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1 GOES-12 Eccentricity Control (Co-Location with Brasilsat B1) Richard McIntosh a.i. solutions, Inc. AIAA SOSTC Workshop April 15, 2008

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2 Co-Location Requirements GOES-12 located at 75 deg W +/- 0.5 deg longitude. Brasilsat B1 given OK to move from 70 deg W to 75 deg W and maintain +/- 0.1 deg longitude. B1 now occupies the middle 0.2 deg of GOES-12 box. StarOne (B1 owners) suggested eccentricity vector control to avoid close approaches. GOES maneuver control software not capable of planning East- West stationkeeping (EWSK) maneuvers that include eccentricity vector control. NOAA desires to not perform any extra maneuvers for eccentricity control. Analysis performed to determine how eccentricity control could be incorporated into the normal 1-burn EWSK operations.

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4 Eccentricity Control Strategy Recommended By StarOne Eccentricity Vector ex = e cos(Ω+ω) ey = e sin(Ω+ω)

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5 V V ECC VECTOR ΔV from SRP Raises Apogee ΔV from SRP Lowers Perigee SRP Effect of Solar Radiation Pressure on Eccentricity

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6 EX = e cos(Ω+ω) EY = e sin(Ω+ω) Natural Eccentricity Circle (size depends on Area/Mass)

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8 Eccentricity Control Eccentricity vector will tend to follow the natural circle throughout the year. Desired control circle size is usually smaller. Objective is to try to make a short arc of the natural circle closely follow the control circle over the next EWSK cycle. EWSK frequency: –GOES-12every 11 or 12 weeks –B1every 3 weeks

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9 β β Control Circle Natural Circle Δα Δα = Change in Sun RA over 1 East-West Maneuver Cycle Sun at Start Sun at End EX EY

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10 ΔeΔe Control Circle Natural Circle Δα β β EY EX Next E-W Cycle

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11 Equations (1 of 3)

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12 Equations (2 of 3) ΔeΔe RA1

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13 Equations (3 of 3) Note: Delta-Vs are normally in negative velocity direction for 75 West

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14 1-Burn vs 2-Burn Control 1-Burn -0.268 m/s 2-Burns -0.478 and +0.211 m/s

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15 Single Burn at Perigee

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16 2-Burn Control 0.0003 Circle

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17 2-Burn Control 0.0002 Circle

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18 GOES-12 4-Year Simulation 1-Burn East-West Maneuvers

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24 Conclusions Analysis has shown that sufficient eccentricity control can be accomplished by GOES-12 with little or no impact to the normal EWSK operations (single-burn). Only requirement is a change in the time of the burn (move from the normal perigee burn location). NOAA has incorporated the equations presented here into a spreadsheet that computes the nominal time of the burn. GOES-12 successfully performed the first EWSK maneuver with eccentricity control on July 24, 2007. Subsequent EWSK maneuvers have shown that the single-burn strategy provides adequate eccentricity control. Further analysis needs to be done to verify that the desired spacecraft separation can be maintained in the long term.

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