005.

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2
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47
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50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
ACCEPTED MANUSCRIPT
Moe, K., Moe, M. M. Gas-surface interactions and satellite drag coefficients, Planetary and Space
Sciences 53, 793-801, 2005.
Offermann, D., Grossmann, K. U. Thermospheric density and composition as determined by a mass
spectrometer with cryo ion source, J. Geophys. Res. 78, 8296-8304, 1973.
Pardini, C., Anselmo, L. SATRAP: Satellite Reentry Analysis Program, Internal Report C94-17,
Istituto CNUCE, CNR, Pisa, 30 Agosto 1994.
Pardini, C., Anselmo, L. Impact of the time span selected to calibrate the ballistic parameter on
spacecraft re-entry predictions, Advances in Space Research 41 (7), 1100-1114, 2008.
Picone, J. M., Hedin, A. E., Drob, D. P., Aikan, A.C. NRLMSISE-00 empirical model of the
atmosphere: statistical comparisons and scientific issues, Journal of Geophysical Research 107
(A12), 1468, doi:10.1029/2002JA009430, 2002.
Pilinski, M., personal communication, 2009.
Qian, L., Solomon, S. C., Kane, J. K. Seasonal variation of thermospheric density and composition,
Journal of Geophysical Research, in press, 2008.
Reiter, G. S., Moe, K. Surface-particle interaction measurements using paddlewheel satellites, Sixth
International Symposium on Rarefied Gas Dynamics, Vol. 2, 1543-1555, 1969.
Rice, S. O. Mathematical analysis of random noise, in Wax, Nelson. Selected Papers on Noise and
Stochastic Processes, Dover Publications, NY, 1954.
Riley, J. A., Giese, C. F. Interaction of atomic oxygen with various surfaces, Journal of Chemical
Physics 53, 146-152, 1970.
Schaaf, S. A., Chambré, P. L. The flow of rarefied gases, Section H of Fundamentals of Gas
Dynamics, ed. H. W. Emmons, Princeton, New Jersey, USA, pp. 687-739, 1958.
Schamberg, R. A new analytic representation of surface interaction for hyperthermal free molecule
flow with application to neutral-particle drag estimates of satellites, RM-2313 Rand Corp.,
Santa Monica, CA, USA, 1959a.
Schamberg, R. Analytic representation of surface interaction for free molecule flow with
application to drag of various bodies, in Masson, D. J., R-339, Aerodynamics of the Upper
Atmosphere, pp. 12-1 to 12-41, Rand Corp., Santa Monica, CA, USA, 1959b.
Sentman, L. H. Comparison of the exact and approximate methods for predicting free molecule
aerodynamic coefficients. American Rocket Soc. J. 31, 1576-1579, 1961a.
Sentman, L. H. Free molecule flow theory and its application to the determination of aerodynamic
forces, Lockheed Missile and Space Co., LMSC-448514, AD 265-409, Sunnyvale, CA, USA,
1961b.
SET, 2008. Space Environment Technologies: http://www.spacewx.com/.
Tobiska, W. K., Bouwer, S. D., Bowman, B. R. The development of new solar indices for use in
thermospheric density modeling, Journal of Atmospheric and Solar-Terrestrial Physics 70 (5),
803-819, 2008.
Vaquero, J. M. Historical sunspot observations, a review, Adv. Space Res., 40 (7), 929-941, 2007.
Volkov, I. I. Earth’s upper atmosphere density model for ballistic support of the flight of artificial
Earth satellites GOST R 25645.166-2004. Publishing House of the Standards, Moscow, 2004.
Willis, P., Deleflie, F., Barlier, F., et al. Effects of thermosphere total density perturbation on LEO
orbits during severe geomagnetic conditions (Oct - Nov 2003) using DORIS and SLR data,
Adv. Space Res., 36(3), 522-533, 2005.
Wolverton, R. W. Flight Performance Handbook for Orbital Operations. Wiley, N.Y. and London,
pp. 2-336 – 2-339, 1963.
Wood, B. J. The rate and mechanism of interaction of oxygen atoms and hydrogen atoms with
silver and gold, Journal of Physical Chemistry 75, 2186-2193, 1971.

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Figure 1. Graphical representation of the Student Nitric Oxide Explorer (SNOE) satellite. Courtesy
of Stan Solomon of University Corporation for Atmospheric Research (UCAR).
Figure 2. Graphical representation of the Surrey satellite Clementine. Courtesy of Martin Sweeting
and Audrey Nice of Surrey Satellite Technologies LTD.
Figure 3. 81-day centered smoothed values of the v3.8 JB2006 solar indices F10.7 (F81c), S10.7
(S81c) and M10.7 (M81c) during the sunspot maximum of solar cycle 23 (1 October 1999 – 31
December 2002).
Figure 4. SNOE observed perigee/apogee altitude and mean semi-major axis decay from October
1999 to December 2002.
Figure 5. Fitted drag coefficients, inverse ballistic coefficients and rms residuals on semi-major
axis for SNOE.
Figure 6. Clementine observed perigee/apogee altitude and mean semi-major axis decay from
December 1999 to December 2002.
Figure 7. Cosmos 2265 observed perigee/apogee altitude and mean semi-major axis decay from
October 1999 to December 2002.
Figure 8. Cosmos 2332 observed perigee/apogee altitude and mean semi-major axis decay from
October 1999 to December 2002.
Figure 9. Fitted drag coefficients, inverse ballistic coefficients and rms residuals on semi-major
axis for Cosmos 2265.
Figure 10. Fitted drag coefficients, inverse ballistic coefficients and rms residuals on semi-major
axis for Cosmos 2332.

Satellite
Name
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Table 1
Sample of satellites analyzed by
Bowman and Moe (2005) during the maximum of solar cycle 22 (1989-1990)
Catalog
Number
Diameter
[m]
Mass
[kg]
Sphere
Surface
Inclination
[deg]
Launch
Height
[km]
Launch
Date
Decay
Date
CALSPHERES
Calsphere 3 4957 0.254 0.73 Aluminum 88.3 775 17-Feb-71 17-Oct-89
Calsphere 4 4958 0.254 0.73 Aluminum 88.3 775 17-Feb-71 20-Sep-89
Calsphere 5 4963 0.254 0.73 Gold 88.3 775 17-Feb-71 7-Jan-90
Cosmos 1179 11796 2.000 75010
TAIFUN YUGS
Smooth 82.9 300 *
14-May-80 18-Jul-89
Cosmos 1427 13750 2.000 75010 Smooth 65.8 450 29-Dec-82 5-Oct-89
Cosmos 1615 15446 2.000 75010 Smooth 65.8 450 20-Dec-84 15-Apr-90
* The orbit of Cosmos 1179 was elliptical, the launch height refers to the perigee

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Table 2
Sample of satellites analyzed
during the sunspot maximum of solar cycle 23 (1999-2002)
Satellite Catalog Area
Name Number [m 2 Mean Orbital Elements
Time span
Mass
at the beginning of the time span over which
] [kg] Inclination Perigee Apogee the orbital
[deg] Altitude Altitude decay was
[km] [km] analyzed
Cylinder-like body with a hexagonal cross section
SNOE 25233 0.8377 115.5 97.7 515 570 1-Oct-99
31-Dec-02
Spinning box with solar panels and a long rod for gravity-gradient stabilization
Clementine 25968 0.568 50 98.1
TAIFUN YUGS
643 663 8-Dec-99
31-Dec-02
Cosmos 2265 22875 3.142 750 82.8 280 1279 1-Oct-99
31-Dec-02
Cosmos 2332 23853 3.242 750 82.9 286 1383 1-Oct-99
31-Dec-02

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Table 3
Percentage by which density models are too high at sunspot maximum
(percentage by which CD is too low)
Altitude
[km]
J70 MOD JB2006
150 4 7
200 6 9
250 8 11
300 9 12
350 10 13
400 12 15
500 12 15

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Table 4
Physical drag coefficients of Clementine
Accommodation Physical drag coefficient
Coefficient of Clementine
1.00 2.281
0.99 2.327
0.98 2.364
0.95 2.440
0.90 2.531
0.85 2.609

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Table 5
Drag and accommodation coefficients at sunspot maximum
Altitude [km] Observed Drag Coefficient Corresponding
200 2.08
[Cosmos 1179, Cosmos 1427, Cosmos 1615]
275 2.08
[Cosmos 2265]
2.14
[Cosmos 2332]
300 2.13
[Cosmos 1179, Cosmos 1427, Cosmos 1615]
2.16
[Calsphere 3, Calsphere 4, Calsphere 5]
400 2.24
[Cosmos 1427, Cosmos 1615]
2.24
[Calsphere 3, Calsphere 4, Calsphere 5]
480 2.485
[SNOE]
500 2.31
[Calsphere 3, Calsphere 4, Calsphere 5]
630 2.57
[Clementine]
1.00
1.00
0.993
0.995
0.990
0.960
0.960
0.95
0.915
0.875

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Table 6
Accommodation coefficients at sunspot minimum
Altitude
[km]
150 1.00
175 1.00
200 0.99
225 0.98
250 0.96
275 0.94
300 0.92
325 0.89

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