Low energy method for changing the inclinations of orbiting satellites using weak stability boundaries and a computer process for implementing same

• US 6,577,930 B2
• Filed: 05/07/2001
• Issued: 06/10/2003
• Est. Priority Date: 04/24/1997
• Status: Expired due to Fees

• Current Assignee: Galaxy Development LLC
• Original Assignee: Galaxy Development LLC
• Inventors: Belbruno, Edward A.
• Primary Examiner(s): Zanelli, Michael J.
• Assistant Examiner(s): Gibson, Eric M
• Application Number:
  US09/849,273
• Publication Number:
  US 20020007233A1
• Time in Patent Office: 764 Days
• Field of Search: 701/3, 701/4, 701/13, 701/226, 244/158.R, 244/164, 244/167
• US Class Current: 701/13
• CPC Class Codes: B64G 1/242 Orbits and trajectories
• CPC Class Codes: B64G 1/2427 Transfer orbits
• CPC Class Codes: B64G 1/247 Advanced control concepts for autonomous, robotic spacecraft, e.g. by using artificial intelligence, neural networks or autonomous agents

Abstract

A fuel efficient technique for changing the inclination, with respect to the Earth'"'"'s equator, for a satellite includes first maneuvering the satellite to the moon on a BCT (Ballistic Capture Transfer). At the moon, the satellite is in the so-called fuzzy boundary or weak stability age boundary. A negligibly small maneuver can then bring it back to the Earth on a reverse BCT to the desired Earth inclination. Another maneuver puts it into the new ellipse at the earth. In the case of satellites launched from Vandenberg AFB into LEO in a circular orbit of an altitude of 700 km with an inclination of 34°, approximately 6 km/s is required to change the inclination to 90°. The previous flight time associated with this method was approximately 170 days. A modification of this method also achieves a significant savings and unexpected benefits in energy as measured by Delta-V, where the flight time is also substantially reduced to 88 or even 6 days.

Claims

1. A method of changing at least one of an inclination and an altitude of an object including at least one of a space vehicle, satellite and rocket by generating a combination first Hohmann transfer for the object emanating substantially at earth or earth orbit to arrive at a weak stability boundary (WSB) or WSB orbit at or near the moon or moon orbit and generating a second Hohmann transfer for the object emanating at the WSB or the WSB orbit to return to the earth or the earth orbit, using a computer implemented process, comprising the sequential or non-sequential steps of:

(a) generating the first Hohmann transfer for convergence of first target variables at the WSB or the WSB orbit;

(b) traveling from a first altitude relative to the earth or the earth orbit to a weak lunar capture in the WSB or the WSB orbit using the first Hohmann transfer;

(c) optionally performing an inclination change at the WSB or the WSB orbit;

(d) generating the second Hohmann transfer for convergence of second target variables at the earth or the earth orbit from the WSB or the WSB orbit, optionally including the inclination change performed in step (c); and

(e) traveling from the WSB or the WSB orbit to the earth or the earth orbit at a predetermined arbitrary altitude different from said first altitude using the second Hohmann transfer; and

wherein said first and said second transfers are generated using a forward targeting method.

2. A navigational system for changing at least one of an inclination and an altitude of an object including at least one of a space vehicle, satellite and rocket by generating a first Hohmann transfer for the object emanating substantially at earth or earth orbit to arrive at a weak stability boundary (WSB) or WSB orbit at or near the moon or moon orbit and generating a second Hohmann transfer for the object emanating at the WSB or the WSB orbit to return to the earth or the earth orbit, using a computer, wherein the computer implements the sequential or non-sequential functions of:

(a) generating the first Hohmann transfer for convergence of first target variables at the WSB or the WSB orbit;

(b) generating the second Hohmann transfer for convergence of second target variables at the earth or the earth orbit from the WSB or the WSB orbit; and

(c) navigating the object from a first altitude relative to the earth or the earth orbit to a weak lunar capture in the WSB or the WSB orbit using the first Hohmann transfer, and navigating the object from the WSB or the WSB orbit to the earth or the earth orbit at a predetermined arbitrary altitude different from said first altitude using the second Hohmann transfer; and

wherein said first and said second transfers are generated using a forward targeting method.

3. A computer program memory, storing computer instructions for changing at least one of an inclination and an altitude of an object by generating a first Hohmann transfer for the object emanating substantially at earth or earth orbit to arrive at a weak stability boundary (WSB) or WSB orbit at or near the moon or moon orbit and generating a second Hohmann transfer for the object emanating at the WSB or the WSB orbit to return to the earth or the earth orbit using a computer, the computer instructions including:

(a) generating the first Hohmann transfer for convergence of first target variables at the WSB or the WSB orbit;

(b) iterating step (a) until sufficient convergence to obtain the first Hohmann transfer from a first altitude relative to the earth or the earth orbit to a weak lunar capture in the WSB or the WSB orbit;

(c) generating the second Hohmann transfer for convergence of second target variables at the earth or the earth orbit from the WSB or the WSB orbit; and

(d) iterating step (c) until sufficient convergence to obtain the second Hohmann transfer from the WSB or the WSB orbit to the earth or the earth orbit for changing the at least one of the inclination and the first altitude; and

wherein said first and said second transfers are generated using a forward targeting method.

4. A method of changing at least one of an inclination and an altitude of an object including at least one of a space vehicle, satellite and rocket, using a computer implemented process, comprising the sequential or non-sequential steps of:

(a) traveling from a first altitude relative to the earth or the earth orbit to a weak lunar capture in a weak stability boundary (WSB) or WSB orbit using a first Hohmann transfer;

(b) performing at least one of a maneuver and a negligible maneuver, and optionally performing an inclination change at the WSB or the WSB orbit; and

(c) traveling from the WSB or the WSB orbit to the earth or the earth orbit at a predetermined arbitrary altitude different from said first altitude and optionally at the inclination change using a second Hohmann transfer; and

wherein said first and said second transfers are generated using a forward targeting method.

5. A method according to claim 4, wherein said performing step (b) further comprises the step of performing the negligible maneuver of between 2-20 meters per second at the WSB or the WSB orbit for ejection therefrom.

6. A method according to claim 4, wherein said traveling step (a) further comprises the step of maneuvering around the moon by performing a negligible maneuver of between 2-20 meters per second at the WSB or the WSB orbit for at least one of timing and positioning of the object prior to ejection therefrom.

7. A method according to claim 4, wherein the at least one of the WSB or the WSB orbit is realizable at the predetermined arbitrary altitude by specifying a predetermined velocity magnitude of the object, thereby defining a predetermined capture eccentricity.

8. A method according to claim 4, wherein said method performs said steps (a)-(c) in anywhere from approximately 6 to approximately 88 days.

9. A method according to claim 4, wherein the at least one of the WSB or the WSB orbit is nonlinear and being substantially at a boundary of capture and escape, thereby allowing the capture and the escape to occur for a substantially zero or relatively small maneuver.

10. A method according to claim 4, wherein the at least one of the WSB or the WSB orbit is substantially at a boundary of capture and escape, and wherein solar gravitational perturbations influence the first and second Hohmann transfers.

11. A method according to claim 4, wherein the at least one of the WSB or the WSB orbit is substantially at a boundary of interaction between gravitational fields of the moon and the earth as the object moves.

12. A method according to claim 4, wherein a motion in the at least one of the WSB or the WSB orbit is at least one of parabolic and elliptic.

13. A method according to claim 4, wherein as the object moves in the at least one of the WSB or the WSB orbit, a Kepler energy of the object is slightly negative and substantially near to zero.

14. A method of changing at least one of an inclination and an altitude of an object including at least one of a space vehicle, satellite and rocket, using a computer implemented process, comprising the sequential or non-sequential steps of:

(a) traveling from a first altitude relative to the earth or the earth orbit to a first periapsis at a weak lunar capture in a weak stability boundary (WSB) or WSB orbit using a first Hohmann transfer;

(b) maneuvering around the moon by performing a first negligible maneuver at the WSB or the WSB orbit;

(c) optionally performing an inclination change at the WSB or the WSB orbit;

(d) ejecting from the WSB or the WSB orbit by performing a second negligible maneuver; and

(e) traveling from the WSB or the WSB orbit to a second peniapsis at the earth or the earth orbit at a predetermined arbitrary altitude different from said first altitude and optionally at the inclination change using a second Hohmann transfer; and

wherein said first and said second transfers are generated using a forward targeting method.

15. A method of changing at least one of an inclination and an initial altitude of an object including at least one of a space vehicle, satellite and rocket, using a computer implemented process, comprising the sequential or non-sequential steps of:

(a) traveling from the moon or the moon orbit to a weak lunar capture in a weak stability boundary (WSB) or WSB orbit using a first Hohmann transfer;

(b) performing at least one of a maneuver and a negligible maneuver, and optionally performing an inclination change at the WSB or the WSB orbit; and

(c) traveling from the WSB or the WSB orbit to the moon or the moon orbit at a predetermined arbitrary altitude different from said initial altitude and optionally at the inclination change using a second Hohmann transfer; and

wherein said first and said second transfers are generated using a forward targeting method.

16. A method of changing at least one of an inclination and an altitude of an object including at least one of a space vehicle, satellite and rocket, using a computer implemented process, comprising the sequential or non-sequential steps of:

(a) traveling from a first altitude relative to a first planet or first planet orbit to a weak lunar capture in a weak stability boundary (WSB) or WSB orbit using a first Hohmann transfer;

(b) performing at least one of a maneuver and a negligible maneuver, and optionally performing an inclination change at the WSB or the WSB orbit; and

(c) traveling from the WSB or the WSB orbit to at least one of the first planet or the first planet orbit and a second planet and a second planet orbit at a predetermined arbitrary altitude different from said first altitude and optionally at the inclination change using a second Hohmann transfer; and

wherein said first and said second transfers are generated using a forward targeting method.

17. A method of generating a transfer for an object emanating substantially at earth or earth orbit to arrive at the moon or moon orbit using a computer implemented process, comprising the steps of:

(a) entering parameters for said method of generating the transfer;

(b) implementing at least one of a forward targeting process and a forward transfer process by varying the parameters for convergence of target variables at the moon; and

(c) iterating step (b) until sufficient convergence to obtain the transfer from the earth or the earth orbit to the moon or the moon orbit.

18. A method of traveling from substantially at earth or earth orbit to the moon or moon orbit in a space vehicle or rocket using a transfer, comprising the steps of:

(a) generating the transfer by implementing at least one of a forward targeting process and a forward transfer process by varying parameters for said method until convergence of target variables at the moon; and

(b) traveling from, substantially at the earth or the earth orbit to the moon or the moon orbit using the transfer by the space vehicle or the rocket.

19. A method of generating a transfer for an object emanating substantially at a first heavenly object or first heavenly object orbit to arrive at a second heavenly object or second heavenly object orbit, comprising the sequential, non-sequential or sequence independent steps of:

(a) entering parameters for said method of generating the transfer;

(b) implementing at least one of a forward targeting process and a forward transfer process by varying the parameters for convergence of target variables at the second heavenly object or the second heavenly object orbit from the first heavenly object or the first heavenly object orbit; and

(c) iterating step (b) until sufficient convergence to obtain the transfer from the first heavenly object or the first heavenly object orbit to the second heavenly object or the second heavenly object orbit.

20. A method according to claim 19, wherein said iterating step (c) further comprises the step of iterating step (b) until sufficient convergence to obtain the transfer from the first heavenly object or the first heavenly object orbit to the second heavenly object or the second heavenly object orbit via a weak stability boundary (WSB) orbit interposed therebetween.

21. A method according to claim 20, wherein said implementing step (b) further comprises the step of generating a trajectory around the second heavenly body or the second heavenly body orbit comprising at least a negligible maneuver of between 2-20 meters per second at the WSB or the WSB orbit for at least one of timing and positioning of at least one of a space vehicle, satellite and rocket, prior to ejection therefrom.

22. A method according to claim 19, wherein said implementing step (b) further comprises the step of implementing the at least one of the forward targeting process and the forward transfer process by varying at least two spherical parameters for convergence of the target variables at the second heavenly object or the second heavenly object orbit, while maintaining at least one classical variable substantially fixed.

23. A method according to claim 19, wherein said implementing step (b) further comprises the step of implementing the at least one of the forward targeting process and the forward transfer process by varying velocity magnitude VE, and flight path angle γ

E for convergence of the target variables at the second heavenly object or the second heavenly object orbit, the target variables including radial distance, rM, and inclination iM.

24. A method according to claim 23, further comprising the steps of:

(d) transforming converged values of VE, γ

E into classical elements;

(e) transforming the classical elements to spherical coordinates, wherein the spherical coordinates include the converged values of VE, γ

E, and longitude α

E, latitude δ

E, flight path azimuth/angle with vertical σ

E are changed.

25. A method according to claim 23, wherein the velocity magnitude VE, and the flight path angle γ

E are decoupled from the second heavenly body or the second heavenly body orbit in the transfer.

26. A method according to claim 23, wherein the velocity magnitude VE, and the flight path angle γ

E are decoupled from angular elements of the first heavenly body including inclination iE, ascending node relative to earth Ω

E, and argument of periapsis relative to the first heavenly body ω

E.

27. A method according to claim 19, wherein said implementing step (b) further comprises the step of implementing the at least one of the forward targeting process and the forward transfer process comprising a second order Newton algorithm, and wherein the second order Newton algorithm utilizes two control variables including velocity magnitude VE, and flight path angle γ

E that are varied to achieve at least one of transfer and capture conditions at the second heavenly body or the second heavenly body orbit using two target variables including radial distance, rM, and inclination iM.

28. A method according to claim 19, wherein said implementing step (b) further comprises the step of generating a trajectory around the second heavenly body or the second heavenly body orbit comprising a negligible maneuver of between 2-20 meters per second at a weak stability boundary (WSB) or WSB orbit associated with the second heavenly body.

29. A method according to claim 28, wherein the WSB or the WSB orbit is nonlinear and being substantially at a boundary of capture and escape, thereby allowing the capture and the escape to occur for a substantially zero or relatively small maneuver, and wherein solar gravitational perturbations influence the first and second transfers.

30. A method according to claim 28, wherein the WSB or the WSB orbit is substantially at a boundary of interaction between gravitational fields of the first heavenly body and the second heavenly body.

31. A method according to claim 28, wherein as at least one of a space vehicle, satellite and rocket moves in at least one of the WSB or the WSB orbit, a Kepler energy of the at least one of a space vehicle, satellite and rocket is slightly negative and substantially near to zero.

32. A method according to claim 28, wherein the at least one of the WSB or the WSB orbit is realizable at the predetermined arbitrary altitude by specifying a predetermined velocity magnitude of the at least one of a space vehicle, satellite and rocket, thereby defining a predetermined capture eccentricity.

33. A method according to claim 19, wherein the forward targeting process is a second order Newton algorithm.

34. A method according to claim 19, wherein the first heavenly body or the first heavenly body orbit comprises earth or earth orbit, and wherein the second heavenly body or the second heavenly body orbit comprises moon or moon orbit.

35. A method of traveling by an object emanating substantially at a first heavenly object or first heavenly object orbit to arrive at a second heavenly object or second heavenly object orbit using a transfer, comprising the sequential, non-sequential or sequence independent steps of:

(a) generating the transfer by implementing at least one of a forward targeting process and a forward transfer process by varying parameters for said method until substantial convergence of target variables at the second heavenly object or the second heavenly object orbit; and

(b) traveling from substantially at the first heavenly object or first heavenly object orbit to the second heavenly object or second heavenly object orbit using the transfer by the object.

36. A spacecraft or satellite implementing a method of traveling from substantially a first heavenly object or first heavenly object orbit to arrive at a second heavenly object or second heavenly object orbit using a transfer, wherein the transfer is generated via at least one of said spacecraft, said satellite and a remote system, by implementing at least one of a forward targeting process and a forward transfer process by varying parameters for said method until substantial convergence of target variables at the second heavenly object or the second heavenly object orbit;

and said spacecraft or said satellite travel from substantially at the first heavenly object or first heavenly object orbit to the second heavenly object or second heavenly object orbit using the transfer.