Stationkeeping techniques for spacecraft in inclined geosynchronous orbit
A constellation of Earth-orbiting spacecraft, the constellation having an orbital maneuver lifetime life (OML), includes a first spacecraft disposed in a first orbit and a second spacecraft disposed in a second orbit, each of orbit being substantially circular with a radius of approximately 42,164 km and having a respective inclination with respect to the equator specified within a range of 10° to 20°. The first orbit has, at beginning of life (BOL), a first right ascension of ascending node (BOL-RAAN1) and the second orbit has, at BOL, a second RAAN (BOL-RAAN2) the BOL-RAAN1 and the BOL-RAAN2 being separated by a first angular separation Δ-RAAN1. A first stationkeeping delta-V (ΔV1) applied over the OML to the first spacecraft, in combination with a second delta-V (ΔV2) applied over the OML to the second spacecraft, maintains the Δ-RAAN1 approximately constant and an actual inclination within specification, and ΔV1 approximately equals ΔV2.
1. A constellation of Earth-orbiting spacecraft, the constellation having an orbital maneuver lifetime life (OML) and comprising:
two or more spacecraft, including a first spacecraft disposed in a first orbit and a second spacecraft disposed in a second orbit, wherein:
each of the first orbit and the second orbit is substantially circular with a radius of approximately 42,164 km;
the first orbit has a first specified inclination with respect to the equator and the second orbit has a second specified inclination with respect to the equator, the first specified inclination and the second specified inclination each being within a range of 10° to 20°;
the first orbit has, at beginning of life (BOL), a first right ascension of ascending node (BOL-RAAN1) and the second orbit has, at BOL, a second RAAN (BOL-RAAN2) the BOL-RAAN1 and the BOL-RAAN2 being separated by a first angular separation Δ-RAAN1;
a first stationkeeping delta-V (ΔV1) applied in a first series of stationkeeeping maneuvers over the OML to the first spacecraft, in combination with a second delta-V (ΔV2) applied in a second series of stationkeeeping maneuvers over the OML to the second spacecraft, is sufficient to maintain the Δ-RAAN1 approximately constant and an actual inclination of the first orbit and the second orbit approximately equal, respectively, to the first specified inclination and second specified inclination;
ΔV1 approximately equals ΔV2 and
stationkeeping maneuvers in the first and second series of stationkeeeping maneuvers are determined so as to concurrently adjust a propagated value of RAAN to a target value for RAAN and to maintain actual orbital inclination approximately equal to a respective specified inclination.
2. The constellation of claim 1 , wherein each spacecraft is disposed only in the first orbit or the second orbit and the Δ-RAAN1 is approximately 90°.
3. The constellation of claim 1 , wherein the two or more spacecraft include a third spacecraft disposed in a third orbit having a third specified inclination, wherein:
the third orbit has, at BOL, a third RAAN (BOL-RAAN3) the BOL-RAAN1 and the BOL-RAAN3 being separated by a second angular separation Δ-RAAN2; and
ΔV1, in combination with a third delta-V (ΔV3) applied over the OML to the third spacecraft, is sufficient to maintain the Δ-RAAN2 approximately constant and an actual inclination of each orbit approximately equal, respectively, to the first specified inclination, the second specified inclination and the third specified inclination.
4. The constellation of claim 3 , wherein the Δ-RAAN1 is approximately equal to the Δ-RAAN2.
5. The constellation of claim 1 , wherein the ΔV1 and the ΔV2 are sufficient only to maintain the Δ-RAAN and the actual first inclination and actual second inclination approximately constant.
6. The constellation of claim 5 , wherein ΔV1/OML corresponds to less than 45 meters per second per year.
7. The constellation of claim 1 , wherein the first specified inclination approximately equals the second specified inclination.
8. The constellation of claim 1 , wherein the BOL-RAAN1 and the BOL-RAAN2 are determined by executing, on a processor, at least two cycles of an optimization loop, the optimization loop including:
(i) a first calculation, for a current set of beginning of life (BOL) orbit parameters and a current set of end of life (EOL) orbit parameters, a first stationkeeping delta-V requirement for the first spacecraft and a second stationkeeping delta-V requirement for the second spacecraft, sufficient to maintain the Δ-RAAN1 and the specified inclination approximately constant;
(ii) a second calculation of a difference between the first stationkeeping delta-V requirement and the second stationkeeping delta-V requirement; and
(iii) a decision block wherein, when the difference is not greater than a specified value, a first decision of the decision block is that the constellation stationkeeping strategy is sufficiently optimized, and when the difference is greater than the specified value, a second decision of the decision block is to enter a step of adjusting the current set of beginning of life (BOL) orbit parameters and the current set of end of life (EOL) orbit parameters and repeat steps (i) and (ii).
9. A method comprising:
selecting, for a constellation of Earth-orbiting spacecraft, a current set of beginning of life (BOL) orbit parameters and a current set of end of life (EOL) orbit parameters, the constellation including a first spacecraft disposed in a first orbit and a second spacecraft disposed in a second orbit, each of the first orbit and the second orbit being substantially circular with a radius of approximately 42,164 km, the first orbit being disposed in a first orbital plane and the second orbit being disposed in a second orbital plane, each of the first orbital plane and the second orbital plane having a specified inclination with respect to the equator within a range of 10° to 20°, the current set of BOL orbit parameters including, for the first orbital plane, a first BOL right ascension of ascending node (BOL-RAAN1) and, for the second orbital plane, a second BOL RAAN (BOL-RAAN2), the BOL-RAAN1 and the BOL-RAAN2 being separated by a BOL angular separation, BOL Δ-RAAN, the current set of EOL orbit parameters including, for the first orbit, a first EOL right ascension of ascending node (EOL-RAAN1) and, for the second orbit, a second EOL RAAN (EOL-RAAN2), the EOL-RAAN1 and the EOL-RAAN2 being separated by an EOL angular separation EOL Δ-RAAN that is approximately equal to BOL Δ-RAAN; and
optimizing a constellation stationkeeping strategy, by executing, on a processor, at least two cycles of an optimization loop, the optimization loop comprising:
(i) a first calculation, for the current set of beginning of life (BOL) orbit parameters and the current set of end of life (EOL) orbit parameters, a first stationkeeping delta-V requirement for the first spacecraft and a second stationkeeping delta-V requirement for the second spacecraft, sufficient to maintain the Δ-RAAN and the specified inclination approximately constant;
(ii) a second calculation of a difference between the first stationkeeping delta-V requirement and the second stationkeeping delta-V requirement; and
(iii) a decision block wherein, when the difference is not greater than a specified value, a first decision of the decision block is that the constellation stationkeeping strategy is sufficiently optimized, and when the difference is greater than the specified value, a second decision of the decision block is to enter a step of adjusting the current set of beginning of life (BOL) orbit parameters and the current set of end of life (EOL) orbit parameters and repeat steps (i) and (ii).
10. The method of claim 9 , wherein the first stationkeeping delta-V requirement and the second stationkeeping delta-V requirement are sufficient only to maintain the Δ-RAAN and the specified inclination approximately constant.
11. The method of claim 9 , wherein the specified value is less than 5 meters per second.
12. A method comprising:
executing a stationkeeping strategy for a constellation of Earth-orbiting spacecraft, the constellation having an orbital maneuver lifetime life (OML) and including two or more spacecraft, including a first spacecraft disposed in a first orbit and a second spacecraft disposed in a second orbit, wherein:
each of the first orbit and the second orbit is substantially circular with a radius of approximately 42,164 km;
the first orbit has a first specified inclination with respect to the equator and the second orbit has a second specified inclination with respect to the equator, the first specified inclination and the second specified inclination each being within a range of 10° to 20°;
the first orbit has, at beginning of life (BOL), a first right ascension of ascending node (BOL-RAAN1) and the second orbit has, at BOL, a second RAAN (BOL-RAAN2) the BOL-RAAN1 and the BOL-RAAN2 being separated by a first angular separation Δ-RAAN1;
the stationkeeping strategy includes applying a first stationkeeping delta-V (ΔV1) in a first series of stationkeeeping maneuvers to the first spacecraft over the OML, and applying a second delta-V (ΔV2), approximately equal to ΔV1, to the second spacecraft in a second series of stationkeeeping maneuvers over the OML, such that the Δ-RAAN1 over the OML is approximately constant and an actual inclination of the first orbit and the second orbit approximately equal, respectively, the first specified inclination and the second specified inclination; and
stationkeeping maneuvers in the first and second series of stationkeeeping maneuvers are determined so as to concurrently adjust a propagated value of RAAN to a target value for RAAN and to maintain actual orbital inclination approximately equal to a respective specified inclination.
13. The method of claim 12 , wherein the Δ-RAAN1 is approximately 90°.
14. The method of claim 12 , wherein the two or more spacecraft include a third spacecraft disposed in a third orbit, wherein:
the third orbit has, at BOL, a third RAAN (BOL-RAAN3) the BOL-RAAN1 and the BOL-RAAN3 being separated by a second angular separation Δ-RAAN2; and
the stationkeeping strategy includes applying a third delta-V (ΔV3) to the third spacecraft over the OML, such that the Δ-RAAN2 is approximately constant and an actual inclination of each orbit approximately equal, respectively, to the first specified inclination, the second specified inclination and the third specified inclination.
15. The method of claim 14 , wherein the Δ-RAAN1 is approximately equal to the Δ-RAAN2.
16. The method of claim 12 , wherein the ΔV1 and the ΔV2 are sufficient only to maintain the Δ-RAAN and the actual first inclination and the actual second inclination approximately constant.
17. The method of claim 16 , wherein ΔV1/OML corresponds to less than 45 meters per second per year.
18. The method of claim 12 , wherein the first specified inclination approximately equals the second specified inclination.
19. The method of claim 12 , wherein the BOL-RAAN1 and the BOL-RAAN2 are determined by executing, on a processor, at least two cycles of an optimization loop, the optimization loop including:
(i) a first calculation, for a current set of beginning of life (BOL) orbit parameters and a current set of end of life (EOL) orbit parameters, a first stationkeeping delta-V requirement for the first spacecraft and a second stationkeeping delta-V requirement for the second spacecraft, sufficient to maintain the Δ-RAAN1 and the specified inclination approximately constant;
(ii) a second calculation of a difference between the first stationkeeping delta-V requirement and the second stationkeeping delta-V requirement; and
(iii) a decision block wherein, when the difference is not greater than a specified value, a first decision of the decision block is that the constellation stationkeeping strategy is sufficiently optimized, and when the difference is greater than the specified value, a second decision of the decision block is to enter a step of adjusting the current set of beginning of life (BOL) orbit parameters and the current set of end of life (EOL) orbit parameters and repeat steps (i) and (ii).
20. The method of claim 19 , wherein the specified value is less than 5 meters per second.