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.