E.M. Gaposchkin andAJ. Coster
Analysis of Satellite Drag
The use of thermospheric density models for calculation of the drag force on satellites is evaluated. These models are essential for precision orbit determination and for geophysical research. Drag data plays an important role in understanding the thermosphere and can contribute in a unique way to the monitoring of the next solar cycle. Nevertheless, determining the atmospheric drag on a satellite presents several problems. The current suite oftherm6spheric models is described and a subset ofthese models is ,analyzed quantitatively. These models are evaluated by using precision tracking data on three spherical satellites. At the lowest altitude, 270 kIn, all models performed equallywell, butat the higher altitudes, the models did not all performaswell. The tracking data also permits an evaluation ofthe atmospheric indexes currently used in thermospheric models, and ofthe precipitation index, which is notyet included in the models. Significant correlation is found between the data and the precipitation index.
Atmosphertc drag affects all satellites - in all 270 km, 780 km, and 1,500 km. The data were altitude regimes - from low altitudes to beyond used to evaluate the following thermospheric geosynchronous altitudes. And atmospheric densitymodels: ClRA 1972 [1], Jacchia 1977 [2], dragisthelargestsourceoferrorinmodelingthe DTM [3], and MSIS83 [4]. Cook's [5] definition of force on many of these satellites. Through the the ballistic coefficient, Cd' was used in this use of good models, however, the effect of analysis. atmospheric drag on satellites can be Figure 1 illustrates several aspects of the calculated. atmospheric drag problem. The drag force is a The prtmary uses of drag models are for product of four factors: Cd; the area-to-mass precision orbit determination, mass ratio, AIM; the atmospheric density, p; and the determination or weighing of satellites, and speed of the satellite with respect to the atmosphere, V. Each ofthese quantities will be investigation of geophysical phenomena. The 5 first two applications, precision orbit discussed in this paper, but note now that none determination and weighing of satellites, are of these terms are known precisely. An error considered time-crttical; results must be made inthe calculationofatmospheric drag can available within hours to be useful. Geophysical be due to an error made in determining any of investigations, however, which include these factors, and is more than likely due to a atmosphertc physics, areless time-crttical. An a combination of errors in all of them. posteriori analysis can be used to obtain an A second aspect of the atmospheric drag optimal estimate of the orbit. Table I problem is indicated by the two separate terms summarizes the applications of atmosphertc for density that are listed directly below the drag models and the areas in satellite tracking drag-force equation in Fig. 1. Two terms are that reqUire drag measurements. used becausenone ofthe standard atmospheric Satellite tracking provides an excellent models predict reliable denSities above 2,000 vantage pointfor the study ofatmospheric drag. km, eventhoughdrageffects are observed above The dataanalysis presented inthis papercomes this altitude. The reason is that. until recently, from precision radar tracking databeginning in the primaryinterestin drag has been inthe low 1985 on two spherical satellites, and from laser altitude regime. All data used in building the ranging data taken in 1986 on a third spherical atmospheric models comes from regions below satellite. The satellites have perigee heights of 1,000 km; additional data are needed above
The Lincoln Laboratory Journal. Volume 1. Number 2 (1988) 203 Gaposchkin et aI. - Analysis ojSatellite Drag
Table 1. Uses of Drag Models
Precision Orbit Determination crime-Critical) Catalog Maintenance SOl Prediction/Forecasting ASAT TargetinglThreat Analysis Data Screening and Calibration Collision Avoidance Navigation Satellites (eg, Transit)
Weighing of Satellites (Time-Critical) SOl Damage Assessment Decoying of Space Assets Space Debris Characterization
Geophysical Investigations Atmospheric Physics Model Development Calibration of Other Thermosphere Sensors Synthesis with Other Data Other Investigations Polar Motion and Earth Rotation Scientific Satellites Precision Orbits (eg, MAGSAT, SEASAT, GEOSAT, TOPEX, ERS)
1,000 kIn. Also, it is probable that different the time for drag to change the satellite position physical processes apply to the two regions by 12 kIn. This is. in a sense, the orbital error (above and below 2,000 kIn). caused by ignoring drag altogether. For satellite In our analysis we use an integrated COSMOS1179, which is a calibration sphere atmospheric density model. Below 2,000 km, with perigee at about 300 km. the error (along the atmospheric density is determined from one track) is 12 km after 0.92 days, or 13.6 of the previously mentioned thermospheric revolutions. For LCS4, another calibration models, which uses such inputs as the sphere with perigee at about 800 km. there will ' geomagnetic index. Kp and the FlO.7-cm flux. be a 12-km error after 22.8 days. or 323 The FlO.7-cm flux is the solar flux of radiation revolutions, and for LCS1. a calibration sphere at 2.800 MHz; this flux is assumed to scale with with perigee at2.800 km. the erroris 12 km after the flux of extreme ultraviolet radiation (which 38.9 days. or 386 revolutions. Clearly, though drives the thermosphere. but can'tbe measured the drag effect is far more noticeable at lower from the earth's surface). We also assume that altitudes, significant drag is observed at all the loweratmosphere is corotatingwith the solid altitudes. earth. Above 2,000 km. an empirically determined density fixed in inertial space is Precision Orbit Determination used. The size of the drag effect is shown by a The main use of drag models is for the simplified model calculation in Fig. 1. All determination of precision orbits. Because satellites are assumed to be spheres with the atmospheric drag is one of the largest forces on same AIM. which is chosen to be O. 1 cm2 Ig. a a satellite. obtaining precision orbits requires typical value for satellite payloads. We calculate accurate modeling of the atmosphere.
204 The Lincoln Laboratory Journal. Volume 1, Number 2 (1988) Gaposchkin et aI. - Analysis ojSatellite Drag
2 F = C (A)P V 2.-2 d M S
19 -[(h-h OJ/H] 3 P=P(t, 10.7, [10.7], kp) + 3.43 X 10- e (g/cm ) >: co I I 1.0 cE:> Rotating Fixed in CD a: with Earth Inertial Space 12 10 8 2,000 6 4 h (km) 2 0 Time Perigee Height Days Cd = 2.2 0.92 q (km) Satellite Rev 13.6 300 COS CAL SPH 11796 Days Cd = 2.2 22.8 Rev 323 800 LCS 4 5398 Days Cd = 2.2 35.9 Rev 356 2,800 LSC 1 1361
Days Cd = 1.0 (390) 94 5,800 LAGEOS 8820 Rev (2,574) 600
Days Cd = 1.13 320 20,000 ROCKET 14264 Rev 640 BODY
Days Cd = 0.803 774 42,000 LES 6 3431 Rev 774
Days Cd = 6.28 99 42,000 ATS 5 Rev 99
Fig. 1 - Drag effect for (AIM) = 0.1 cf7i!/g.
The ability to know precise satellite positions Catalog maintenance depends on knowledge contributes to a variety of areas in satellite of a satellite's orbital elements to within a tracking. For example, precision orbits on given accuracy. For data of a given quality, satellites are needed for catalog maintenance, the best dynamical model of the orbit gives satellite orbit identification (SOl), collision the most accurate element set for a satellite (a avoidance, satellite navigation (eg, Transit), satellite's position and velocity). This orbital antisatellite (ASAT) targeting and threat model necessarily includes the best model of analysis, and data screening and calibration. atmospheric drag. By maintaining an
The Lincoln Laboratory Journal. Volume 1. Number 2 (l988) 205 Gaposchkin et aI. - Analysis ofSatellite Drag accurate catalog, one has available precision altitude, means that the possibility of collision, element sets for each satellite. A critical use of though small, is nevertheless real. Despite the these element sets is SOL Reliable and accurate low probability, the cost of the collision of a orbits provide the most commonly used satellite, or even worse, ofdebris, with a foreign technique for the identification of satellites. asset is so high that every step must be taken to Precision elements are essential for predicting prevent such an occurrence. Precise and timely and forecasting satellite orbits. Prediction is monitoring, ie, maintenance of the catalog, is needed for such applications as acquiring more the only way to accomplish this task. tracking data from a pencil-beam radar, or determining when an orbit will decay, a Mass Determination requirement that stresses the use of atmospheric models at low altitude. Predictions The effects of all nongravitational forces, eg, are also necessary for the maneuver planning drag and radiation pressure, are proportional to and execution needed for orbit maintenance. AIM. Therefore AIM can be found from an Furthermore, highly accurate and timely observed change in satellite orbit. If the size (A) predictions of satellite position are required to of a satellite is known, say from radar cross target a given volume (ASAT targeting), or to section (RCS) observations, then the drag force assess the threat to an asset of another vehicle can be used to determine the mass (M) of a (threat analysis). And orbit predictions play an satellite. In fact, this process has been important role in testing new surveillance performed more or less accurately for some systems. New systems, such as the space-based years; it hinges on knowing the density and the radar and the visible optical satellite-tracking Cd contribution to the drag-force equation. system - both currently under development Therefore, it requires accurate assessment of need real-time precision predictions ofposition, the atmospheric density. up to 24 hours in advance, to interpret sensor The determination of a satellite's mass and data properly. size has important implications for SOL The Operational satellites also depend on combination of information about a satellite's atmospheric drag analysis for accurate mass and size (and perhaps its shape, attitude, predictions. The Navy Transit Navigation and spin rate) is a second discrimination tool for satellites, for example, are limited by the SOl, perhaps as powerful as the information accuracy of drag models. Currently, there are contained in the element sets. By monitoring several surface-force-compensated, drag-free, this information, a change in either the orbit or Transit satellites flown at great expense to the operational status of a satellite can be overcome the drag problem. Better drag models observed. Such changes can indicate, for would alleviate the dragissues in a fundamental example, possible damage due to a collision or way. an ASAT attack. Atmospheric models also play an important Another use of weighing satellites is for role in the calibration of satellite-tracking data. decoying space assets. The decoy problem is To have confidence in inferences based on usually viewed in terms of replicating the size, tracking data, it must have been validated, RCS, and optical characteristics of an asset. screened, and calibrated. This is an ongoing However, the ability to weigh objects means that data analysis function that requires reliable and the mass would also have to be replicated in accurate orbit computation. Calibration order to be credible. Because the cost of space computations are no more accurate than the objects depends on the mass in orbit, such a precision ofthe orbit, which, in low altitudes, is requirement sharply reduces the attractiveness limited by the estimation of the drag force. of decoying. Issues such as response time and A fmal application for precision orbits is accuracy become paramount, of course, since collision avoidance. A growing population of decoy strategies are manifold. cataloged objects in space, almost 7,000 in low Weighing satellites can also be used inthe low-
206 The Lincoln Laboratory Journal. Volume 1. Number 2 (1988) Gaposchkin et aI. - Analysis ojSatellite Drag altitude regime, where there is considerable atmospheric drag force. The calculation of debris. The debris population is continually neutral density from thermospheric models is changing as it is depleted by atmospheric drag only one piece ofthe problem; a number ofother and replenished by a variety of sources, issues have to be addressed to achieve the including breakups and new rocket launches. desired capabilities. An organized observation and analysis program As shown in Fig. 1, the drag force per unit is required to assess properly the population mass on a satellite, which is the measured force, statistics and thus the hazard presented by is debris. A critical element of space debris 1 ( A ) 2 characterization is the measurement of each F=2 Cd M pVs (1) particle's mass, which is feasible with a good drag model and accurate tracking data. where Cd is the ballistic coefficient, AIM the area-to-mass ratio, p is the atmospheric density, and V is the speed of the satellite with respect Geophysical Investigations 5 to the atmosphere. Vs is the vector sum of the Drag models used for operational tracking can ' speed of the satellite, Vsat and the speed of the provide significant insights into the atmosphere, Vatms (wind speed). In our analysis, fundamental physics of the thermosphere. we assume that the lower atmosphere corotates Excellent models have been derived from with the earth. analysis of tracking data. Such tracking data One of the main problems in determining the can also provide basic information for testing drag on a satellite is that none of the quantities models. For example, drag data can be used to in Eq. 1 are known exactly. Consider the assess the models' performance and to definition of Cd' given in Fig. 2. Cd' which must determine basic constants within models. Drag be determined for each satellite, depends on the data can also be used to calibrate other type of scattering that takes place between the atmospheric sensors, such as instrumented surface ofthe satellite and the neutral particles satellites. Over the longterm, we hope to develop in the atmosphere. But there are fundamental a complete thermospheric model, based on unknowns in the physics of scattering. For physical principles, that combines observations example, we cannot reliably predict how of constituents from satellite instruments with particles in free molecular flow scatter from a total density obtained from analysis of satellite surface in space, nor do we know how that drag. surface and the scattering change after IOIJ.g Other geophysical investigations depend on exposure in space. precision orbit computation. Currently, there A theory ofscattering is summarized in Fig. 2. are low-altitude satellites that measure the Verification of the theory is needed, along with earth's geopotential, its motion in space, its determination of several constants. Figure 2 polar motion, and its rotation rate. Atmospheric gives the mathematical formalism for solar drag is a significant error source in the analysis radiation pressure, neutral drag, and charge of these low-altitude satellites. In addition, drag, three effects thatshare common elements. several low-altitude geophysical sensors (eg, It is, therefore, instructive to consider them MAGSAT, SEASAT, GEOSAT, TOPEX, ERS) together. In all three cases, the force on a general need to know the position of a satellite at the surface element depends on the scattering time of measurement. Again, improvement in mechanism and on the flux of photons, neutral drag modeling will directly improve the analysis particles, or charged particles. of this type of geophysical data. Two scattering mechanisms are indicated: Outline of Drag Problems specular scattering and a Lambert's law "diffuse" scattering. These two are considered to The satellite-tracking community is mainly be the limiting cases, one in which the scatterer interested in the determination of the completely "remembers" the information about
The Lincoln Laboratory Journal. Volume 1. Number 2 (1988) 207 Gaposchkin et aI. - Analysis ojSatellite Drag
SURFACE ELEMENT SPHERE
w a: :::> k, + k = 1 If Element Reradiates All Energy (/) 2 (/) w a: a.. s =s fa 0 )2 So = 1.35 X 106 erg/(cm2s) z o 0\ rO ~ o So 5 2 <{ qo =C =4.65 X 10- dynes/cm a:
2.- 2 F= 2 cd (A)pVM s 6[2.~(~:)2 ,25(~:f]
<.9 <{ a: 6 [ ~ (~:). ,8 (~~)] o 5 ....J <{ a: I 0, = CJ.L sin 20\ :::> 2(, -} - w \' (1 + J.L)2 ) Z
2 <.9 <{ 1 _ e U(R) R a: --0 o E(kT) D w D = --€a kT) Debye Length <.9 2 a: ( e ne <{ R I --00 U D Fig. 2 - Mathematical formalism - nongravitational forces. the incoming flux vector-momentum (specular), surfaces do not behave completely as specular and the other in which no information is or diffuse. A better model would be to assume a "remembered" (diffuse). Other scattering fractional part of both the diffuse and specular mechanisms are also possible; in general, components on the satellite surface. 208 The Lincoln Laboratory Journal. Volume 1, Number 2 (1988) Gaposchkin et at. - Analysis ojSatellite Drag For neutral drag, the scattering interaction as low-altitude drag; the cumulative effects take depends on the surface material ofthe satellite, months to be operationally significant. Yet the and on the molecular weight and temperature, existence ofthis drag, notpredicted byany ofthe or thermal velocity (V~. of each particle. The current models. indicates a flaw in our thermal dependence is theoretically modeled in understanding ofthe thermosphere. We cannot terms of the ballistic coefficient. The molecular accept a model as comprehensive if it does not weight ofthe atmospheric constituentand ofthe satisfactorily explain all observed atmospheric surface material of the satellite are modeled phenomena. through an accommodation factor. 8 (81 for Further difficulties in determining specular scattering and 82 for diffuse scattering). atmospheric drag are caused by the geophysical However, even if the chemical constituents of inputs to drag models. In the previous section the atmosphere are known (using laboratory we identified a number of uses that are time measurements (6)), the value of Cd can not be critical, ie, that need results within hours to be determined to better than 5% (7). useful. Most of the present suite of models use A, K The projected cross section in Eq. 1. also geophysical parameters such as FlO.7 and p as mustbe determined for the majority ofsatellites. measures of energy input to the atmosphere. In general. the cross section depends on a These are surrogate parameters to begin with. satellite's aspect angle. which is often difficult to since direct measurements of the ionospheric calculate and probably has to be observed. In current and the solar extreme ultraviolet (EUV) our study we determined the atmospheric drag flux are not available. The indexes that are used K A on selected spherical satellites so thatquestions have certain inherent problems. The p and p of aspect did not arise. To calculate AIMin Eq. are planetary indexes and so cannot represent localized disturbances. (K and A are both I, the true mass must also be known. This value p p is essential ifdrag measurements are to be used measures of the geomagnetic index; they are to predict absolute density. monotonically related by a nonlinear function.) The next term in Eq. 1 is p. the atmospheric The F10.7-cm flux. on the other hand. can density. This value is usually predicted by represent the EUV solar flux, although it. in thermospheric models. although the models itself, has no direct influence on the themselves do not predict the density to better atmosphere. The models also assume that we than 15% at low altitudes (less than 300 km). use data obtained after careful calibration and The model prediction becomes worse with reduction by the geophysical service operated increasing altitude. jointly by NOAA (National Oceanic and The last term in Eq. 1 is the speed ofa satellite Atmospheric Administration) and the USAF. with respect to the atmosphere. The speed of a Generally. the final data values are available satellite with respect to the earth is known with only after some weeks or months and are not fairly high precision. However. Vs also depends available for time-critical missions. We must. on the speed of atmospheric winds. Satellite therefore. use predictions ofthese values based experiments. drag analysis, and theoretical on incomplete information. models show that there are significant winds Table 2 summarizes the problems associated and gravity waves in the thermosphere. Since with determining atmospheric drag. these winds can have speeds ofseveral hundred meters persecond. a speed that is comparableto Present Drag Models satellite velocities, any advance in modeling of satellite drag must therefore include Thermospheric density models for heights information about winds. above 120 km have been derived from the Abundant evidence shows that atmospheric analysis of satellite drag since the launch of drag affects all satellites. even though the effect Sputnik 1. Satellite drag measures only total may be small at high altitudes. For space density and contains no direct information surveillance. high-altitude dragis notas serious about satellite composition. Early models The Lincoln Laboratory Journal, Volume 1, Number 2 (1988) 209 Gaposchkin et aI. - Analysis ojSatellite Drag identified the fundamental dependence of the upper atmosphere on solar flux; geomagnetic Table 3. Seven Density Models Tested index; and diurnal, monthly, and seasonal variations. Atmospheric models based on J71 Jacchia 71, aka CIRA 1972 DTM Barlier et al., 1978 satellite drag data are typified by the COSPAR MSIS83 Hedin, 1983 International Reference Atmosphere of 1972 J77 Jacchia 77, as defined in SAO (CIRA72), which is based on the Jacchia 1971 SR 375 model [1], and by the DTM 1978 model [3]. J77' Jacchia 77 + analytical Atmospheric composition can be inferred or approximation measured using both ground-based incoherent J77" Jacchia 77 + 1981 changes in AFGL report backscatter radar measurements and satellites J77'" Jacchia 77 + 1981 changes + instrumented with mass spectrometers and analytical approximation accelerometers. This type ofdata has been used to construct the so-called mass spectrometer and incoherent backscatter (MSIS) models [4.8,91. Jacchia attempted to merge drag and composition data into a combined model: Jacchia 1971 (CIRA72) model, because it is a Jacchia 1977 [2]. The Jacchia 1977 model has widelyused standard, and the DTM 1978 model, two modifications: a 1977 addendum, and a which was designed specifically to evaluate revision [10]. An additional version of the satellite drag. During the analysis. however, a Jacchia 1977 model, known as the Jacchia number ofissues concerning the Jacchia model Bass model [11. 12]. was developed at the Air arose. which required testing ofseveralvariants. Force Geophysical Laboratory. At this point, the results on seven models have These models are all relatively simple. They been assembled. The development and testing of can be characterized as static diffusion models these models led to insights into the models and that only incorporate dynamics implicitly. The the scattering mechanisms they use. processes are. as yet, too complex to formulate The seven models are listed in Table 3. The a model based on physical principles alone. four versions ofthe Jacchia 1977 model evolved The modelswe tested initiallywere theJ acchia because of two revisions dealing with 1977and the MSIS83 models. We also tested the geomagnetic effects. The first was an analytic approximation to a geomagnetic effect described by Eq. 32 in Ref. 2. The second revision resulted from combining drag data with ESR04 satellite data [10]. These revisions are discussed in more detail in Ref. 7. J77' includes the analytic Table 2. Summary of Problems approximation, J77" includes the revision in Associated with Atmospheric Drag Ref. 10. and J77'" includes both sets of revisions. Physics The J71. J77, J77', and DTM models are Satellite Aspect Geophysical Input: predominantly based on satellite drag Accuracy and Prediction measurements obtained in the region from 250 Composition, Temperature, to 1.000 km. The J77" and J77''' models also and Density Models incorporate a considerable amount of satellite Winds and Super-Rotation measured composition data from the ESR04 Gravity Waves satellite at altitudes ranging from 250 to 800 km High-Altitude Drag and less than 40 degrees in latitude. The MSIS model is completely based on satellite mass 210 The Lincoln Laboratory Journal. Volume 1. Number 2 (1988) Gaposchkin et aI. - Analysis ojSatellite Drag ratios of the densities predicted by the Jacchia Table 4. Timing Test of 71, J77, J77', J77"', and MSIS83 models to the Atmospheric Models those predicted by the J77" model for the 300 km altitude. This simulation was performed to J71 11 .1 0 seconds see how the models differ. The J77" model was DTM 16.22 seconds selected as the standard model because it was J77 35.38 seconds found to be the best overall model in predicting J77' 41 .98 seconds satellite drag for our data set. All hour angles J77" 33.26 seconds were. sampled with latitude coverage between J77'" 36.70 seconds MSIS83 116.84 seconds (86.74) +60 and -60 degrees. The daily and average solar flux values were set at 74 (a low solar flux condition), and a Julian date of46144was used. spectrometer and ground-based incoherent The results for two different K values p scatter data, the latter used primarily to corresponding to a typical mean K value p measure neutral temperatures. The majority of (K = 2.5) and to a high K value (K = 5.0) are p p p mass spectrometer data was obtained from the presented in Table 5. In each case, 2,500 data Atmospheric Explorer satellites in the altitude values were averaged. regions from 100 to 500 km. The results show that at 300 km the models A timing test was performed on each of the are all in reasonable agreement. A 15% different models. In the test, each model was difference betweenthe mean ratios ofthe models called 4,000 times in a variety of positions and is apparent. Although it is known that hour angles. The results are presented in atmospheric models cannot predict densities to Table 4. better than 15% (a number that increases at The two times listed for the MSIS83 model higher altitudes), we would like a 5% prediction refer to the geomagnetic A parameters that p capability of drag, and aim for a 1% capability. were used as input. The MSIS83 program has We have found thattheJ77,J77', andJ77"'are the option of using either the daily value of the clearly inferior to the J77" in all cases (7). These A or an array ofseven A indexes, including the p p models were not evaluated further. daily A index and time averages of the three p hour A indexes. The shorter time listed for p Measurements of Satellite Drag MSIS83 refers to a program run with only the daily A value input. From the standpoint of p The rest of this paper investigates orbital decay, no significant difference was measurements of satellite drag and suggests found between these two options. In our improvements that can be implemented in standard procedure, the array of A values as p future drag models. In particular, we describe inputs to the MSIS83 model was used. the measurementswe made ofatmospheric drag Our timing test shows that the MSIS83 model and howwe used the measurements to evaluate is significantly slower than any of the Jacchia the atmospheric models. We also used these models. This result contradicts the general measurements to evaluate different consensus in the community, which is that the atmospheric indexes, including those currently J77 model is much slowercomputationallythan used as inputs and a new index that is not yet either the J71 model or the MSIS model [13, 14). being used by the models. We assume that this discrepancy is caused by Measurements of satellite drag were acquired our implementation ofthe J77 model; we used a by taking daily tracks ofspherical satellites from look-up table similar to that used in the J71 Lincoln Laboratory and NASA facilities. Lincoln program. Note also that the DTM model runs Laboratory operates two satellite-tracking faster than any the models except the J71 radars that provide datawith an accuracy of 1 m model. [15-17). One ofthese systems is the Altair radar We ran a computer simulation comparing the on the Kwajalein Atoll (Marshall Islands); the The Lincoln Laboratory Journal. Volume 1. Number 2 (l988) 211 Gaposchkin et aI. - Analysis ojSatellite Drag Table 5. Comparison of Densities Derived by the Various Atmospheric Models to the J77" Model at 300 km K = 2.5 K = 5.0 p p Mean Ratio Standard Deviaton Mean Ratio Standard Deviation (Modef!J77'') (%) (Model/J77") (%) 1. Jacchia 71 1.082 6.5 1.16 9.1 2. Jacchia 77 J77 0.886 6.3 0.81 8.7 J77' 0.872 7.3 0.81 9.4 J77" 1.000 0.0 1.00 0.0 J77''' 0.880 8.4 0.78 14.3 3. DTM78 0.867 5.3 0.81 5.1 4. MSIS83 0.934 9.3 0.93 10.2 other is the Millstone L-band radar in Westford, until convergence. Figure 3 shows this MA. NASA operates a network of laser-ranging procedure. In addition to a model for stations that provide data on satellites equipped atmospheric drag, DYNAMO uses a full with cube comer reflectors. The accuracy of geopotential model (20), plus models for lunpr these data is better than 2 cm (18). and solar perturbations (ephemeris in the For two satellites, LCS4 and COSMOSl179, J2000 system (19)), body and ocean tides (21), dailytracks havebeentakensincethebeginning solar radiation pressure, earth-reflected albedo of 1985. Daily tracks on the third satellite, EGS pressure, and general relativity. (also known as Agasii), have been taken since Atmospheric density models were used in the launch in 1986. Data from all of 1985 have been orbit computation ofthese data sets to calculate analyzed for the former satellites, as well as the atmospheric drag. When used, these models initial two months ofdataon EGS in 1986.These include the final F10.7-cm solar flux and satellites are described in Table 6, where the geomagnetic index Kp data (22). A scale semi-majoraxis (a) and the perigee height (q) are parameter (5) is also introduced in the least- given in km, AIM is given in cm2 Ig, and the squares orbit determination program. inclination (1) in degrees. The eccentricity is e. S is a least-squares-fit parameter that is used The orbit computation program DYNAMO for each orbital arc and that scales the entire uses an iterative least-squares procedure to fit drag model. It can be interpreted as an the data. The program begins with an initial or indication ofthe adequacy ofthe drag, and thus reference state that is differentially corrected ofthe thermospheric model used to computethe Table 6. Satellites Used for Evaluation of Density Models Cospar# NSSC# Name a(km) e 1(0) q(km) AIM 198037 A 11796 COSMOS1179 7,028 0.051 82.9 270 0.038 1971 67 E 5398 LCS4 7,207 0.008 87.6 780 0.285 198661 A 16908 EGS 7,878 0.001 50.1 1,500 0.045 212 The Lincoln Laboratory Journal, Volume 1, Number 2 (1988) Gaposchkin et aI. - Analysis ojSate!lite Drag True State X Satellite Estimate X" Estimated State X* Differential Correction F* = S ~ Cd (~) p V~ (X*) Fig. 3 - Orbit determination procedure. Satellite Fdrag Is the Along-Track Drag Force per Unit Mass Acting on a Satellite F* = 2- C (A) P V2 Used In X* Reference State drag 2 d M s - - ~ (A) 21 Used In X. Fdrag - S[2 Cd M P V~ _ Estimated State Cd = Ballistic Coefficient - Known for Most Spheres A M = Area-to-Mass Ratio of Satellite - Known for Most Spheres vs = Satellite Velocity Known p = Atmospheric Drag Fig. 4 - Estimation of drag force. The Lincoln Laboratory Journal. Volume 1. Number 2 (1988) 213 Gaposchkin et aI. - Analysis ojSatellite Drag drag. If S is less than unity, then the model over a year's time. atmospheric density predicted by the model is Scale factors were computed for each satellite too large; if S is greater than unity, then the and for each atmospheric model. In addition, atmospheric density predicted by the model is scale factors were computed for both the too small. See Fig. 4 for further clarification ofS. specular- and diffuse-scattering case. These With a complete force model, and the scale data are summarized in Table 7. The first term factor, the orbital arcs do generally fit within the under each satellite is the average scale factor. accuracy of the data (several meters). The S. for that data set; the second term is the orbital arcs are computed with one-day standard deviation, G. spacing, using between two and four days of The results for each satellite will now be data; anygiven pass ofdatawill be in atleast two discussed. orbit fits. This procedure is used for data validation, as well as for checking orbital COSMOSl179 consistency. The computed scale factors can be plotted as a function ofepoch and the plots used COSMOS1179 (COSMOS Series # 1179) is to give an indication ofhow the density model known to be a sphere. Its mass. however. is not involved in the drag calculation may be known from independent information. deficient. Figure 5 is an example of the scale Therefore, an AIM ratio based on an average factor data for COSMOS1179 and for the J77" drag has been adopted. Because of the use of 2.5 Mean = 1.073 Sigma = 0.143 2.0 • • ...0 1.5 •• (.) • • co • • LL • ,.• ~ , Q) • . . co ~. t~ ~( (.) en 1.0 ~ .. ~~ ••• 'I \fA].• •,. • 'I. • 0.5 0.0 ""'"----L--...... ---'--_-L...._---'-__..l..-_....I..-_--L.__L-----J 46068 46146 46223 46301 46378 46456 46107 46184 46262 46339 46417 Modified Julian Day Fig. 5 - Jacchia 77" diffuse scale for COSMOS1179. 214 The Lincoln Laboratory Journal. Volume 1. Number 2 (1988) Gaposchkin et aI. - Analysis ojSatellite Drag 200 Hour Angle 150 Ci 100 0) ~ 0) Cl 50 c <{... ::l 0 :::c0 0)' "0 ::l -50 ''::;... C1l ....J -100 -150 -200 ...... -_""'----__""'----__""'----__....l..-__....l..-__....l..-__....l..-_---J 46050 46100 46150 46200 46250 46300 46350 46400 46450 Modified Julian Day Fig, 6 - Latitude and hour angle for COSMOS1179. this assumption, COSMOS11 79 can only be and diffuse cases, because the drag at 295 kIn is used for a relative assessment of atmospheric primarily from oxygen and nitrogen. The mean models. The scale factors for J77" were molecular weight is approximately 16, which computed assuming a diffuse-scattering results in a value for the accommodation mechanism and are presented in Fig. 5. coefficient, the term used in the model for diffuse Throughout the time period analyzed, the scattering, of nearly 1. An accommodation eccentricity of COSMOS1l79 has been large coefficient of 1 results in the same value ofCd as enough that drag occurs mainly at perigee, that predicted by the model for specular where the scale height is about 7 kIn. Therefore, scattering. The scale factors for the specular the orbit only samples the density at one scattering are not significantly different. geographic point per revolution. Figure 6 gives As mentioned, the absolute mean scale factors the latitude and solar hour angle of the perigee are not significant in this satellite. However, the pointfor the interval analyzed. Bothlatitude and fact that the scale factors differ by at most 5% hour angle are completely sampled, and there is indicates that all the models are in good no simple correlationwith thevariationinS seen agreement. The variation about the mean is in Fig. 5. smallest for the J77" model, though all the These factors were computed for the satellite models differ by 2% at most. On this basis one using the assumption of specular scattering. could marginally choose the J77" as the best The mean values of the scale factors for the two model. This difference is not believed to be cases are fairly similar, as can be seen in Table significant. All models are equally good (or bad) 7. From the theoretical standpoint, a significant at 275-kIn altitude for all latitude, hour angle, difference is not expected between the specular and geophysical data. The Lincoln Laboratory Journal, Volume 1, Number 2 (I 988) 215 Gaposchkin et aI. - Analysis ojSatellite Drag LCS4 LCS4 on launch. Both spheres were carefully measured, including the mass. which was given LCS4 (Lincoln Calibration Sphere #4), a sat in the records as 38.186 kg for the "G" sphere, ellite in a circularorbitat approximately 780-krn and 35.203 kg for the "C" sphere. Because the altitude, was built by Lincoln Laboratory. Its two spheres were unmarked and virtually in physical characteristics, such as AIM and the distinguishable, we cannot rule out the composition ofits outersurface (aluminum), are possibility that they were interchanged dUring known. Because of its nearly circular orbit, the ground handling, and that the "G" sphere satellite does not provide a clear association of actually made it to orbit as LCS4. Recent positionwith the effect ofdrag; nevertheless, the analysis of LCS4 solar radiation pressure average drag can be analyzed. perturbations has resulted in estimates of the At 780 krn, the scale factors for the models are mass consistent with the originally adopted "C" quite different from those found for sphere. In this case. all the recent density COSMOS1179. The orbital fits have been models are in betteragreement with the data. To carefully scrutinized. The observed variability in account for this possibility, the scale factors can S is believed to represent real variations in the be multiplied by 1.085. Then. assuming atmospheric density at 780-krn altitude, which specular reflection. the MSIS83 has a mean are not predicted by any of the models. In all scalefactorofvirtual unity, and theJ77" is 0.95. cases, it can be seen that the scale factors are Both values are within the uncertainty ofCd' In 20% to 30% less than unity. indicating that the any event, the recent models are in acceptable predicted drag is too large by this factor. average agreement at 780 krn, although there At 780-krn altitude, the principal atmospheric are large variations in the density that are not constituents are hydrogen and helium. For modeled. DTM is the model with the smallest these constituents. the difference between Variability for LCS4. specular and diffuse scattering is quite large, resulting in diffuse ballistic coefficients 20% to EGS 30% larger than specular ones. The mean scale factors, assuming the specular-scattering EGS (Experimental Geodetic Satellite) is a mechanism. are all approximately 0.9. The spherical satellitein a circularorbitat 1,500-krn general agreement among the various models altitude, eqUipped with laser cube comer persuades us that reflectors. The laser ranging data. provided by a) the specular-scattering model is correct NASA since launch in July 1986. has allowed for the polished aluminum spherical the study ofthe density model at 1.500 krn. This satellite, and altitude is higher than any of the data used in b) there may be a systematic overestimate constructingthe models and measures howwell of the density.by as much as 12%. the predicted densities of the models can be The J71 model has the best mean value and extrapolated. The EGS satellite has a known the DTM has the smallest Variability. However, AIM, which is given in Table 7, and a surface the differences may not be significant - the un made of aluminum with holes for the laser cube certainty in Cd may be as much as 4%. comer reflectors. A further issue arises because of uncertainty Preliminary calculations on two months of about LCS4. This satellite was one of two data have been performed with the MSIS83 and satellitesfabricated by Lincoln Laboratoryatthe J77" models. The scale factors were computed same time. Both satellites were one-square for both a diffuse- and a specular-scattering meter radar calibration spheres made of mechanism. Since the atmosphere at 1.500 krn polished aluminum, identical in all but one is mostly hydrogen. a significant difference in respect. The records show that one sphere, the the result would be expected. In Table 7, the "G" sphere. failed on launch and never made it specular-scattering assumption leads to scale to orbit. The second, the "C" sphere. became factors of 1.9 and greater; the MSIS83 mean 216 The Lincoln Laboratory Journal. Volume 1, Number 2 (1988) Gaposchkin et aI. - Analysis ojSatellite Drag value is 2.39. The conventional diffuse-scat quantifies the intensity and spatial extent of teringmodel gives an average scale factor of 1.39 high-latitude particle precipitation, based on fortheJ77" and 1.67for the MSIS83. Apnonone observations made along individual passes of would choose diffuse scattering for aluminum, the NOAA/TIROS weather satellites, The and this was adopted. The analysis shows that satellites, which are in circular sun J77" underestimates the density at 1,500 km synchronous orbits at 850 km [23], measure the by about 30%; MSIS83 underestimates the precipitation index in near real time. We density by about 60%. This is consistent with analyzed the power levels of the precipitation the results for LCS4, where J77" was found to index. give larger densities than MSIS83 atthe 780-km The atmospheric parameters were averaged altitude. over the same time interval as the data used to Evaluation of Atmospheric Indexes compute the orbital arcs. For COSMOS11 79, three days of data were averaged for each In addition to evaluating the atmospheric parameter; for LCS4, four days of data were models, the derived scale factors can be used to averaged. Each series of atmospheric data was determine how well the effects of the different then correlated againstthe series ofscale factors indexes are being modeled and to evaluate determined for both satellites, using each ofthe whether a new index is of value to future four different atmospheric models. In some modeling efforts. We did this by correlating the cases, a single model had two series of scale series of derived scale factors with different factor data - the scale factors corresponded to series of atmospheric indexes, including the specular and diffuse scattering. Whether daily F10.7-cm flux, the K, and the scattering was specular or diffuse did not affect p precipitation index. the correlation of the series of atmospheric The precipitation index is the only parameter parameters against the series of scale factors. we studied that is not being used as an input to The results for each atmospheric parameter any of the atmospheric models. This index are presented inTables 8a, b, and c. In all cases, The Lincoln Laboratory Journal, Volume 1, Number 2 (1988) 217 Gaposchkin et aI. - Analysis ojSatellite Drag the correlation coefficients were computed from data sets that are correlated. scale factors and geophysical data with the Based on the data for the lower satellite, the average subtracted. ie. these data have zero MSIS model shows slightly less correlation with mean. A correlation coefficient was determined Kp than does the Jacchia 1977 model, indicating for each atmospheric model and each satellite; a that it better models the atmospheric response value of greater than 0.2 was considered to be to changes in this index. We should point out significant correlation. The data discussed in that the MSIS model uses the A index, rather p Table 8 are from the first six months of data in than the K index. We computed the correlation p 1985. with one exception. The bracketed value between the A index and these data sets. The p intheJ77" columns for COSMOS11 79 Diffuse is resultswerevery similarto the results presented the data for all of 1985. in Table 8b. The correlation of the DTM model The results of the correlation between the with K at 275 km is similar to the others (0.40). p series ofdaily FlO.7-cm values and the series of but at 780 km it has a significantly smaller determined scale factors are given in Table 8a. correlation (0.09). For the lower satellite. the F10.7-cm flux is The results of the correlation between the modeled fairly accurately. Problems that existed precipitation power index and the scale factors in the J71 model seem to have been corrected in are given inTable 8c. As theTable 8c shows. this the later models. indexhas a significant correlationwith the scale The results of the correlation between the Kp factors of the atmospheric models and both indexes and the scale factors are given in Table satellites. Ofall the parameters we investigated. 8b. The K index is used to model the influence the highest average correlation coefficients were p of geomagnetic fluctuations in the atmosphere. seen with this index. Figure 8 illustrates in The K values and the series of scale factors greater detail the correlation between the scale p determined for both satellites appear to have a factor data and the precipitation index. The significant correlation. precipitation index is not used by any of the Figure 7 shows the correlation between the K p models to predict the atmospheric response to data and the scale factors for the Jacchia 1977 geomagnetic activity. Based on these data. we S and the MSIS83 S models. (S indicates think that the precipitation index should be specular scattering.) The mean of each data set included in future atmospheric models. There is has been determined and subtracted from the significantcorrelation between the precipitation series. The y-axis therefore represents the data, index and the K p' The correlation coefficient with the mean subtracted; the x-axis represents between the K and precipitation data sets is p time. These data illustrate the features in the 0.47; some of the correlation observed with the Table 8a. Correlation Coefficients for F10.7 cm Flux COSMOS1179 LCS4 Specular Diffuse Specular Diffuse J71 0.18 0.35 J77" -0.14 -0.15 (-0.02) -0.07 -0.01 DTM78 0.02 0.12 0.12 MSIS83 0.04 0.06 0.11 0.02 218 The Lincoln Laboratory Journal, Volume 1, Number 2 (1988) Gaposchkin et al. - Analysis ojSatellite Drag Table ab. Correlation Coefficients for Kp COSMOS1179 LCS4 Specular Diffuse Specular Diffuse J71 0.21 -0.24 J77" 0040 0.39 (0.27) 0.27 0.29 DTM 0040 0.09 0.14 MSIS83 0.28 0.35 0.28 Jacchia 19775 M515 19835 Correlation = 0.40 Correlation = 0.28 145 100 105 70 65 40 (0 x en Q) 1'"0 ,.... C ,....- 25 10 • -15 -20 -55 -50 0 50 100 150 200 0 50 100 150 200 Correlation = 0.27 Correlation = 0.35 50 50 30 20 10 co x en Q) ("1)"0LOE -10 -10 -40 -30 -50 -70 L....._...... -'-__--" -'-__---I 0 50 100 150 200 o 50 100 150 200 Day (1985) Day (1985) Fig. 7 - Correlation of Kp index with scale factors. The Lincoln Laboratory Journal, Volume 1, Number 2 (1988) 219 Gaposchkin et aI. - Analysis ojSatellite Drag Kp could actually be leakage ofthe precipitation such as the precipitation index, as input index correlation. Clearly this issue needs more to the density models. data to be resolved. 4. Expanding the source of accurate tracking data on these satellites in order to increase the space and time resolution Summary of the drag determinations. We have tested atmospheric density models at 5. Examining the accuracy of forecasting 275 krn, 780 krn, and 1,500 krn. At the two lower drag for prediction of satellite orbits. altitudes, all models are in good agreement - in 6. Obtaining data on other low-altitude the sense that they give the same average satellites. performance. But they all exhibit significant departures from the actual density, and it is Conclusions necessary to include "solve for" parameters in 1. No model does an adequate job of orbit determination to match the tracking data. modeling the atmospheric density. We are continuing work in six areas: 2. There is no agreement on which model is 1. Extendingthe data for all three satellites, best. We find that the differences among to avoid any biasing due to seasonal models, though measurable, are much effects, and to improve the sampling. less than the agreement among the 2. Determining the mass of COSMOS 11 79 models. and LCS4 using satellite orbit 3. There are real physical variations in the perturbations. At present it is routine to atmosphere that are not modeled by any determine the mass of high-altitude of the current suite of atmospheric satellites from perturbations due to solar models. New model parameters are radiation pressure. For lower satellites, needed (eg, winds, gravity waves) [24]. • this method has not been possible until 4. The inclusion of the precipitation index now because the effects of geopotential in future atmospheric models should be model errors dominated the solution. investigated. Significant correlation was Recent geodetic solutions show promise observed between the precipitation ofchangingthe situation. In this case we index and the scale factors at 275 and can hope to make some statement about 780 krn. the absolute densities at 275-km 5. Overall, these models have at most 18% altitude and to clarify the ambiguity difference about the mean, when aver about the mass of LCS4. aged over all latitudes and hour angles 3. Exploring alternate indexes or variables, below 800 krn. However, the variance of Table 8c. Correlation Coefficients for the Precipitation Index COSMOS1179 LCS4 Specular Diffuse Specular Diffuse • J71 0.42 -0.15 J77" 0.48 0.46 (0.37) 0.36 0.40 DTM78 0.53 0.28 0.19 MSIS83 0.42 0.42 0.45 0.36 220 The Lincoln Laboratory Journal. Volume 1. Number 2 (1988) Gaposchkin et aI. - Analysis ojSatellite Drag Jacchia 1977S MSIS 1983S Correlation = 0.48 Correlation = 0.42 160 r------+....., 110 r------r------., 130 80 • 100 50 (0 x 70 0'1 Q) ""'"0,.... c: ,....- 40 20 10 -10 -20 -50 L..-__..L...-__....L...__....::.L__----' -40 '--__.L...-__....L.-__--J..__---' o 50 100 150 200 o 50 100 150 200 Correlation = 0.36 Correlation = 0.45 50 r------....",....------. 55 r------...... ,..---~ 30 ~ 25 co x 10 0'1 Q) ('t)"O LCl-=: -5 -10 -35 -30 -65 ...... __....L...__----' ...... __ -50 '----"'-----...... ---'-----' o 50 100 150 200 o 50 100 150 200 Day (1985) Day (1985) Fig. 8 - Correlation ofprecipitation index with scale factors. The Lincoln Laboratory Journal, Volume 1. Number 2 (1988) 221 Gaposchkin et aI. - Analysis ojSatellite Drag the model differences exceeds 16%. and in contributing unique data to 6. The J71 continues to perform monitor the next solar cycle. exceptionally well and is the fastest overall. The MSIS83 is, by a large factor, Acknowledgments the slowest. 7. For our overall use, balancing accuracy, We would like to acknowledge the individuals computer speed, and range ofheight, we who made this data available to us through the use the J77". radar tracking support provided by the Altair 8. Satellite drag data plays an important and Millstone radars. This work was sponsored role in understandingthe thermosphere, by the Department of the Air Force. • 222 The Lincoln Laboratory Journal. Volume 1. Number 2 (1988) Gaposchkin et aI. - Analysis ofSatellite Drag References 1980). AD-A-085781. 12. J.N. Bass, "Condensed Storage of Diffusion Equation 1. L.G. Jacchia, "Atmospheric Models in the Region from Solutions for Atmospheric Density Model Computations: 110 to 2000 kIn: in COSPAR International Reference AFGL-TR-80-0038 (Air Force Geophysics Laboratory, Atmosphere 1972, International Council of Scientific Hanscom Air Force Base. MA, 1980), AD-A-086863. Unions (Akademie-Verlag, Berlin, 1972), pg 227. 13. J.F. Liu. RG. France. and H.B. Wackernagel. "An 2. L.G. Jacchia, 'lhermospheric Temperature, Density. Analysis of the Use of Empirical Atmospheric Density and Composition: New Models: S.A.O. Special Report No. Models in Orbital Mechanics, Spacetrack Report No.4," 375 (Smithsonian Astrophysical Observatory, Cambridge. Space Command. U.S. Air Force (Peterson Air Force Base, • MA,1977). CO, 1983). 3. F. Barlier. C. Berger, J.L. Falin, G. Kockarts, and G. 14. G. Afonso, F. Barlier, C. Berger, F. Mignard. and J.J. ThuilIier, "A Thermospheric Model Based on Satellite Drag Walch, "Reassessment of the Charge and Neutral Drag of Data: Ann. Geophys. 34, 9 (1978). Lageos and Its Geophysical Implications: J. Geophys. Res. 4. A.E. Hedin. "A Revised Thermospheric Model Based on B 90. 9381 (1983). Mass Spectrometer and Incoherent Scatter Data: MSIS 15. E.M. Gaposchkin, "Metric Calibration of the Millstone 83," J. Geophys. Res. A 88, 10,170 (1983). Hill L-Band Radar," T.R. 721 (MIT Lincoln Laboratory, 5. G.E. Cook, "Satellite Drag Coefficients," Planet. Space Sci. Lexington, MA, 1985). AD-A-160362. 13. 929 (1965). 16. E.M. Gaposchkin, "Calibration of the Kwajalein 6. FA Herrero, ''The Drag Coefficient of Cylindrical Radars." T.R. 748 (MIT Lincoln Laboratory. Lexington, MA, Spacecraft in Orbit at Altitudes Greater Than 150 kIn: 1986), AD-B-104457. NASA, Technical Memorandum 85043 (Goddard Space 1.7. E.M. Gaposchkin, RM. Byers, and G. Conant, "Deep Flight Center. Greenbelt, MD. 1983). Space Network Calibration 1985." STK-144 (MIT Lincoln 7. E.M. Gaposchkin and A.J. Coster. "Evaluation of Recent Laboratory. Lexington, MA, 1986). Atmospheric Density Models: Adv. Space Res. 6, 157 18. E.M. Gaposchkin, L.E. Kurtz, and A.J. Coster, "Matera (1986). Laser Collocation Experiment," T.R. 780 (MIT Lincoln 8. A.E. Hedin, J.E. Salah, J.V. Evans. CA Reber. G.P Laboratory, Lexington, MA, 1987). Newton, N.W. Spencer, C. Kayser. D. Alcayd. P. Bauer, L. 19. G.H. Kaplan (ed.). 'lhe!AU Resolutions ofAstronomical Cogger, and J.P. McClure, "A Global Thermospheric Model Constants, Time Scales and the Fundamental Reference Based on Mass Spectrometer and Incoherent Scatter Data: Frame." Naval Observatory Circular No. 163 (Naval MSIS 1; N2 Density and Temperature." J. Geophys. Res. 82, Observatory. Washington, DC, 1981). 2139 (1977). 20. F.J. Lerch, S.M. Kloski. and G.P. Patel, "A Refined 9. A.E. Hedin. C.H. Reber. G.P. Newton. N.W. Spencer, H.C. Gravity Model from Lageos" (GEM-L2). Geophys. Res. Brinton, and H.G. Mayr. "A Global Thermospheric Model Letters 9, 1263 (1982). Based on Mass Spectrometer and Incoherent Scatter Data. 21. E.W. Schwiderski, "Global Ocean Tides, Part 1. A MSIS 2. Composition: J. Geophys. Res. 82,2148 (1977). Detailed Hydrodynarnical Model: Rep TR-3866 (U.S. Naval 10. L.G. Jacchia and J.W. Slowey, "Analysis of Data for the Surface Weapons Center, Dahlgren, VA, 1978). Development of Density and Composition Models of the 22. Solar-Geophysical Data (U.S. Dept. of Commerce. Upper Atmosphere: AFGL-TR-81-0230 (Air Force Boulder. CO, 1985). Geophysics Laboratory. Hanscom Air Force Base. MA. 23. J.C. Foster, J.M. Holt. RG. Musgrove, and D.S. Evans, 1981), AD-A-100420. "Ionospheric Convection Associated with Discrete Levels of 11. J.N. Bass. "Analytic Representation ofthe Jacchia 1977 Particle Precipitation." Geophys. Res. Let. 13, 656 (1986). Model Atmosphere." AFGL-TR-80-0037 (Air Force 24. S.H. Gross. "Global Large Scale Structures in the F Geophysics Laboratory, Hanscom Air Force Base. MA, Region," J. Geophys. Res. A 90,553 (1985). The Lincoln Laboratory Journal. Volume 1. Number 2 (1988) 223 Gaposchkin et aI. - Analysis ojSatellite Drag EDWARD MICHAEL GA ANTHEA J. COSTER is a POSCHKIN is a senior staff staff member in the member in the Surveillance Surveillance Techniques • Techniques Group. He has Group, where she con received a BSEE from Tufts centrates on studies of the University. a Diploma in atmosphere. She conducts numerical analysis from her research at Lincoln's Cambridge University, and a Millstone radar site in PhD in geology from Harvard Westford, Mass. She re University. Mike's work at Lincoln Laboratory has been ceived a BA degree from the University of Texas in centered on problems in satellite surveillance; his efforts mathematics and an MS and a PhD degree from Rice have enabled Lincoln's Millstone radar to produce data of University in space physics and astronomy. Before joining geodetic quality. Before joining Lincoln Laboratory, Mike Lincoln Laboratory, Anthea worked for the Radar and spent 22 years with the Smithsonian Astrophysical Instrumentation Laboratory of the Georgia Tech Research Observatory. He is the author ofover 100journal articles in Institute. the fields of satellite geodesy, metric orbit analysis, and radar metric data improvements. " • 224 The Lincoln Laboratory Journal. Volume 1, Number 2 (1988)