1 goes-12 eccentricity control (co-location with brasilsat b1) richard mcintosh a.i. solutions, inc....
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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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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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B1 and G-12 Longitude vs Time With EWSK Maneuvers
284.5
284.6
284.7
284.8
284.9
285
285.1
285.2
285.3
285.4
285.5
0 30 60 90 120 150 180 210 240 270 300 330 360 390
Days
Lo
ng
itu
de
(deg
E)
GOES-12
B1
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Eccentricity Control Strategy Recommended By StarOne
0
20
40
60
20 40 60-20-40
-60
-20
-40
-60
ex (*10-5)
ey (
*10-5
)
Eccentricity
B1
GOES 12
? @ γΔeseparation
X
Eccentricity Vector
ex = e cos(Ω+ω)ey = e sin(Ω+ω)
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V
V
ECCVECTOR
ΔV from SRPRaises Apogee
ΔV from SRPLowers Perigee
SRP
Effect of Solar Radiation Pressure on Eccentricity
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-0.0004
-0.0003
-0.0002
-0.0001
0
0.0001
0.0002
0.0003
0.0004
-0.0005 -0.0004 -0.0003 -0.0002 -0.0001 0 0.0001 0.0002 0.0003 0.0004 0.0005
EX
EY Eccentricity Vector Over 1 Year
2-Body Only + SRP
EX = e cos(Ω+ω)
EY = e sin(Ω+ω)
Natural Eccentricity Circle(size depends on Area/Mass)
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-0.0005
-0.0004
-0.0003
-0.0002
-0.0001
0
0.0001
0.0002
0.0003
0.0004
0.0005
-0.0005 -0.0004 -0.0003 -0.0002 -0.0001 0 0.0001 0.0002 0.0003 0.0004 0.0005
EX
EY Eccentricity Vector Over 1 Year
2-Body Only + SRP + Sun + Moon
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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-12 every 11 or 12 weeks– B1 every 3 weeks
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β
β
Control Circle
Natural Circle
Δα
Δα = Change in Sun RA over 1 East-West Maneuver Cycle
Sun at Start
Sun at End
0e
1e
EX
EY
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Δe
Control Circle
Natural Circle
Δα
β
β
EY
EX
Next E-W Cycle
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Equations (1 of 3) coseex
sineey
00032.0nr Natural radius for GOES-12 m
ACr rn 01115.0
0003.0cr (or 0.0002) Control radius
= Sun RA at burn time = Change in Sun RA over one EW cycle (75.9 deg in 77 days)
2
2sin
arcsin
c
n
r
r
= 3.0 deg for cr = 0.0003
= 41.9 deg for cr = 0.0002
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Equations (2 of 3)For circle centered on Y-axis at Y = +0.0002 targets are
cosarg cetT rex
0002.0sinarg cetT rey
Required change
0arg exexex etT
0arg eyeyey etT
ex
eyRA arctan1 RA2 = RA1 + 180
22 eyexe
ΔeRA1
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Equations (3 of 3)
eV = Delta-V to change eccentricity
dV = Delta-V to change drift (SMA change)
2
eVVe
SMARgeo
VVd
2
1
Compute two delta-Vs
ed VVV 2
1
2
11
ed VVV 2
1
2
12
Note: Delta-Vs are normally in negative velocity direction for 75 West
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-0.0002
-0.0001
0
0.0001
0.0002
0.0003
0.0004
0.0005
0.0006
-0.0005 -0.0004 -0.0003 -0.0002 -0.0001 0 0.0001 0.0002 0.0003 0.0004 0.0005
PREBURN GOES-12
1 BURNONLY
2 BURNS
Ex, Ey Achieved With 1 Burn vs 2 Burns
TARGET
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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-0.0006
-0.0005
-0.0004
-0.0003
-0.0002
-0.0001
0
0.0001
0.0002
0.0003
0.0004
0.0005
0.0006
-0.0008 -0.0006 -0.0004 -0.0002 0 0.0002 0.0004 0.0006 0.0008
Current GOES StrategyBurns at Perigee
Single Burn atPerigee
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-0.0006
-0.0004
-0.0002
0
0.0002
0.0004
0.0006
-0.0008 -0.0006 -0.0004 -0.0002 0 0.0002 0.0004 0.0006 0.0008
CONTROL CIRCLE RADIUS 0.00032-BURN CONTROLBETA OFFSET -3 DEG
2-Burn Control0.0003 Circle
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-0.0006
-0.0004
-0.0002
0
0.0002
0.0004
0.0006
-0.0008 -0.0006 -0.0004 -0.0002 0 0.0002 0.0004 0.0006 0.0008
CONTROL CIRCLE RADIUS 0.00022-BURN CONTROLBETA OFFSET -42 DEG
2-Burn Control0.0002 Circle
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GOES-12 4-Year Simulation1-Burn East-West Maneuvers
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-0.0003
-0.0002
-0.0001
0
0.0001
0.0002
0.0003
0.0004
0.0005
0.0006
-0.0006 -0.0005 -0.0004 -0.0003 -0.0002 -0.0001 0 0.0001 0.0002 0.0003 0.0004 0.0005 0.0006
GOES-12 SINGLE BURN CONTROL84 DAY FIRST CYCLEREMAINING CYCLES 77 DAYSYEAR 1
1-DAY AVERAGE EX, EY
1
NO N-S BURNS
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-0.0003
-0.0002
-0.0001
0
0.0001
0.0002
0.0003
0.0004
0.0005
0.0006
-0.0006 -0.0005 -0.0004 -0.0003 -0.0002 -0.0001 0 0.0001 0.0002 0.0003 0.0004 0.0005 0.0006
GOES-12 SINGLE BURN CONTROL77 DAY CYCLE
YEAR 2
1-DAY AVERAGE EX, EY
2
NO N-S BURNS
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-0.0003
-0.0002
-0.0001
0
0.0001
0.0002
0.0003
0.0004
0.0005
0.0006
-0.0006 -0.0005 -0.0004 -0.0003 -0.0002 -0.0001 0 0.0001 0.0002 0.0003 0.0004 0.0005 0.0006
GOES-12 SINGLE BURN CONTROL77 DAY CYCLE
YEAR 3
1-DAY AVERAGE EX, EY
3
NO N-S BURNS
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-0.0003
-0.0002
-0.0001
0
0.0001
0.0002
0.0003
0.0004
0.0005
0.0006
-0.0006 -0.0005 -0.0004 -0.0003 -0.0002 -0.0001 0 0.0001 0.0002 0.0003 0.0004 0.0005 0.0006
GOES-12 SINGLE BURN CONTROL77 DAY CYCLE
YEAR 4
1-DAY AVERAGE EX, EY
4
NO N-S BURNS
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-0.0003
-0.0002
-0.0001
0
0.0001
0.0002
0.0003
0.0004
0.0005
0.0006
-0.0006 -0.0005 -0.0004 -0.0003 -0.0002 -0.0001 0 0.0001 0.0002 0.0003 0.0004 0.0005 0.0006
GOES-12 SINGLE BURN CONTROL84 DAY FIRST CYCLEREMAINING CYCLES 77 DAYS4 YEARS
1-DAY AVERAGE EX, EY
12
3
4
NO N-S BURNS
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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.