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The Impact of Maneuver Failures on the Eos Afternoon Constellation

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The Impact of Maneuver Failures on the Eos Afternoon Constellation THE IMPACT OF MANEUVER FAILURES ON THE EOS AFTERNOON CONSTELLATION Peter Demarest, Ph.D. Member AIAA, Member AAS a.i. solutions Inc. Lanham, MD ABSTRACT ground track and orbital spacing. And third, to ex- amine the effect of up to two satellites within the The first four satellites, Aqua, CloudSaL Calipso, constellation failing to perform a scheduled maneu- and Parasol, in NASA's EOS Afternoon constella- vet. tion will fly in similar orbits within 4 minutes of each other. This study was undertaken to exam- ine the effect of one or more missions failing to ESTABLISH CONSTELLATION perform a scheduled orbit maintenance maneuver. Tools were developed to rapidly calculate the ini- The first task performed was to determine the set of tial orbital elements for the satellites that estab- orbital elements which would place each satellite in lished the formation. Baseline maneuver strategies the desired position in the EOS-PM constellation, were implemented to maintain the desired spacing also called the PM train. Aqua is the lead satellite of the satellites. Maneuver failures were examined in the PM train and was placed in an orbit which and close approach opportunities were identified. It has a 16 day, 233 orbit repeat cycle corresponding to was found that close-approaches between CloudSat the World Reference System (WRS-2) grid used by and Calipso could occur in less than one day after a Terra and Landsat-7. In this orbit, a satellite will missed maneuver if close coordination between the fly over the same point on the ground every 16 days. missions is not achieved. Aqua's nominal mean local time at the ascending node is I:30PM, though it is allowed to drfit between I:30PM and l:45PM. Parasol is also on the WRS-2 PURPOSE grid, but will follow behind Aqua by 240 seconds, The first four satellites inlt_e Earth Observing measured at the ascending node (this lag is referred System Afternoon (_) Constellation: Aqua, to as orbit phasing or phase time). CloudSat and CloudSat, Calipso, and Parasol, will fly in relatively Calipso will fly in close formation with each other, close proximity. Though each satellite can be main- Calipso 120 seconds behind Aqua and CloudSat 105 tained independently within its desired control box, seconds behind Aqua. CloudSat and Calipso both failure to perform expected maneuvers could impact have a 16 day, 233 orbit repeat cycle but their mean the other missions. This study was performed to local time at the ascending node will be 75 seconds examine and characterize the effect of selected se_s later than Aqua's, resulting in a ground track offset of satellites failing to perform scheduled maneuvers. relative to Aqua's and the WRS-2 grid. The focus was on understanding the level of coordi- A starting epoch of October 10, 2004, a date af- nation and responsiveness needed between missions ter all missions will be operational and after Aqua's to avoid close approaches between the spacecraft. mid-mission inclination maneuver, was chosen for The analysis was broken up into three tasks. this analysis. All of the orbits were assumed to First, to determine a set of initial orbital elements have an inclination of 98.144 ° . An eccentricity(e) of for each satellite that establishes the constellation 0.0012 and argument of perigee(w) of 90° was chosen and meets mission requirements. Second, to imple- to maintain each satellite in a frozen orbit which has ment a nominal maneuver strategy for each satellite. no secular drift in either eccentricity or argument of These strategies will maintain the satellite's required perigee. To determine the semi-major axis(a) and right tenance maneuvers. This emphasizes the need to match the initial elements to the gravity model when ascension(f_) for Aqua, a two-level iterative process was developed. The nonlinear solvers in MatLab [1] calculating maneuvers. were used to drive a FreeFlyer TM script that prop- Figures 1-4 show the ground track error relative to agated the orbit and calculated the desired orbital the WRS-2 grid for each satellite. The small(< 150 parameters. The inner iterations of the two level m) variations are typical and due to the tesseral scheme would adjust a and f_ until the satellite was terms in the gravity field. The important character- placed in a repeating orbit; on the WRS-2 grid. The istic is the zero average slope, which confirms that outer iterations would adjust the initial epoch and the orbit has the desired repeat cycle. It can also repeat the inner iterations until the desired mean be seen that Aqua and Parasol are on the WRS-2 local time at the ascending node was achieved. This grid while CloudSat and Calipso are offset 13.9 kln approach is similar to that used by Lim [2] and and 20.85 km westward, respectively. Without at- Webb [3] to calculate the ICESat repeating ground mospheric drag, the three trailing satellites maintain track. a constant, fixed distance behind Aqua, measured A similar process was used to place the three both in phase, Figure 5, and range, Figure 6. trailing satellites in line relative to Aqua. A single level iteration scheme was used in which semi-major Aqua Ground Track Error axis, longitude of the ascending node, and the initial epoch were varied until the desired phasing, repeat 0.40 orbit, and mean local time offset were achieved. 0.20 Aqua Parasol 0.00 Epoch Oct 10 2004 Oct 10 2004 01:29:08.181 01:32:51.701 ill -0.20 BLJ2 a (km) 7077.675317 7077.674753 BLJ2 e 0.0012 0.0012 -0.40 BLJ2 i (o) 98.144 98.144 BLJ2 f_ (°) 221.439870 222.442370 10102104 10/16/04 10130104 11/13/04 11/27104 BLJ2 w (°) 90 90 Epoch BLJ2 M (°) 1 0 Mean Local Time 1:30:00 1:30:00 Figure 1: Aqua Ground Track Error, No Drag, 4x4 eloudSat Calipso Geopotential Epoch Oct 10 2004 Oct 10 2004 01:30:36.701 01:30:51.701 BLJ2 a (km) 7077.674276 7077.674251 CloudSat Ground Track Error BLJ2 e 0.0012 0.0012 BLJ2 i (°) 98.144 98.144 -13.60 BLJ2 f_ (°) 221.753372 221.753541 BLJ2 co (°) 90 90 -13.80 BLJ2 M (°) 0 0 Mean Local Time 1:31:15 1:31:15 -14.00 U3 Table 1: Initial Orbital Elements, 4x4 Geopotential -14.20 -14.40 The initial or reference Brouwer-Lyddane(J2) ele- ments for the four satellites are listed in Table 1. 10102104 1O/16/04 10130/04 11 /13/04 11127104 Similar results were achieved using higher order Epoch gravity fields. It is worth noting that although the behavior of the orbit doesn't change based on the Figure 2: CloudSat Ground Track Error, No Drag, number of geopotential terms modeled, the change 4x4 Geopotential in semi-major axis, compared to the 4x4 case shown, is of the same magnitude as the required orbit main- Calipso Ground Track Error -20.60 -20.70 Satellite Phasing 350.00 -20.80 CloudSatbefiind Aq_Ja Calipso behind Aqua ........... 300.00 -20.90 Parasol behind Aqua -- -21.00 "6" 250.00 tlJ -21.10 200.00 -21.20 -21.30 150.00 -21.40 100.00 10/02/04 10116104 10/30/04 11/13/04 11/27/04 Epoch 50.00 10102/04 10/16/04 10/30/04 11/13/04 11/27/04 Figure 3: Calipso Ground Track Error, No Drag, Epoch 4x4 Geopotential Figure 5: Orbit Phase behind Aqua, No Drag, 4x4 Geopotential Parasol Ground Track Error 0.40 0.20 Intersatellite Range 0.00 2400.00 CloudSat behind Aqua -0.20 Calipso behind Aqua ........... 2000.00 Parasol behind Aqua -- -0.40 g 1600.00 10102/04 10/16/04 10/30/04 11/13/04 11/27/04 g Epoch 1200.00 Figure 4: Parasol Ground Track Error, No Drag, 800.00 4x4 Geopotential 400.00 10102/04 10116/04 10/30/04 11113/04 11/27/04 Epoch NOMINAL MANEUVER STRATEGIES Figure 6: Intersatelite Range from Aqua, No Drag, Atmospheric drag is the dominant perturbing force 4x4 Geopotential on the satellite orbits and results in the need to perform maneuvers to maintain the satellites in for- mation. For this analysis the following maneuver strategies were chosen for each satellite. Aqua maneuvers independently, maintaining its ground track relative to the WRS-2 grid within 4-10 kin. This is equivalent to a 4-22 second control box relative to the reference orbit. Parasol is also maintained independently within a 4-10 km ground Aqua CloudSat Calipso Parasol track control box. Calipso is maintained within +10 km a control box relative to its initial -20 km offset ground track. The relative motion of the maneu- Figure 7: Constellation Relative Motion vered satellites is shown in Figure 7. CloudSat's maneuvers are tied to Calipso due to Aqua Parasol Geopotential JGM-2 Order 4 Dry Mass (kg) 3039 120 Fuel Mass (kg) 200 2O Degree 4 Area (m _) 47.95 1.0 Solar Gravity No Co 2.2 2.7 Lunar Gravity No Thrusters 4 3 Solar Radiation Pressure No Thrust (N) 0.09 1.0 Atmospheric Density Model Harris-Preister Isp (sec) 200 220 Table 3: Force Model Parameters CloudSat Calipso Dry Mass (kg) 821 600 Maneuver Epoch Duration* (sec) Fuel Mass (kg) 76 27.2 Cloud 1 Oct 26 2004 07:30:00 -6.42684 8.3 9.5 79.34851 Area (m _) Calipso 1 Nov 11 2004 13:27:00 CD 2.2 2.7 Cloud 2 Nov 11 2004 13:27:20 19.36560 Thrusters 2 2 Aqua 1 Nov 15 2004 17:57:00 54.86191 Thrust (N) 4.45 1.0 Parasol 1 Nov 27 2004 00:18:00 7.595172 212 Isp (sec) 220 Cloud 3 Dec 03 2004 02:07:14 -5.79300 Calipso 2 Dec 24 2004 14:46:00 65.56777 Table 2: Spacecraft Properties Cloud 4 Dec 24 2004 14:46:30 15.96962 Aqua 2 Jan 04 2005 16:04:00 44.62905 Cloud 5 Jan 18 2005 08:53:25 -5.06473 their close proximity.
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