Methods and apparatus for controlling a plurality of satellites using node-synchronous eccentricity control

1. A method for controlling a plurality of satellites, the method comprising:

establishing a first inclination vector associated with a first satellite of the plurality of satellites, the first satellite travelling in a first inclined geosynchronous orbit;

establishing a second inclination vector associated with a second satellite of the plurality of satellites, the second satellite travelling in a second inclined geosynchronous orbit; and

controlling the first satellite and the second satellite such that the first satellite and the second satellite are synchronized with a node, wherein the first and second inclination vectors are offset from each other such that a radial offset is defined between orbital paths of the first and second satellites at the node, and such that latitude separation is defined between the orbital paths of the first and second satellites away from the node.

2. A method in accordance with claim 1 , wherein controlling the first satellite and the second satellite further comprises:

controlling the first satellite in accordance with the first inclination vector, such that the first satellite is associated with a first portion of the node; and

controlling the second satellite in accordance with the second inclination vector, such that the second satellite is associated with a second portion of the node, the second portion spaced from the first portion, wherein the first and second inclined geosynchronous orbits both have a non-zero eccentricity.

3. A method in accordance with claim 1 , wherein controlling the first satellite further comprises starting a control maneuver for the first satellite at a first time, and controlling the second satellite further comprises starting a control maneuver for the second satellite at a second time different from the first time.

4. A method in accordance with claim 1 , wherein at least one of establishing a first inclination vector and establishing a second inclination vector further comprises:

averaging a value of a right ascension of the node for at least one of the first inclination vector and the second inclination vector over a period of a control cycle; and

managing a plurality of predominately tangential corrections for at least one of the first satellite and the second satellite such that an eccentricity vector, directed at perigee, is substantially collinear with and substantially tracks the at least one of the first inclination vector and the second inclination vector such that latitude control of the at least one of the first satellite and the second satellite is not required to maintain the at least one of the first satellite and the second satellite in an orbit.

5. A method in accordance with claim 4 further comprising:

minimizing a maximum variation of the eccentricity vector based on an orbit initialization;

reducing the eccentricity vector to facilitate maintaining a longitude of at least one of the first satellite and the second satellite within a predetermined slot;

averaging at least one of the first inclination vector and the second inclination vector over the period of the control cycle; and

managing corrections for the at least one of the first satellite and the second satellite such that the eccentricity vector rotates at substantially the same rate as the at least one of the first inclination vector and the second inclination vector.

6. A method in accordance with claim 4 , wherein averaging a value of a right ascension comprises averaging the value based on at least one of an influence based on an oblateness of the earth and lunar and solar gravity on the at least one of the first inclination vector and the second inclination vector.

7. A method in accordance with claim 4 , wherein managing a plurality of predominately tangential corrections for the satellite comprises:

computing the eccentricity vector over the period of the control cycle from a perturbation model; and

computing corrections of the eccentricity vector by computing thruster firing durations and locations along the orbit based on a configuration of the thrusters.

8. A method in accordance with claim 4 , wherein managing a plurality of predominately tangential corrections for the satellite comprises utilizing at least one of a velocity change, two velocity changes approximately 180 degrees apart along the orbit, a velocity change approximately six hours prior to the node, and a velocity change approximately six hours after the node.

9. A method in accordance with claim 4 , wherein managing a plurality of corrections for the satellite comprises removing the variations of orbital eccentricity that are normal to the inclination vector.

10. A method in accordance with claim 9 , wherein removing the variations of orbital eccentricity comprises causing an argument of perigee for the eccentricity vector to be one of substantially zero and substantially 180°, based upon one or more algorithms within the at least one of the first satellite and the second satellite.

11. A control system for controlling a plurality of satellites, said control system comprising:

a memory device containing a first inclination vector associated with a first satellite of the plurality of satellites, and a second inclination vector associated with a second satellite of the plurality of satellites, the first satellite travelling in a first inclined geosynchronous orbit, and the second satellite travelling in a second inclined geosynchronous orbit; and

a processing device configured to control the first satellite and the second satellite such that the first satellite and the second satellite are synchronized with a node, wherein the first and second inclination vectors are offset from each other such that a radial offset is defined between orbital paths of the first and second satellites at the node, and such that latitude separation is defined between the orbital paths of the first and second satellites away from the node.

12. A control system in accordance with claim 11 , wherein the processing device is further configured to:

control the first satellite in accordance with the first inclination vector, such that the first satellite is associated with a first portion of the node; and

control the second satellite in accordance with the second inclination vector, such that the second satellite is associated with a second portion of the node, the second portion spaced from the first portion.

13. A control system in accordance with claim 11 , wherein the processing device is further configured to:

start a control maneuver for the first satellite at a first time; and

start a control maneuver for the second satellite at a second time different from the first time.

14. A control system in accordance with claim 11 , wherein the processing device is further configured to:

average a value of a right ascension of the node for at least one of the first inclination vector and the second inclination vector over a period of a control cycle; and

manage a plurality of corrections for at least one of the first satellite and the second satellite such that an eccentricity vector, directed at perigee, is substantially collinear with and substantially tracks the at least one of the first inclination vector and the second inclination vector such that latitude control of the at least one of the first satellite and the second satellite is not required to maintain the at least one of the first satellite and the second satellite in an orbit.

15. A control system in accordance with claim 14 , wherein the processing device is further configured to:

minimize a maximum variation of the eccentricity vector based on an orbit initialization;

reduce the eccentricity vector to facilitate maintaining a longitude of at least one of the first satellite and the second satellite within a predetermined slot;

average at least one of the first inclination vector and the second inclination vector over the period of the control cycle; and

manage corrections for the at least one of the first satellite and the second satellite such that the eccentricity vector rotates at substantially the same rate as the at least one of the first inclination vector and the second inclination vector.

16. A control system in accordance with claim 14 , wherein the processing device is further configured to average the value of the right ascension based on at least one of an influence based on an oblateness of the earth and lunar and solar gravity on the at least one of the first inclination vector and the second inclination vector.

17. A control system in accordance with claim 14 , wherein the processing device is further configured to

compute the eccentricity vector over the period of the control cycle from a perturbation model; and

compute corrections of the eccentricity vector by computing thruster firing durations and locations along the orbit based on a configuration of the thrusters.

18. A control system in accordance with claim 14 , wherein the processing device is further configured to utilize at least one of a velocity change, two velocity changes approximately 180 degrees apart along the orbit, a velocity change approximately six hours prior to the node, and a velocity change approximately six hours after the node.

19. A control system in accordance with claim 14 , wherein the processing device is further configured to remove the variations of orbital eccentricity that are normal to the inclination vector.

20. A control system according to claim 19 , wherein the processing device is further configured to cause an argument of perigee for the eccentricity vector to be one of substantially zero and substantially 180°, based upon one or more algorithms within the at least one of the first satellite and the second satellite.