1

GOES-12 Eccentricity Control(Co-Location with Brasilsat B1)

Richard McIntosh

a.i. solutions, Inc.

AIAA SOSTC Workshop

April 15, 2008

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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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

4

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

10

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

17

-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

19

-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

21

-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

22

-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.