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A free molecule aerodynamic investigation using multiple satellite analysis
Phcr. Pergamon
SI)LIWSki.. Vol. 44. No. 2. pp. 171 1x0. IYY6 Copyright (’ 1996 Elsevicr Science Ltd Printed in Great Britain. All rights reserved 0032--0633’96 $15.00-tO.OO
0032-0633(95)00077-1
A free molecule aerodynamic investigation using multiple satellite analysis 1.K.
Harrison and G. G. Swinerd
Department
of Aeronautics
and Astronautics.
University
Received 3 April l(JY5: revised 21 May 1995; accepted
of Southampton,
Southampton
SO1 7 I BJ. L .K.
22 May 1995
Abstract. The inaccuracies of numerical satellite positioning in Low Earth Orbit are predominantly due to the errors in calculating the aerodynamic forces. This is due to the unknown interactions of the rarefied atmosphere on the satellite surface, and the errors of the atmospheric density models. To improve knowledge of the gas-surface interactions, the effects of aerodynamic forces upon the orbits of satellites can be isolated, using precise orbital analysis (POA). When examining the orbit of a single satellite, the solution is restricted by the limited observational data, atmospheric model errors and the inevitable correlations between the atmospheric and aerodynamic models. To address these, three satellite orbits are examined simultaneously. The satellite orbits analysed are those of ERSl, a remote sensing satellite, and the geodetic satellite’s STARLETTE and STELLA. They orbit at 800 to 1000 km where helium and atomic oxygen are dominant. The collisional energies of helium and atomic oxygen upon the spacecraft surface are 1.25 and 5 eV, respectively. This preliminary analysis suggests that the re-emission of these particles are at lower speeds and lower emitted angles than those measured in laboratory molecular beam experiments. The analysis suggests that the bulk speed of the emitted particles is about 2 km s-l, and in a direction approximately half way between the specular direction and the surface normal. This emission produces a drag coefficient on an aluminium sphere of 2.52.
Introduction
Any vehicle travelling through a fluid will experience a force. the magnitude of which depends upon the fluid, the characteristics of the vehicle and their interaction. In the space environment the collision and re-emission of the sparse atmospheric particles on the fast moving spacecraft
produce both aerodynamic drag and lift. The force caused by the atmosphere is solely dependent upon the gas- surface interaction, as the effects of gas-gas collisions in the rarefied gas regime (above 2 I.50 km) can be assumed negligible. An increasing number of satellites in Low Earth Orbit (LEO). within the regime of significant atmospheric density, are typically platforms carrying Earth-viewing remote sensing equipment. Knowledge ofthe position and orientation of the satellite and instrumentation is vital. A dynamic force model is therefore needed to calculate expected position and velocity vectors of’ the satellite. which can then be fitted to the tracking data to properly determine the orbit. The dynamic force model must rcpresent all the forces in the near-Earth environment. that could cause perturbations to the satellite orbit of the order of the required orbital accuracy, over the time period it is determined (typically days in the LEO). At altitudes below 800 km (dependent upon solar conditions) the aerodynamic forces are the largest non-gravitational forces acting on the spacecraft. Due to the errors in current atmospheric density models. they are also the largest cause of orbit positional error. To resolve this difficulty, both the gas-surface interaction and atmospheric modelling needs to be improved. This paper looks at improving the former. The most common method of investigating gas surface interactions has been through laboratory-based molecular beam experiments. These experiments use pure gas and clinically finished surface materials. to reduce the number of experimental parameters. Unfortunately it is not gcnerally possible to exactly simulate the space environment in ground-based facilities, and space-Hewn materials often differ greatly from those examined in laboratories. The gas-surface interactions experienced by the satellite arc therefore generally different to those observed terrestrially, although the trends should bc similar. Conscquently the aerodynamic models derived from integrating the passsurface interaction models over the whole spacecraft surface are imprecise and highly parameterized. Precise Orbital Analysis (POA) of satellite orbits. deter-
172
I. K. Harrison and G. G. Swinerd : Multiple satelhte
mined from Satellite Laser Ranging (SLR) data has proved successful at investigating the gas--surface interactions occurring on ERSI. By isolating the orbital perturbations due to the aerodynamic forces. knowledge of the cause of’ the forces can be inferred. This is conducted by fitting the ,variables of a proposed gas-surface interaction model to the perturbations. Unfortunately the information available from the analysis of a single satellite orbit is limited. ‘The errors in the atmospheric density model are also difficult to remove from the aerodynamic data, corrupting the analysis of the gas-surface interaction. By combining the orbits of several satellites using Multiple Satellite .4nalysis (MSA). some of these effects can be decorrelated and the errors reduced. The results of single satellite analyr;is, at 800 km altitude. suggested that the particles are emitted at low velocities ( 2 2 km s-l). in a near specular direction (Harrison and Swinerd. 1995).
Gas-surface
interactions
The aerodynamic forces encountered on a spacecraft surface travelling through a rarefied atmosphere. are due to the momentum flux difference between the incident and emitted particles. The momentum of the incident particles is defined by the satellite relative velocity to the atmoIsphere, and the atmospheric conditions. The velocity and direction of the emitted particles are influenced by the interaction between the gas particles and the surface material. This produces emission distributions between (a) the specular case, where the particles leave at the same Ispeed, but with an inverted normal velocity, and (b) the (diffuse case, with the particles drifting away from the Isurface at a thermal velocity related to the surface temperature. The aerodynamic force in continuum flow is historically expressed as drag, the force parallel to the atmospheric svelocity direction, and lift, the perpendicular force. These forces are represented by the aerodynamic coefficients (C,, C,) of the vehicle. The force due to the particles incident upon the vehicle is Force(l(fi,
clrq)
= if) 1 C’i,,,,S( CD. C,).
(1)
Here p is the atmospheric density, S some reference area. llbulk the velocity of the satellite relative to the atmosphere ;and the geometry of the forces is shown in Fig. 1. This representation of aerodynamic forces is still applicable in
a rarefied atmosphere. as p C,‘&li.is the momentum flux ol‘ an atmosphere travelling at the spacecraft velocity. The incident particles do not strike the surface at ;1 constant speed and direction. but at variable speeds and directions, dependent on the atmospheric Lemperature. ‘The interaction between atmospheric particle and surface is not static. so the emitted particles also have ;I broad range of speed and direction. The total momentum Hus is therefore an integral over all speeds and directions of the particle momentum flux striking and leaving the xpacecraft surface. The exact distribution of the particle velocities is important in this integral,
Peters ef trl. (1988) have shown that the atmosphere striking the surface has a Maxwellian type velocity distribution, consisting of the atmosphere’s random thermal velocity C, superimposed on the satellite’s bulk velocity. The three-dimensional number density of the random thermal velocity distribution is given by
(3) where
(3) Here R,) is the universal gas constant. Tthe atmospheric temperature, M the molecular mass, N the number densitj of particles and z~J,\\ are orthogonal velocities shown in Fig. 1. Using this distribution the flat plate aerodynamic coefficients (CD ,, C,,), due to the incident momentum 11~ (Hurlbut and Sherman, 1968) are e -riCD, = 2 sin (fl,) ___ +0.5( 1+erf(o)) ‘Jna
(
I+ $ i
,!! (4)
&
c’, , = 2cos(H,)
(T = S, sin (H,).
(I fcrf(0))
1
/
i
Fig. 1. Geometry of incident parlicle and the associated forces
analp~
s‘
,
=
I.~~~!? c
(5)
Here 0, is the angle between the surface and the incidcnr flow and V,,,, (or (i,) the bulk velocity of the satellite. The reference area for these coefficients is the actual flat plate area. As S, tends to infinity (a hyperthermal flow) C’[, tends to 2.0 and C, tends to zero. The thermal velocity C of the atmosphere leads to lift forces. and directly effects the drag, by increasing the average velocity of the particles striking the surpdce.
I K. Harrison
and G. G. Swinerd : Multiple
The emitted particles carry away momentum flux. This must be taken away from the incident momentum flux. when calculating the total force exerted on the surface. II i5 generally accepted that emitted particles do not leave the surface randomly. but form a distribution that is approximately invariant with time. The relationship between incident and emitted distributions is poorl! understood. though a number of models have been proposed that represent the emission of gaseous particles fl-om a solid surface. Due to the complex interaction between gas and surface particles. all models are highly parameterized, with many parameters undefined. These gas-surface models fall into two main categories: very specific numerical simulations (SNS) that tend to accuI-ately represent only the experimental data from which they are derived. and satellite aerodynamic models (SAM) which are based upon experimental results, but use both theory and empirical engineering approximations to form The satellite aerodynamic ?
Nocillrr
rt77i.\.viot7
173
satellite analysis
tlistrihuriot7
When a particle strikes a surface there will be an exchange of energy and momentum. The energy of the emitted particle will be partially redistributed amongst its various degrees of freedom, kinetic and thermal energy. So the distribution of particles leaving the surface will still have both thermal and bulk velocities. The emitted distribution should therefore be expected to be similar to the Maxuellian protile found in the atmosphere. The velocity vector direction of the emitted particles will vary due to the thermal. molecular and macroscopic surface structure. as well as due to their initial angles of incidence to the surface. The efrects of surface structure scattering arc indistinguishable to those possibly caused by the particles thermal velocity. Nocilla’s model (Nocilla, 1963) absorbs the effects of structure scattering into the thermal velocit), of the emitted particles. representing the distribution of the emitted particles by their bulk direction. bulk speed and thermal speed. assuming a Maxwellian thermal velocity distribution. This model has been shown to fit the majority of single nodal emission distributions observed
Fig. 2. Grometry
of the emitted particle distribution
in molecular beam experiments (Gregory and Peters. 1986). As such it is an appropriate starting point. from which to build a general gas-~surface interaction model for use in precise orbital analysis. The particle flux intensity N,(4) modelled by Nocilla is
~(1+.3~+,~~(l.S.~+.~~)1l+erl‘(.~l~)c~
)
(6)
where
Here N,,,, is the total number of particles lea\ing the surface. which to first approximation equals the number incident upon it. C, and C‘, arc the thermal and bulk velocities of the emitted particles. and the angles arc represented in Fig. 2. This distribution when integrated o\er the whole range of emission velocities produces the emitted tlat plate aerodynamic coefficients (C,, ). C‘, ,)
where .Y(o) = em”‘+v,nci(l
+erfIrr))
, B=j;. / Here the reference area is the actual tlat plate surface arca. The total drag or lift coefficient due to the atmosphere is
174
the sum of the incident and emitted coefficients (CD,++D.r? CLI+CL.r). The parameters of the incident flow are defined by the satellite orientation and orbit and the atmospheric conditions. The parameters of the emitted Nocilla distribution are not well defined. and are the cause of the aerodynamic uncertainty.
Measureable interaction One of the objectives of the research is to improve the knowledge of the relationship between the incident and the emitted particle distributions. The apparatus for the investigation is the orbiting satellite. The satellite exposes a variety of surface materials to the atmosphere and encounters a variety of atmospheric conditions. The information retrievable is therefore an average of all the interactions occurring over the whole spacecraft. and to a certain degree an average of those occurring around a whole orbit. Hence it is inappropriate to use a highly specific numerical gas-surface model in the investigation, as these tend to be realistic only for the specific surface materials, incident particle species and velocity vectors used in terrestrial experiments. So alternately a more robust, general engineering SAM is used to represent the interaction. The results from fitting the SAM to the orbits, will not have the accuracy associated with specific molecular beam results, though as they are fitted to actual flight data. the results will hopefully better represent the overall gas-surface interactions occurring on the spacecraft surfaces. It should be noted that only the contribution of the emitted flow to the aerodynamic force is affected by the gas-surface interaction. The emitted flow is the major contributor to the aerodynamic lift, but has a relatively minor effect on the aerodynamic drag.
Initial gas-surface interaction equations from experimental data
I. K. Harrison
and G. G. Swinerd : Multiple satellite analysis
placed on the beam data. is that the kinetic energy of the incident beam be larger than the particles’ thermal energy at the surface temperature, T, < MU2/3R0. This is to limit the results to the regime of structural scattering, which is that encountered in LEO conditions, rather than thermal scattering. This reduces the effect of the surface temperature on the emission distribution. The results of over I 10 published molecular beam experiments were analysed. each being converted into a standard form which is compatible with the Nocilla model. The results come from papers by Gregory and Peters (1986), Hinchen and Foley (1966), Kreck et al. (1993), Nocilla (1963). Fujimoto et al. (1976), Comsa et al. (1979), Hurlbut (1985), Onji (1986). Kolodney et ul. (1985). McFall (1980)” Miller and Subbarao (1970), Goodman and Wachman (1976). ‘Subbarao and Miller (1973) and Collins and Knox (1994). Each molecular beam run was represented where possible by the values of incident angle 4, (rad), incident energy E, (eV), gas particle mass to surface particle mass ratio p, surface temperature T, (K), surface quality. emitted angle $I (rad) emitted speed ratio S, and energy accommodation coefficient c(. For the majority of runs, values for only some of the above parameters were available from the published results. The angles d)I and 4, are measured from the surface normal rather than the surface. From the literature it became apparent that the parameters 4,. E,, p. & S, and a “best” described the incident and emitted flow. General trends in the emitted distribution were visually determined by graphically plotting the incident characteristics &, E,, p against the emitted characteristic @r. S,, c(. They were then equated to simple equations assuming that & = Fl (q5,, E,, p), S, = F3( I$,, E,. p). ct = F3(& E,, ,u). The simple equations were then fitted to the beam data using least squares routines. to produce the following etnpirical equations : (9)
S, = 0.71+0.63$,-0.19~1 cx= (4.8+0.08E,-
To perform the precise orbital analysis of the gas-surface interaction, a parameterized model must be developed which can be fitted to the observations. In this analysis a specific numerical simulation was considered to be too restrictive, so a parameterized empirical relationship fitted to experimental data was used. The results of published molecular beam experiments are used to generate an initial model. A Maxwellian distribution is assumed in the incident flow, and the Nocilla model is assumed for the emitted flow. The empirical model provides the relationship between the two flows. Very little relevant experimental data is available for spacecraft materials in the LEO environment, the results of Gregory and Peters (1986) being one of the few. Consequently the empirical relationship is based on the results of terrestrial molecular beam experiments. executed under a variety of different conditions, in an attempt to reduce any biasing. This is particularly true of the incident energy, as for most experiments E, < 5 eV. The only restriction
1.15&)
1 -exp
(10) (-0.5~~)
exp (0.75~1)
(11)
Generally, as can be seen the gas-surface interaction models are characterized by a significant number of parameters. Hence, the underlying reason for the adopted approach is to attempt to reduce the number of parameters to be solved for in the subsequent orbital analysis. The main trends determined and represented in equations (9)-(11) are shown in Figs 3-5, respectively. The solid lines represent typical values of the equations which have been fitted to the data points, the dotted lines join points which have only one of their incident characteristics varying. Error bars have not been included, but are significant. These reflect experimental errors, the interpretation of the results and the conversion into the Nocilla form. The variation of u with ~1 fits the hard sphere theory, that particles of the same mass will have the largest exchange of energy and momentum during collision. Figure 4 shows a near specular direction of re-emission, while the variation of S, shows a strong & dependence, producing a
and Ci. G. Swinerd : Multiple
I. k, Harrison
175
satellite analysis
is added to each of the equations. The values of x1. S,? and Or2are used to calculate the aerodynamic forces in the computer model. where 23_ = I -(I
-%).3,,,,,,.
.y2 = B,,,,,..S:
(I,, = C:,,,,,fl,. The parameters ,4,,,,,. B,,,,,, and t’%,,,,,are titted to the orbital aerodynamic perturbations.
Fig. 3. Man co&ficient
2 1.5 Gas to Surfacemass ratio
0.5
0
dependence
907-T
of
the
p
energy
Method
J
2.5
1
3
accommodation
1
1
I
60 70 60 50 I 40 30 I
This analysis uses a modified form of Prccisc Orbital Analysis (POA) to solve for the aerodynamic parameters ,4.x,,,, B,t,,,, and C‘,,,,,,. The technique described as POA. is the fitting of a numerically calculated orbital trajectory to Satellite Laser Ranging (SLR) data. This process is carried out by solving for specific parameters within the satellite environment force models. If the force model is realistic. the value of the solved-for parameter will bc meaningful. A realistic force model should produce a significant improvement in the orbital fit. giving consistent values for its solved-for parameters. within the accuracies of the laser ranging and numerical routines. The measure of orbital tit used. is the r.m.s. difference between the laser ranges and the calculated rang from satellite to laser station.
10
0
10
0
dependence
Fig. 4. Main
20
Incid%
40
50
60
Angletothe Normal $
of the emission
70
60
1 (degrees)
angle
2
04
:
0.2
*
Ob 0
10
Fig. 5. Main dqxndence
20
Inc%nt
40 Angle
of the
&
50 60 to Normal @
70
80
i (degrees)
speed ratio
narrower nodal emission with increasing 4, and decreasing Incident normal momentum h! V,,,,,,cos (4,). The emission distributions observed from the engineering materials used on the spacecraft surface. after being exposed to different levels of atomic oxygen erosion. are expected to difler from those observed in the laboratory. To account for this and provide parameters that can be fitted to the clrhital observations. a multiplying parameter
The SLR observations are quoted as having a precision of 2-5 cm. with a comparable accuracy. This is ofa similar order of magnitude to the orbital perturbations of ERSI. caused by the once per orbit periodic variations of (‘r, and C,.. SLR data is typically concentrated during the nighttime, in the northern hemisphere. so a large fraction ot the orbit is poorly defined. The orbital noise caused by the laser range errors. and poor global distribution will therefore affect any analysis of the aerodynamics of ERSI The main effect is to increase the scatter of results. so that statistical analysis is necessary. A modified SATellite ANalysis (SATAN) (Sinclair and .4ppleby. 1986) suite of programs is used for the POA. This uses an eighth-order Gauss -Jackson numerical integrator. and a least-squares fitting routine. Typically 6 day long arcs of data are analysed. containing 300 -1 500 SLR observations. The determined orbit usually ha5 an r.m.s. orbital fit of 5 40 cm. with 3 rejection level oi‘ IYl m. The magnitude of the re.jection level. is so that no observations other than those which are detinitely in crrol are automatically rejected. With the improved SLR data from 1994. it was found that the data either titted the orbit well. or had tens of metres range residuals and obviously in error. The thinking “if an arc of normal points is not obviously in error it should not be rejected” was followed. For c;~ch arc the starting trajectory state vector. \olal radiation coefficient. once-per-rcb and once-per-d.74 dab along-track corrections, daily atmospheric density multipliers. and the aerodynamic parameters are solved for. No parameters from Earth related models, including the gravity field and station coordinates. are solved for. interaction The solved-f-or values of the ga-surface parameters .4;,,,,,. B,,,,, and C’.,,,,,. are sensitive to the method of calculating the total satellite aerodynamic
I. K. Harrison
176
and G. G. Swinerd : Multiple satellite anJy~
r SOkU Array
I
Fig. 6. Panel representation
Fig. 7. The geodetic
satellites
I Fig. 8. Matching the density correction terms from ERSl and STARLETTE orbits. by varying the aerodynamic coefficients
of ERS 1
STARLETTE
and STELLA
force. A panel method is used to calculate the satellite aerodynamics, with every major surface panel represented by its area, surface normal. molecular mass, solar absorptivity and diffusivity. The attitude of the satellite to the incident atmosphere means that effects of shadowing are minimal, the only likely shadowing is between the slim wind scatterometers on ERSI. Similarly the diffuse and specular emission directions from all the surface panels passes a significant distance away from every other surface panel, so multiple reflections may be assumed negligible. The geometry of the satellites analysed are shown in Figs 6 and 7 (modified from STELLA research announcement, CNES ( 1992)).
The results from the analysis of a single satellite orbit are limited by the amount of data and the difficulty in the removal of atmospheric density errors. The density errors mean that the magnitude of the aerodynamic coefficient is not well defined, and that a density correction multiplier (DCM) A must also be solved for in the equation
Hence only ation of the are orbit, parameters, being caused
the perturbations caused by the relative variaerodynamic lift and drag forces around an used to tit the gas-surface interaction the variations in the aerodynamic coefficients by the changing incidence of the satellite to
the atmosphere. The gas-surface model is therefore poorly defined and highly correlated with the DCMs. Ideally the aerodynamic force should be well defined in both magnitude and variation. However. in practice this is only so if the atmospheric density errors are removed. or solved for correctly. To accomplish this. two or more satellites’ orbits at similar altitudes, are analysed over the same time span. The error in the calculated atmospheric density can be assumed to be the same for orbits of similar altitude and inclination. Therefore. the solved-for DCMs .4,, i = I.. , II (n is the number of satellites considered) should also be the same for each orbit. Similarly WC assume that the gas-surface interactions occurring on each surface of each satellite will be governed by the same interaction laws. If the proposed modelled laws are physically reasonable, the values of gas--surface interaction parameters which produce the correctly calculated aerodynamic coefficient for each of the satellites. will be the same. These values of the gas-surface interaction parameters. should be the solved-for values obtained from each orbital arc analysed. Analysis of the aerodynamic orbital perturbation of each satellite, defines the actual aerodynamic force. 41~~~ F~Iw, experienced by each satellite. In turn. the modelled aerodynamic force is described by the variables .4, and the gas surface parameters
Therefore. each of the satellite orbits simultaneously analysed effectively generates an equation in these unknowns, which may be solved simultaneously. hopefully producing a unique and physically meaningful solution. The more orbits analysed simultaneously the greater the likelihood of acquiring the “correct” solution. This is assuming that the spacecraft are of different aerodynamic shapes. so contributing independent equations. The objective is to obtain the “best” value of the density correction multiplier, and the “best fit” values of the gasssurface interaction parameters. The solution relies on the consistency of the values of A, between orbits. This consistency is shown in Fig. 8. The drag coefficients of STARLETTE and ERSI were varied to achieve the match. STARLETTE is in a 50 inclination. 800-1000 km orbit while ERSl is in a 98 inclination circular orbit at 780 km. STELLA. in a very similar orbit
Fig. 9. (Tomhining !MOorbits
in a least-squares
mlution
_ _
L
49400 tc) ERSl , would be expected to produce a better match 1.0 the ERSI data. The values of ~(Sjhf)C,,~_ for the satellites are calculated numerically, using a panel mel.hod at each time step. Thih increases the accuracy of the a.e:rodynamic calculations, but slows down the force model integration. Since this method is very sensitive to the spacecraft surfact: area to mass ratio, it is imporlant that the li:orrect values IIL the time of the orbit epoch be used.
The SATAN code uses matrix algebra squares solution to the equation
to obtain
the least,-
\v here DD
q
=
‘4” 1v.4.
RHS =
AT lw;B.
x ==L,D ’ RHS.
Matrix ,4 contains the rates (of change of the residuals with respect to each parameter. W a diagonal matrix c,F laser range weights. R contains the range residuals and y the corrections to the parameters. The L.U and RlfS matrices are square and single column mutricl:x, respeI:.rively, with the largest dimension equal to the number of
49420
-__-
---_-i__I
49440 49460 40480 Modified JulianData (days)
Fig. 10. Values of the- parameter
49500
49520
I,,,,,,
Due to the high interdependence of the gas-surface parameters and the aerodynamic coefficient, the correlation:, between the parameters in the solutions are high. Even with many satellites the data is not sufficient to allow the simultaneous solution of all the gas-surface parameters. Therefore. one parameter must be kept constant. B,,,,, wa?, chosen and kept constant at 1.O. since S, has the least effect upon the calculated value of the aerodynamic coefficients The correlations between A,,,,, and C,,,,, in the solution ,lre still large. but within reasonable limrts. and the par.tmeters are relatively well determined by the data. The values of the DCMs generally fall between 0.8 and 1.2. which is as expected for a period three years after solar maximum. The DCMs act as flags. lfthe values are outside the range O.&l.? they suggest a non-sensible solution. The DCMs are also useful in their own right. as the) represent an accurate absolute density multiplier which :an be used to assess and ultimately improve the perrormance of the atmospheric models. at the altitude itnalyced. Results The solved-for 1’7 preliminary
values of parameters A;,,,,, and C’,,,,. ovel arcs are sho\vn in Figs 10 and I I. The ---r--
1.4 I
I-
1.2
1
l-
0.6
i
0.4 0.2 O-
fII1 ‘1
..! ../I.....j
0.8
’
--
1-I -1 -f
ij
1 I-j-j.--./ f
/
P
-0.2
/ 1
-0.4 49400
II 49420
Fig. II. Values of the
49440 49460 49480 Modified JulianDate (days) parameter
( ',,_,
49500
49520
I. K. Harrison
178
and G. G. Swinerd : Multiple
/ ,.:
40 30 .,,
0:
0
0.5
Gals
to
Surfk~
2 Mass Ratio
2.5
Fig. 12. Solved-for variation of the energy accommodation coefficient, compared to the molecular beam derived variation
significant fluctuation of the values is mainly due to the large correlations between the two parameters, and the limited resolution of the SLR data. Even so the general trends of the results are clearly visible, even if an accurate quantitive solution is not. All the solutions produced realistic values for the DCM and solar coefficients, suggesting that the results themselves are sensible. All but one of the values of A,,,, are below one, the majority taking a value around 0.5. This shows that the degree of energy accommodation occurring between the spacecraft surfaces and the atmosphere is higher than that expected from the molecular beam derived equations. The effects of surface contamination, roughness and erosion are not typically observed in the beam experiments, and would be expected to increase the energy accommodation. These effects alter the surface structure, changing the local incidence and increase the probability of multiple reflections on the same surface. The mean value coof A,,,” = 0.46 f 0.37 produces the accommodation efficients shown in Fig. 12. The solid line represents atomic oxygen, the dashed line helium and the dotted line is a molecular beam derived value. The values of C,,,, are similarly all less than one, but have more consistent values. So it appears that the emitted particle distributions, have a bulk velocity away from the surface nearer the surface normal direction, than that expected from the beam experiments. This is probably again due to the imperfections in the spacecraft surfaces. The value of C,,,, = 0.47 + 0.20 produces the surface emission angles shown in Fig. 13. The solid line represents atomic oxygen, the dashed line helium and the dotted line is the molecular beam derived value. The single dot shows the result of an atomic oxygen scattering experiment flown on the space shuttle. by Gregory and Peters (1986). This is one of the few beam experiments actually experiencing LEO conditions for an extended period of several days. As such it is an ideal value for comparison, to check the MSA results. The single point lies on the atomic oxygen line (somewhat luckily), helping to justify our hope that the results are physically meaningful. The empirical gas+ surface interaction equations may similarly be assumed reasonable.
10
0
3
,,,..‘~
20
,,..”
_,_.f
_______ /ye /..-.. __,.._’
/A0
30 40 50 60 incident Angle to the Normal
on on on on
30 incident
70
60
90
angle, compared
to
characteristics
Velocity (km SK’) Helium Helium Oxygen Oxygen
,....... --.L __-----
Fig. 13. Solved-for variation of the emitted the molecular beam derived variation
Table 1. Emission
satellite analysis
aluminium gold/silver aluminium gold/silver
2.8 3.3 1.2 2.6
Emitted angle (deg) 20 20 12 I?
Velocity ratio (ST) 0.98
I .03 0.81 0.98
angle.
Emission yropcrtks When dividing up the satellite surfaces, two main material types were considered; (1) silicon oxide and aluminium oxide for the majority of the surface, (2) gold and silver thermal and protective coatings. The molecular masses of these two materials are considerably different with a ratio of about 4: 1. Table 1 shows the values of the calculated emission characteristics, for helium and atomic oxygen with respect to these two surface types. The dominant interaction with respect to the aerodynamic coefficients is the atomic oxygen. followed by helium on aluminiuml silicon oxide. The solution is therefore primarily driven by these interactions, which are therefore expected to have the best definition. The mean emission has a velocity of just under 2 km S _I, in a direction mid-way between diffuse and specular. Previous theoretical analysis of satellite aerodynamics has suggested a low speed diffuse emission (Crowther and Stark, 1991), and a 1.6 km s-’ nearer specular emission (Harrison and Swinerd, 1995). The current results are comparable to those previously obtained. Future work will involve increasing the accuracy of the spacecraft surface material models and a more focused analysis of the gas-surface interaction, to try to increase the consistency of the results. It will also involve further analysis of the nodal breadth of the emitted distribution through the values of S, and B,,,,.
179
and G G. Swinerd : Multiple satellite analysis
I. K. Harrison
1
I
--
'Y-lift' 0.8
‘Z-lift’____.. ,,..l
.
'helium'T 0
1
2.5
-0.6
1 .,
-0.8
‘\
,,(
‘\
I’
,’
r‘..
/ ‘.‘ . ...,’
.’
.’
_.I
0.5 I 0.17
Fig. 14. Solved-for auis z’. %
0.18
0.19
0.2 0.21 0.22 Time(days)
lift coeficients
of ERSl.
0.23
0.24
0.25
--
0 0
10
20
30 40 50 60 70 IncidentAngletothe Normal
80
90
100
in the body fixed Fig. 16. Lift and drag coeficients I rarefied flab
encountered
by ;I Rat plate in
STARLETTE drag coefficients in Fig. IS. arc due to atmospheric composition variations around the orbit. The drag coefficients are signiticantly larger than the value of 1.2 typically accepted. The results produced DCMs within the 0.8 1.2 range and the solved-for parameters arc sensible. The drag coefficient?, therefore also appear realistic. The value of CI) larger than 2.2 is due to a significant fraction of the atmosphere bcinp helium. which is expected to have a lower energy accommodatic~li coefficient. and lower reactivity than atomic oxygen.
21
I
I 0.17
0.18
0.19
Fig. 15. SolvcJ-Vor drag LASTARLETTE. around
0.2 0.21 0.22 Time (days)
coefficients one orbit
0.23
of ERSI
0.24
0.25
and
STEL-
The aerodynamic lift and drag coefficients, with respect to the projected area in the flow direction, of ERSl and STELLA:STARLETTE for A.,,, = 0.46 and C,,,, = 0.47 are shown in Figs 14 and 15. They represent the variation around a complete orbit. The front and back faces of ERSl’s solar array will be normal to the flow at particular times during the orbit period. The C,, maxima occur when the solar array surface is at about 90” and 0’ to the flow. The direction of the re-emitted particles off the array are in the negative velocity direction. when the array is at 90 . so causing a large momentum exchange in the flow direction. When the array surface is parallel to the flow the projected flow area is almost zero. but the drag is not. So the array contributes to the total drag but not the flow projected area. At near zero surface incidences, both sides of the array are also acted upon by the flow, so doubling the array surface area acted upon by the atmosphere. This is because the C,,. with respect to the total surface area, is greater than zero at 90 normal incidence, as shown in Fig. 16. This demonstrates why the thermal velocity ol the atmosphere should not be ignored in aerodynamic calculationa. The variations of the STELLA.
Conclusion
The use of precise orbital analysis techniques to investigate the gas-surface interaction has proved moderately successful. Multiple Satellite Analysis (MSA) has demonstrated its ability to correctly separate the atmospheric density model errors from the effects of the gas- surface interaction, when calculating the aerodynamic forces encountered by satellites in low Earth orbit. The preliminary results roughly quantify the interaction parameters .4,,,,, = 0.46+0.37 and C,,,,,, = 0.47+0.70. These results mean that the average particle omitted from the surface has a bulk velocity of about 2 km s ’ at an angle half way between specular and the surface normal. The aerodynamic coefficients calculated from these results arc larger than expected. primarily due to the effects of atmospheric helium. .~~litlol~lcr!yc~~7~~tz~,\. We thank Simon Barrow,. Nick Hat-wood. Graham Appleby and Andrew Sinclair for useful discussions. This work was supported by a PPARC research studentship.
References
CNES, Stella research announcement,
December 1997. Collins, F. G. and Knox, E. C., Parameters of nocilla gas/surface measured accommodation from interaction model coefficients. .4AIA J. 32(4), 765. 1994. Comsa, C., David, R. and Schumacher, B.-J., The angular depen-
180
dence of flux, mean energy and speed ratio for d2 molecules desorbing from a Ni(l11) surface. Sur/bcr Sci. 85,45, 1979. Crowther, H. and Stark, J., The determination of the gas/surface interaction from satellite orbit analysis as applied to ans-1 (1975-70a). Planet. Space Sci. 39, 729, 1991. Fujimoto, T., Furuya, Y., Hayashi, T. and Takigawa, H., Scattering of molecular beams on the polycrystalline nickel surface, in 10th S~wposiunz of Rarefied Gus Dynamics, Colorado, 1976. Goodman, F. 0. and Wuchman, W. Y., D~wamics qf’Ga.v-Surfhcc~ Stuttering. Academic Press, New York. 1976. Gregory, J. C. and Peters, P. N., A measurement of the angular distribution of 5 eV atomic oxygen scattered off a solid surface in earth orbit, in 15th Swzposiwn OH Rawfied Cu.\ D~xamics. 1986. Harrison, I. K. and Swinerd, G. G., Analysis of satellite laser ranging data to investigate satellite aerodynamics. Planet. Space Sci. 43, 1023-1033. 1995. Hinchen, J. J. and Foley, W. M., Scattering of molecular beams by metallic surfaces, in RareJed Gus Djwarnics, 1966. Hurlbut, F. C., Gas/surface scattering models for satellite applications, in 201117Xernlosplzysic.F Cnnjkrence, Virginia, 1985. Hurlbut, F. C. and Sherman, F. S., Application of the nocilla wall reflection model to free molecule kinetic theory. P/l)xic.c Fluids 11(3), 486. 1968. Kolodney, E., Amirav, A., Elber, R. and Gerber, R. B., Large energy
I. I<. Harrison
and G. G. Swinerd : Multiple
satt*llitc analysis
transfer in hyperthermal heavy-atom-smfdce scattering : a stud) ol‘Hg/MgO( 100). C’/7cw7.P/IQX Letr. 113(3), 303, 1985. Kreck, 1~. H., Gaulher, M. J. sod Caledonia, G. IL, High celocity atomic o:c~~!.cn~:;urllce accomodation studies. J. S’/xxcc~/fi Roc,ket.~ I 991. McFall, A., The: thermal accomodation coetlicient of helium and argon on an amorphous SiO, surface, in 12//l Rawfid CTu.\ i3p7czmicr ~~~w7fposilr/?l, 1980. Miller, D. R:. ;md Subbarao, R. B., Scattering 01‘ O.W2.:i eV neon and argon atoms from a silver (1 11) crystal. ./. C’/IWI. H7,v.c.5211). 425. 1970. Nocilla, S., The surface re-emission law in free molecule few. in 3~11S>~lnpc~,sitfri? Ktr~/icd Cns D~~mnzics, 1961. Oplji, A., Sca~ering of rare gases from contaminated metal planes, in I .‘:mtl~ RuwJed Gus Dwarnics Cor+vww. I986 I’cters, P. :V., Iibk, IR. C. and Gregory, J. C., Velocity distribution of‘ oxygen atoms incident on spacecraft surfaces. J. Spamw+ Rocket.r 35( I ), .5?.198X. Sinclair. A. 1 . md Appleby, G. M., Satan---programs for the determination and ;tnalysi:j of satellite orbits from sir data. Royal Greenwich Observatory Publication, SL.R Technical Note Number !I, 1086. Subbarao, 1.1.B. and Miller, D. Ei., Velocity distribution measurement of (I.06 to I .4 eV argon and neon atoms :scattercd from ( I I I ) plant: of a silver crystal. J. C%errz. P/IJX. 58( 12). 5247, 197.1.
SI)LIWSki.. Vol. 44. No. 2. pp. 171 1x0. IYY6 Copyright (’ 1996 Elsevicr Science Ltd Printed in Great Britain. All rights reserved 0032--0633’96 $15.00-tO.OO
0032-0633(95)00077-1
A free molecule aerodynamic investigation using multiple satellite analysis 1.K.
Harrison and G. G. Swinerd
Department
of Aeronautics
and Astronautics.
University
Received 3 April l(JY5: revised 21 May 1995; accepted
of Southampton,
Southampton
SO1 7 I BJ. L .K.
22 May 1995
Abstract. The inaccuracies of numerical satellite positioning in Low Earth Orbit are predominantly due to the errors in calculating the aerodynamic forces. This is due to the unknown interactions of the rarefied atmosphere on the satellite surface, and the errors of the atmospheric density models. To improve knowledge of the gas-surface interactions, the effects of aerodynamic forces upon the orbits of satellites can be isolated, using precise orbital analysis (POA). When examining the orbit of a single satellite, the solution is restricted by the limited observational data, atmospheric model errors and the inevitable correlations between the atmospheric and aerodynamic models. To address these, three satellite orbits are examined simultaneously. The satellite orbits analysed are those of ERSl, a remote sensing satellite, and the geodetic satellite’s STARLETTE and STELLA. They orbit at 800 to 1000 km where helium and atomic oxygen are dominant. The collisional energies of helium and atomic oxygen upon the spacecraft surface are 1.25 and 5 eV, respectively. This preliminary analysis suggests that the re-emission of these particles are at lower speeds and lower emitted angles than those measured in laboratory molecular beam experiments. The analysis suggests that the bulk speed of the emitted particles is about 2 km s-l, and in a direction approximately half way between the specular direction and the surface normal. This emission produces a drag coefficient on an aluminium sphere of 2.52.
Introduction
Any vehicle travelling through a fluid will experience a force. the magnitude of which depends upon the fluid, the characteristics of the vehicle and their interaction. In the space environment the collision and re-emission of the sparse atmospheric particles on the fast moving spacecraft
produce both aerodynamic drag and lift. The force caused by the atmosphere is solely dependent upon the gas- surface interaction, as the effects of gas-gas collisions in the rarefied gas regime (above 2 I.50 km) can be assumed negligible. An increasing number of satellites in Low Earth Orbit (LEO). within the regime of significant atmospheric density, are typically platforms carrying Earth-viewing remote sensing equipment. Knowledge ofthe position and orientation of the satellite and instrumentation is vital. A dynamic force model is therefore needed to calculate expected position and velocity vectors of’ the satellite. which can then be fitted to the tracking data to properly determine the orbit. The dynamic force model must rcpresent all the forces in the near-Earth environment. that could cause perturbations to the satellite orbit of the order of the required orbital accuracy, over the time period it is determined (typically days in the LEO). At altitudes below 800 km (dependent upon solar conditions) the aerodynamic forces are the largest non-gravitational forces acting on the spacecraft. Due to the errors in current atmospheric density models. they are also the largest cause of orbit positional error. To resolve this difficulty, both the gas-surface interaction and atmospheric modelling needs to be improved. This paper looks at improving the former. The most common method of investigating gas surface interactions has been through laboratory-based molecular beam experiments. These experiments use pure gas and clinically finished surface materials. to reduce the number of experimental parameters. Unfortunately it is not gcnerally possible to exactly simulate the space environment in ground-based facilities, and space-Hewn materials often differ greatly from those examined in laboratories. The gas-surface interactions experienced by the satellite arc therefore generally different to those observed terrestrially, although the trends should bc similar. Conscquently the aerodynamic models derived from integrating the passsurface interaction models over the whole spacecraft surface are imprecise and highly parameterized. Precise Orbital Analysis (POA) of satellite orbits. deter-
172
I. K. Harrison and G. G. Swinerd : Multiple satelhte
mined from Satellite Laser Ranging (SLR) data has proved successful at investigating the gas--surface interactions occurring on ERSI. By isolating the orbital perturbations due to the aerodynamic forces. knowledge of the cause of’ the forces can be inferred. This is conducted by fitting the ,variables of a proposed gas-surface interaction model to the perturbations. Unfortunately the information available from the analysis of a single satellite orbit is limited. ‘The errors in the atmospheric density model are also difficult to remove from the aerodynamic data, corrupting the analysis of the gas-surface interaction. By combining the orbits of several satellites using Multiple Satellite .4nalysis (MSA). some of these effects can be decorrelated and the errors reduced. The results of single satellite analyr;is, at 800 km altitude. suggested that the particles are emitted at low velocities ( 2 2 km s-l). in a near specular direction (Harrison and Swinerd. 1995).
Gas-surface
interactions
The aerodynamic forces encountered on a spacecraft surface travelling through a rarefied atmosphere. are due to the momentum flux difference between the incident and emitted particles. The momentum of the incident particles is defined by the satellite relative velocity to the atmoIsphere, and the atmospheric conditions. The velocity and direction of the emitted particles are influenced by the interaction between the gas particles and the surface material. This produces emission distributions between (a) the specular case, where the particles leave at the same Ispeed, but with an inverted normal velocity, and (b) the (diffuse case, with the particles drifting away from the Isurface at a thermal velocity related to the surface temperature. The aerodynamic force in continuum flow is historically expressed as drag, the force parallel to the atmospheric svelocity direction, and lift, the perpendicular force. These forces are represented by the aerodynamic coefficients (C,, C,) of the vehicle. The force due to the particles incident upon the vehicle is Force(l(fi,
clrq)
= if) 1 C’i,,,,S( CD. C,).
(1)
Here p is the atmospheric density, S some reference area. llbulk the velocity of the satellite relative to the atmosphere ;and the geometry of the forces is shown in Fig. 1. This representation of aerodynamic forces is still applicable in
a rarefied atmosphere. as p C,‘&li.is the momentum flux ol‘ an atmosphere travelling at the spacecraft velocity. The incident particles do not strike the surface at ;1 constant speed and direction. but at variable speeds and directions, dependent on the atmospheric Lemperature. ‘The interaction between atmospheric particle and surface is not static. so the emitted particles also have ;I broad range of speed and direction. The total momentum Hus is therefore an integral over all speeds and directions of the particle momentum flux striking and leaving the xpacecraft surface. The exact distribution of the particle velocities is important in this integral,
Peters ef trl. (1988) have shown that the atmosphere striking the surface has a Maxwellian type velocity distribution, consisting of the atmosphere’s random thermal velocity C, superimposed on the satellite’s bulk velocity. The three-dimensional number density of the random thermal velocity distribution is given by
(3) where
(3) Here R,) is the universal gas constant. Tthe atmospheric temperature, M the molecular mass, N the number densitj of particles and z~J,\\ are orthogonal velocities shown in Fig. 1. Using this distribution the flat plate aerodynamic coefficients (CD ,, C,,), due to the incident momentum 11~ (Hurlbut and Sherman, 1968) are e -riCD, = 2 sin (fl,) ___ +0.5( 1+erf(o)) ‘Jna
(
I+ $ i
,!! (4)
&
c’, , = 2cos(H,)
(T = S, sin (H,).
(I fcrf(0))
1
/
i
Fig. 1. Geometry of incident parlicle and the associated forces
analp~
s‘
,
=
I.~~~!? c
(5)
Here 0, is the angle between the surface and the incidcnr flow and V,,,, (or (i,) the bulk velocity of the satellite. The reference area for these coefficients is the actual flat plate area. As S, tends to infinity (a hyperthermal flow) C’[, tends to 2.0 and C, tends to zero. The thermal velocity C of the atmosphere leads to lift forces. and directly effects the drag, by increasing the average velocity of the particles striking the surpdce.
I K. Harrison
and G. G. Swinerd : Multiple
The emitted particles carry away momentum flux. This must be taken away from the incident momentum flux. when calculating the total force exerted on the surface. II i5 generally accepted that emitted particles do not leave the surface randomly. but form a distribution that is approximately invariant with time. The relationship between incident and emitted distributions is poorl! understood. though a number of models have been proposed that represent the emission of gaseous particles fl-om a solid surface. Due to the complex interaction between gas and surface particles. all models are highly parameterized, with many parameters undefined. These gas-surface models fall into two main categories: very specific numerical simulations (SNS) that tend to accuI-ately represent only the experimental data from which they are derived. and satellite aerodynamic models (SAM) which are based upon experimental results, but use both theory and empirical engineering approximations to form The satellite aerodynamic ?
Nocillrr
rt77i.\.viot7
173
satellite analysis
tlistrihuriot7
When a particle strikes a surface there will be an exchange of energy and momentum. The energy of the emitted particle will be partially redistributed amongst its various degrees of freedom, kinetic and thermal energy. So the distribution of particles leaving the surface will still have both thermal and bulk velocities. The emitted distribution should therefore be expected to be similar to the Maxuellian protile found in the atmosphere. The velocity vector direction of the emitted particles will vary due to the thermal. molecular and macroscopic surface structure. as well as due to their initial angles of incidence to the surface. The efrects of surface structure scattering arc indistinguishable to those possibly caused by the particles thermal velocity. Nocilla’s model (Nocilla, 1963) absorbs the effects of structure scattering into the thermal velocit), of the emitted particles. representing the distribution of the emitted particles by their bulk direction. bulk speed and thermal speed. assuming a Maxwellian thermal velocity distribution. This model has been shown to fit the majority of single nodal emission distributions observed
Fig. 2. Grometry
of the emitted particle distribution
in molecular beam experiments (Gregory and Peters. 1986). As such it is an appropriate starting point. from which to build a general gas-~surface interaction model for use in precise orbital analysis. The particle flux intensity N,(4) modelled by Nocilla is
~(1+.3~+,~~(l.S.~+.~~)1l+erl‘(.~l~)c~
)
(6)
where
Here N,,,, is the total number of particles lea\ing the surface. which to first approximation equals the number incident upon it. C, and C‘, arc the thermal and bulk velocities of the emitted particles. and the angles arc represented in Fig. 2. This distribution when integrated o\er the whole range of emission velocities produces the emitted tlat plate aerodynamic coefficients (C,, ). C‘, ,)
where .Y(o) = em”‘+v,nci(l
+erfIrr))
, B=j;. / Here the reference area is the actual tlat plate surface arca. The total drag or lift coefficient due to the atmosphere is
174
the sum of the incident and emitted coefficients (CD,++D.r? CLI+CL.r). The parameters of the incident flow are defined by the satellite orientation and orbit and the atmospheric conditions. The parameters of the emitted Nocilla distribution are not well defined. and are the cause of the aerodynamic uncertainty.
Measureable interaction One of the objectives of the research is to improve the knowledge of the relationship between the incident and the emitted particle distributions. The apparatus for the investigation is the orbiting satellite. The satellite exposes a variety of surface materials to the atmosphere and encounters a variety of atmospheric conditions. The information retrievable is therefore an average of all the interactions occurring over the whole spacecraft. and to a certain degree an average of those occurring around a whole orbit. Hence it is inappropriate to use a highly specific numerical gas-surface model in the investigation, as these tend to be realistic only for the specific surface materials, incident particle species and velocity vectors used in terrestrial experiments. So alternately a more robust, general engineering SAM is used to represent the interaction. The results from fitting the SAM to the orbits, will not have the accuracy associated with specific molecular beam results, though as they are fitted to actual flight data. the results will hopefully better represent the overall gas-surface interactions occurring on the spacecraft surfaces. It should be noted that only the contribution of the emitted flow to the aerodynamic force is affected by the gas-surface interaction. The emitted flow is the major contributor to the aerodynamic lift, but has a relatively minor effect on the aerodynamic drag.
Initial gas-surface interaction equations from experimental data
I. K. Harrison
and G. G. Swinerd : Multiple satellite analysis
placed on the beam data. is that the kinetic energy of the incident beam be larger than the particles’ thermal energy at the surface temperature, T, < MU2/3R0. This is to limit the results to the regime of structural scattering, which is that encountered in LEO conditions, rather than thermal scattering. This reduces the effect of the surface temperature on the emission distribution. The results of over I 10 published molecular beam experiments were analysed. each being converted into a standard form which is compatible with the Nocilla model. The results come from papers by Gregory and Peters (1986), Hinchen and Foley (1966), Kreck et al. (1993), Nocilla (1963). Fujimoto et al. (1976), Comsa et al. (1979), Hurlbut (1985), Onji (1986). Kolodney et ul. (1985). McFall (1980)” Miller and Subbarao (1970), Goodman and Wachman (1976). ‘Subbarao and Miller (1973) and Collins and Knox (1994). Each molecular beam run was represented where possible by the values of incident angle 4, (rad), incident energy E, (eV), gas particle mass to surface particle mass ratio p, surface temperature T, (K), surface quality. emitted angle $I (rad) emitted speed ratio S, and energy accommodation coefficient c(. For the majority of runs, values for only some of the above parameters were available from the published results. The angles d)I and 4, are measured from the surface normal rather than the surface. From the literature it became apparent that the parameters 4,. E,, p. & S, and a “best” described the incident and emitted flow. General trends in the emitted distribution were visually determined by graphically plotting the incident characteristics &, E,, p against the emitted characteristic @r. S,, c(. They were then equated to simple equations assuming that & = Fl (q5,, E,, p), S, = F3( I$,, E,. p). ct = F3(& E,, ,u). The simple equations were then fitted to the beam data using least squares routines. to produce the following etnpirical equations : (9)
S, = 0.71+0.63$,-0.19~1 cx= (4.8+0.08E,-
To perform the precise orbital analysis of the gas-surface interaction, a parameterized model must be developed which can be fitted to the observations. In this analysis a specific numerical simulation was considered to be too restrictive, so a parameterized empirical relationship fitted to experimental data was used. The results of published molecular beam experiments are used to generate an initial model. A Maxwellian distribution is assumed in the incident flow, and the Nocilla model is assumed for the emitted flow. The empirical model provides the relationship between the two flows. Very little relevant experimental data is available for spacecraft materials in the LEO environment, the results of Gregory and Peters (1986) being one of the few. Consequently the empirical relationship is based on the results of terrestrial molecular beam experiments. executed under a variety of different conditions, in an attempt to reduce any biasing. This is particularly true of the incident energy, as for most experiments E, < 5 eV. The only restriction
1.15&)
1 -exp
(10) (-0.5~~)
exp (0.75~1)
(11)
Generally, as can be seen the gas-surface interaction models are characterized by a significant number of parameters. Hence, the underlying reason for the adopted approach is to attempt to reduce the number of parameters to be solved for in the subsequent orbital analysis. The main trends determined and represented in equations (9)-(11) are shown in Figs 3-5, respectively. The solid lines represent typical values of the equations which have been fitted to the data points, the dotted lines join points which have only one of their incident characteristics varying. Error bars have not been included, but are significant. These reflect experimental errors, the interpretation of the results and the conversion into the Nocilla form. The variation of u with ~1 fits the hard sphere theory, that particles of the same mass will have the largest exchange of energy and momentum during collision. Figure 4 shows a near specular direction of re-emission, while the variation of S, shows a strong & dependence, producing a
and Ci. G. Swinerd : Multiple
I. k, Harrison
175
satellite analysis
is added to each of the equations. The values of x1. S,? and Or2are used to calculate the aerodynamic forces in the computer model. where 23_ = I -(I
-%).3,,,,,,.
.y2 = B,,,,,..S:
(I,, = C:,,,,,fl,. The parameters ,4,,,,,. B,,,,,, and t’%,,,,,are titted to the orbital aerodynamic perturbations.
Fig. 3. Man co&ficient
2 1.5 Gas to Surfacemass ratio
0.5
0
dependence
907-T
of
the
p
energy
Method
J
2.5
1
3
accommodation
1
1
I
60 70 60 50 I 40 30 I
This analysis uses a modified form of Prccisc Orbital Analysis (POA) to solve for the aerodynamic parameters ,4.x,,,, B,t,,,, and C‘,,,,,,. The technique described as POA. is the fitting of a numerically calculated orbital trajectory to Satellite Laser Ranging (SLR) data. This process is carried out by solving for specific parameters within the satellite environment force models. If the force model is realistic. the value of the solved-for parameter will bc meaningful. A realistic force model should produce a significant improvement in the orbital fit. giving consistent values for its solved-for parameters. within the accuracies of the laser ranging and numerical routines. The measure of orbital tit used. is the r.m.s. difference between the laser ranges and the calculated rang from satellite to laser station.
10
0
10
0
dependence
Fig. 4. Main
20
Incid%
40
50
60
Angletothe Normal $
of the emission
70
60
1 (degrees)
angle
2
04
:
0.2
*
Ob 0
10
Fig. 5. Main dqxndence
20
Inc%nt
40 Angle
of the
&
50 60 to Normal @
70
80
i (degrees)
speed ratio
narrower nodal emission with increasing 4, and decreasing Incident normal momentum h! V,,,,,,cos (4,). The emission distributions observed from the engineering materials used on the spacecraft surface. after being exposed to different levels of atomic oxygen erosion. are expected to difler from those observed in the laboratory. To account for this and provide parameters that can be fitted to the clrhital observations. a multiplying parameter
The SLR observations are quoted as having a precision of 2-5 cm. with a comparable accuracy. This is ofa similar order of magnitude to the orbital perturbations of ERSI. caused by the once per orbit periodic variations of (‘r, and C,.. SLR data is typically concentrated during the nighttime, in the northern hemisphere. so a large fraction ot the orbit is poorly defined. The orbital noise caused by the laser range errors. and poor global distribution will therefore affect any analysis of the aerodynamics of ERSI The main effect is to increase the scatter of results. so that statistical analysis is necessary. A modified SATellite ANalysis (SATAN) (Sinclair and .4ppleby. 1986) suite of programs is used for the POA. This uses an eighth-order Gauss -Jackson numerical integrator. and a least-squares fitting routine. Typically 6 day long arcs of data are analysed. containing 300 -1 500 SLR observations. The determined orbit usually ha5 an r.m.s. orbital fit of 5 40 cm. with 3 rejection level oi‘ IYl m. The magnitude of the re.jection level. is so that no observations other than those which are detinitely in crrol are automatically rejected. With the improved SLR data from 1994. it was found that the data either titted the orbit well. or had tens of metres range residuals and obviously in error. The thinking “if an arc of normal points is not obviously in error it should not be rejected” was followed. For c;~ch arc the starting trajectory state vector. \olal radiation coefficient. once-per-rcb and once-per-d.74 dab along-track corrections, daily atmospheric density multipliers. and the aerodynamic parameters are solved for. No parameters from Earth related models, including the gravity field and station coordinates. are solved for. interaction The solved-f-or values of the ga-surface parameters .4;,,,,,. B,,,,, and C’.,,,,,. are sensitive to the method of calculating the total satellite aerodynamic
I. K. Harrison
176
and G. G. Swinerd : Multiple satellite anJy~
r SOkU Array
I
Fig. 6. Panel representation
Fig. 7. The geodetic
satellites
I Fig. 8. Matching the density correction terms from ERSl and STARLETTE orbits. by varying the aerodynamic coefficients
of ERS 1
STARLETTE
and STELLA
force. A panel method is used to calculate the satellite aerodynamics, with every major surface panel represented by its area, surface normal. molecular mass, solar absorptivity and diffusivity. The attitude of the satellite to the incident atmosphere means that effects of shadowing are minimal, the only likely shadowing is between the slim wind scatterometers on ERSI. Similarly the diffuse and specular emission directions from all the surface panels passes a significant distance away from every other surface panel, so multiple reflections may be assumed negligible. The geometry of the satellites analysed are shown in Figs 6 and 7 (modified from STELLA research announcement, CNES ( 1992)).
The results from the analysis of a single satellite orbit are limited by the amount of data and the difficulty in the removal of atmospheric density errors. The density errors mean that the magnitude of the aerodynamic coefficient is not well defined, and that a density correction multiplier (DCM) A must also be solved for in the equation
Hence only ation of the are orbit, parameters, being caused
the perturbations caused by the relative variaerodynamic lift and drag forces around an used to tit the gas-surface interaction the variations in the aerodynamic coefficients by the changing incidence of the satellite to
the atmosphere. The gas-surface model is therefore poorly defined and highly correlated with the DCMs. Ideally the aerodynamic force should be well defined in both magnitude and variation. However. in practice this is only so if the atmospheric density errors are removed. or solved for correctly. To accomplish this. two or more satellites’ orbits at similar altitudes, are analysed over the same time span. The error in the calculated atmospheric density can be assumed to be the same for orbits of similar altitude and inclination. Therefore. the solved-for DCMs .4,, i = I.. , II (n is the number of satellites considered) should also be the same for each orbit. Similarly WC assume that the gas-surface interactions occurring on each surface of each satellite will be governed by the same interaction laws. If the proposed modelled laws are physically reasonable, the values of gas--surface interaction parameters which produce the correctly calculated aerodynamic coefficient for each of the satellites. will be the same. These values of the gas-surface interaction parameters. should be the solved-for values obtained from each orbital arc analysed. Analysis of the aerodynamic orbital perturbation of each satellite, defines the actual aerodynamic force. 41~~~ F~Iw, experienced by each satellite. In turn. the modelled aerodynamic force is described by the variables .4, and the gas surface parameters
Therefore. each of the satellite orbits simultaneously analysed effectively generates an equation in these unknowns, which may be solved simultaneously. hopefully producing a unique and physically meaningful solution. The more orbits analysed simultaneously the greater the likelihood of acquiring the “correct” solution. This is assuming that the spacecraft are of different aerodynamic shapes. so contributing independent equations. The objective is to obtain the “best” value of the density correction multiplier, and the “best fit” values of the gasssurface interaction parameters. The solution relies on the consistency of the values of A, between orbits. This consistency is shown in Fig. 8. The drag coefficients of STARLETTE and ERSI were varied to achieve the match. STARLETTE is in a 50 inclination. 800-1000 km orbit while ERSl is in a 98 inclination circular orbit at 780 km. STELLA. in a very similar orbit
Fig. 9. (Tomhining !MOorbits
in a least-squares
mlution
_ _
L
49400 tc) ERSl , would be expected to produce a better match 1.0 the ERSI data. The values of ~(Sjhf)C,,~_ for the satellites are calculated numerically, using a panel mel.hod at each time step. Thih increases the accuracy of the a.e:rodynamic calculations, but slows down the force model integration. Since this method is very sensitive to the spacecraft surfact: area to mass ratio, it is imporlant that the li:orrect values IIL the time of the orbit epoch be used.
The SATAN code uses matrix algebra squares solution to the equation
to obtain
the least,-
\v here DD
q
=
‘4” 1v.4.
RHS =
AT lw;B.
x ==L,D ’ RHS.
Matrix ,4 contains the rates (of change of the residuals with respect to each parameter. W a diagonal matrix c,F laser range weights. R contains the range residuals and y the corrections to the parameters. The L.U and RlfS matrices are square and single column mutricl:x, respeI:.rively, with the largest dimension equal to the number of
49420
-__-
---_-i__I
49440 49460 40480 Modified JulianData (days)
Fig. 10. Values of the- parameter
49500
49520
I,,,,,,
Due to the high interdependence of the gas-surface parameters and the aerodynamic coefficient, the correlation:, between the parameters in the solutions are high. Even with many satellites the data is not sufficient to allow the simultaneous solution of all the gas-surface parameters. Therefore. one parameter must be kept constant. B,,,,, wa?, chosen and kept constant at 1.O. since S, has the least effect upon the calculated value of the aerodynamic coefficients The correlations between A,,,,, and C,,,,, in the solution ,lre still large. but within reasonable limrts. and the par.tmeters are relatively well determined by the data. The values of the DCMs generally fall between 0.8 and 1.2. which is as expected for a period three years after solar maximum. The DCMs act as flags. lfthe values are outside the range O.&l.? they suggest a non-sensible solution. The DCMs are also useful in their own right. as the) represent an accurate absolute density multiplier which :an be used to assess and ultimately improve the perrormance of the atmospheric models. at the altitude itnalyced. Results The solved-for 1’7 preliminary
values of parameters A;,,,,, and C’,,,,. ovel arcs are sho\vn in Figs 10 and I I. The ---r--
1.4 I
I-
1.2
1
l-
0.6
i
0.4 0.2 O-
fII1 ‘1
..! ../I.....j
0.8
’
--
1-I -1 -f
ij
1 I-j-j.--./ f
/
P
-0.2
/ 1
-0.4 49400
II 49420
Fig. II. Values of the
49440 49460 49480 Modified JulianDate (days) parameter
( ',,_,
49500
49520
I. K. Harrison
178
and G. G. Swinerd : Multiple
/ ,.:
40 30 .,,
0:
0
0.5
Gals
to
Surfk~
2 Mass Ratio
2.5
Fig. 12. Solved-for variation of the energy accommodation coefficient, compared to the molecular beam derived variation
significant fluctuation of the values is mainly due to the large correlations between the two parameters, and the limited resolution of the SLR data. Even so the general trends of the results are clearly visible, even if an accurate quantitive solution is not. All the solutions produced realistic values for the DCM and solar coefficients, suggesting that the results themselves are sensible. All but one of the values of A,,,, are below one, the majority taking a value around 0.5. This shows that the degree of energy accommodation occurring between the spacecraft surfaces and the atmosphere is higher than that expected from the molecular beam derived equations. The effects of surface contamination, roughness and erosion are not typically observed in the beam experiments, and would be expected to increase the energy accommodation. These effects alter the surface structure, changing the local incidence and increase the probability of multiple reflections on the same surface. The mean value coof A,,,” = 0.46 f 0.37 produces the accommodation efficients shown in Fig. 12. The solid line represents atomic oxygen, the dashed line helium and the dotted line is a molecular beam derived value. The values of C,,,, are similarly all less than one, but have more consistent values. So it appears that the emitted particle distributions, have a bulk velocity away from the surface nearer the surface normal direction, than that expected from the beam experiments. This is probably again due to the imperfections in the spacecraft surfaces. The value of C,,,, = 0.47 + 0.20 produces the surface emission angles shown in Fig. 13. The solid line represents atomic oxygen, the dashed line helium and the dotted line is the molecular beam derived value. The single dot shows the result of an atomic oxygen scattering experiment flown on the space shuttle. by Gregory and Peters (1986). This is one of the few beam experiments actually experiencing LEO conditions for an extended period of several days. As such it is an ideal value for comparison, to check the MSA results. The single point lies on the atomic oxygen line (somewhat luckily), helping to justify our hope that the results are physically meaningful. The empirical gas+ surface interaction equations may similarly be assumed reasonable.
10
0
3
,,,..‘~
20
,,..”
_,_.f
_______ /ye /..-.. __,.._’
/A0
30 40 50 60 incident Angle to the Normal
on on on on
30 incident
70
60
90
angle, compared
to
characteristics
Velocity (km SK’) Helium Helium Oxygen Oxygen
,....... --.L __-----
Fig. 13. Solved-for variation of the emitted the molecular beam derived variation
Table 1. Emission
satellite analysis
aluminium gold/silver aluminium gold/silver
2.8 3.3 1.2 2.6
Emitted angle (deg) 20 20 12 I?
Velocity ratio (ST) 0.98
I .03 0.81 0.98
angle.
Emission yropcrtks When dividing up the satellite surfaces, two main material types were considered; (1) silicon oxide and aluminium oxide for the majority of the surface, (2) gold and silver thermal and protective coatings. The molecular masses of these two materials are considerably different with a ratio of about 4: 1. Table 1 shows the values of the calculated emission characteristics, for helium and atomic oxygen with respect to these two surface types. The dominant interaction with respect to the aerodynamic coefficients is the atomic oxygen. followed by helium on aluminiuml silicon oxide. The solution is therefore primarily driven by these interactions, which are therefore expected to have the best definition. The mean emission has a velocity of just under 2 km S _I, in a direction mid-way between diffuse and specular. Previous theoretical analysis of satellite aerodynamics has suggested a low speed diffuse emission (Crowther and Stark, 1991), and a 1.6 km s-’ nearer specular emission (Harrison and Swinerd, 1995). The current results are comparable to those previously obtained. Future work will involve increasing the accuracy of the spacecraft surface material models and a more focused analysis of the gas-surface interaction, to try to increase the consistency of the results. It will also involve further analysis of the nodal breadth of the emitted distribution through the values of S, and B,,,,.
179
and G G. Swinerd : Multiple satellite analysis
I. K. Harrison
1
I
--
'Y-lift' 0.8
‘Z-lift’____.. ,,..l
.
'helium'T 0
1
2.5
-0.6
1 .,
-0.8
‘\
,,(
‘\
I’
,’
r‘..
/ ‘.‘ . ...,’
.’
.’
_.I
0.5 I 0.17
Fig. 14. Solved-for auis z’. %
0.18
0.19
0.2 0.21 0.22 Time(days)
lift coeficients
of ERSl.
0.23
0.24
0.25
--
0 0
10
20
30 40 50 60 70 IncidentAngletothe Normal
80
90
100
in the body fixed Fig. 16. Lift and drag coeficients I rarefied flab
encountered
by ;I Rat plate in
STARLETTE drag coefficients in Fig. IS. arc due to atmospheric composition variations around the orbit. The drag coefficients are signiticantly larger than the value of 1.2 typically accepted. The results produced DCMs within the 0.8 1.2 range and the solved-for parameters arc sensible. The drag coefficient?, therefore also appear realistic. The value of CI) larger than 2.2 is due to a significant fraction of the atmosphere bcinp helium. which is expected to have a lower energy accommodatic~li coefficient. and lower reactivity than atomic oxygen.
21
I
I 0.17
0.18
0.19
Fig. 15. SolvcJ-Vor drag LASTARLETTE. around
0.2 0.21 0.22 Time (days)
coefficients one orbit
0.23
of ERSI
0.24
0.25
and
STEL-
The aerodynamic lift and drag coefficients, with respect to the projected area in the flow direction, of ERSl and STELLA:STARLETTE for A.,,, = 0.46 and C,,,, = 0.47 are shown in Figs 14 and 15. They represent the variation around a complete orbit. The front and back faces of ERSl’s solar array will be normal to the flow at particular times during the orbit period. The C,, maxima occur when the solar array surface is at about 90” and 0’ to the flow. The direction of the re-emitted particles off the array are in the negative velocity direction. when the array is at 90 . so causing a large momentum exchange in the flow direction. When the array surface is parallel to the flow the projected flow area is almost zero. but the drag is not. So the array contributes to the total drag but not the flow projected area. At near zero surface incidences, both sides of the array are also acted upon by the flow, so doubling the array surface area acted upon by the atmosphere. This is because the C,,. with respect to the total surface area, is greater than zero at 90 normal incidence, as shown in Fig. 16. This demonstrates why the thermal velocity ol the atmosphere should not be ignored in aerodynamic calculationa. The variations of the STELLA.
Conclusion
The use of precise orbital analysis techniques to investigate the gas-surface interaction has proved moderately successful. Multiple Satellite Analysis (MSA) has demonstrated its ability to correctly separate the atmospheric density model errors from the effects of the gas- surface interaction, when calculating the aerodynamic forces encountered by satellites in low Earth orbit. The preliminary results roughly quantify the interaction parameters .4,,,,, = 0.46+0.37 and C,,,,,, = 0.47+0.70. These results mean that the average particle omitted from the surface has a bulk velocity of about 2 km s ’ at an angle half way between specular and the surface normal. The aerodynamic coefficients calculated from these results arc larger than expected. primarily due to the effects of atmospheric helium. .~~litlol~lcr!yc~~7~~tz~,\. We thank Simon Barrow,. Nick Hat-wood. Graham Appleby and Andrew Sinclair for useful discussions. This work was supported by a PPARC research studentship.
References
CNES, Stella research announcement,
December 1997. Collins, F. G. and Knox, E. C., Parameters of nocilla gas/surface measured accommodation from interaction model coefficients. .4AIA J. 32(4), 765. 1994. Comsa, C., David, R. and Schumacher, B.-J., The angular depen-
180
dence of flux, mean energy and speed ratio for d2 molecules desorbing from a Ni(l11) surface. Sur/bcr Sci. 85,45, 1979. Crowther, H. and Stark, J., The determination of the gas/surface interaction from satellite orbit analysis as applied to ans-1 (1975-70a). Planet. Space Sci. 39, 729, 1991. Fujimoto, T., Furuya, Y., Hayashi, T. and Takigawa, H., Scattering of molecular beams on the polycrystalline nickel surface, in 10th S~wposiunz of Rarefied Gus Dynamics, Colorado, 1976. Goodman, F. 0. and Wuchman, W. Y., D~wamics qf’Ga.v-Surfhcc~ Stuttering. Academic Press, New York. 1976. Gregory, J. C. and Peters, P. N., A measurement of the angular distribution of 5 eV atomic oxygen scattered off a solid surface in earth orbit, in 15th Swzposiwn OH Rawfied Cu.\ D~xamics. 1986. Harrison, I. K. and Swinerd, G. G., Analysis of satellite laser ranging data to investigate satellite aerodynamics. Planet. Space Sci. 43, 1023-1033. 1995. Hinchen, J. J. and Foley, W. M., Scattering of molecular beams by metallic surfaces, in RareJed Gus Djwarnics, 1966. Hurlbut, F. C., Gas/surface scattering models for satellite applications, in 201117Xernlosplzysic.F Cnnjkrence, Virginia, 1985. Hurlbut, F. C. and Sherman, F. S., Application of the nocilla wall reflection model to free molecule kinetic theory. P/l)xic.c Fluids 11(3), 486. 1968. Kolodney, E., Amirav, A., Elber, R. and Gerber, R. B., Large energy
I. I<. Harrison
and G. G. Swinerd : Multiple
satt*llitc analysis
transfer in hyperthermal heavy-atom-smfdce scattering : a stud) ol‘Hg/MgO( 100). C’/7cw7.P/IQX Letr. 113(3), 303, 1985. Kreck, 1~. H., Gaulher, M. J. sod Caledonia, G. IL, High celocity atomic o:c~~!.cn~:;urllce accomodation studies. J. S’/xxcc~/fi Roc,ket.~ I 991. McFall, A., The: thermal accomodation coetlicient of helium and argon on an amorphous SiO, surface, in 12//l Rawfid CTu.\ i3p7czmicr ~~~w7fposilr/?l, 1980. Miller, D. R:. ;md Subbarao, R. B., Scattering 01‘ O.W2.:i eV neon and argon atoms from a silver (1 11) crystal. ./. C’/IWI. H7,v.c.5211). 425. 1970. Nocilla, S., The surface re-emission law in free molecule few. in 3~11S>~lnpc~,sitfri? Ktr~/icd Cns D~~mnzics, 1961. Oplji, A., Sca~ering of rare gases from contaminated metal planes, in I .‘:mtl~ RuwJed Gus Dwarnics Cor+vww. I986 I’cters, P. :V., Iibk, IR. C. and Gregory, J. C., Velocity distribution of‘ oxygen atoms incident on spacecraft surfaces. J. Spamw+ Rocket.r 35( I ), .5?.198X. Sinclair. A. 1 . md Appleby, G. M., Satan---programs for the determination and ;tnalysi:j of satellite orbits from sir data. Royal Greenwich Observatory Publication, SL.R Technical Note Number !I, 1086. Subbarao, 1.1.B. and Miller, D. Ei., Velocity distribution measurement of (I.06 to I .4 eV argon and neon atoms :scattercd from ( I I I ) plant: of a silver crystal. J. C%errz. P/IJX. 58( 12). 5247, 197.1.