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

• US 6,253,124 B1
• Filed: 05/07/1999
• Issued: 06/26/2001
• 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:
  US09/306,793
• Time in Patent Office: 781 Days
• Field of Search: 701/13, 701/3, 701/226, 701/4, 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

When a satellite is orbiting the earth in an elliptic orbit, it has a certain inclination with respect to the earth'"'"'s equator. The usual way to change the inclination is perform a maneuver by firing the rocket engines at the periapsis of the ellipse. This then forces the satellite into the desired inclination. There is a substantially more fuel efficient way to change the inclination. This is done by an indirect route by first doing a maneuver to bring 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 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 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 an operational ballistic ejection transfer (BET) 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 Hohmann transfer for convergence of first target variables at the WSB or the WSB orbit;

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

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

(d) generating the BET 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 using the operational ballistic ejection transfer,

wherein said generating step (d) further comprises the step of generating the BET using a forward targeting process for convergence of the 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).

2. 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 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 an operational ballistic ejection transfer (BET) 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 Hohmann transfer for convergence of first target variables at the WSB or the WSB orbit;

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

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

(d) generating the BET 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 using the operational ballistic ejection transfer,

wherein the second target variables are decoupled from the earth or the earth orbit in said step (d) of generating the BET.

3. 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 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 an operational ballistic ejection transfer (BET) 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 Hohmann transfer for convergence of first target variables at the WSB or the WSB orbit;

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

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

(d) generating the BET 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 using the operational ballistic ejection transfer,

wherein the second target variables are decoupled from angular moon elements in said step (d) of generating the BET.

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 by generating a combination 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 an operational ballistic ejection transfer (BET) 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 Hohmann transfer for convergence of first target variables at the WSB or the WSB orbit;

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

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

(d) generating the BET 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 using the operational ballistic ejection transfer,

wherein at least one of the Hohmann transfer and the operational ballistic ejection transfer are dynamically generated in the at least one of the space vehicle, the satellite, and the rocket.

5. 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 operational ballistic capture transfer (BCT) 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 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 BCT for convergence of first target variables at the WSB or the WSB orbit;

(b) traveling from the earth or the earth orbit to a weak lunar capture in the WSB or the WSB orbit using the BCT;

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

(d) generating the 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 using the Hohmann transfer,

wherein said generating step (a) further comprises the step of generating the BCT using a forward targeting process for convergence of the first target variables at the WSB or the WSB orbit from the earth or the earth orbit, optionally including the inclination change performed in step (c).

6. 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 operational ballistic capture transfer (BCT) 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 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 BCT for convergence of first target variables at the WSB or the WSB orbit;

(b) traveling from the earth or the earth orbit to a weak lunar capture in the WSB or the WSB orbit using the BCT;

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

(d) generating the 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 using the Hohmann transfer,

wherein the first target variables are decoupled from the moon or the moon orbit in said step (a) of generating the BCT.

7. 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 operational ballistic capture transfer (BCT) 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 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 BCT for convergence of first target variables at the WSB or the WSB orbit;

(b) traveling from the earth or the earth orbit to a weak lunar capture in the WSB or the WSB orbit using the BCT;

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

(d) generating the 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 using the Hohmann transfer,

wherein the first target variables are decoupled from angular earth elements in said step (a) of generating the BCT.

8. 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 operational ballistic capture transfer (BCT) 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 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 BCT for convergence of first target variables at the WSB or the WSB orbit;

(b) traveling from the earth or the earth orbit to a weak lunar capture in the WSB or the WSB orbit using the BCT;

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

(d) generating the 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 using the Hohmann transfer,

wherein at least one of the Hohmann transfer and the operational ballistic capture transfer are dynamically generated in the at least one of the space vehicle, the satellite, and the rocket.

9. 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 the earth or the earth orbit to a weak lunar capture in a weak stability boundary (WSB) or WSB orbit using at least one of an operational ballistic capture transfer (BCT) and 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 and optionally at the inclination change using at least one of an operational ballistic ejection transfer (BET) and a second Hohmann transfer,

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.

10. A method of generating operational ballistic capture transfer for an object emanating substantially at a first plant or first planet orbit to arrive at a second planet or second planet orbit using a computer implemented process, comprising the steps of:

(a) entering parameters for said method of generating operational ballistic capture transfer;

(b) implementing a forward targeting process by varying the parameters for convergence of target variables at the second planet from the first planet; and

(c) iterating step (b) until sufficient convergence to obtain the operational ballistic capture transfer from the first planet or the first planet orbit to the second planet or the second planet orbit.

11. 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, non-sequential or sequence independent steps of:

(a) traveling using a first transfer from a first heavenly body or a first heavenly body orbit to a weak capture in a weak stability boundary (WSB) or WSB orbit associated with said first heavenly body;

(b) performing at least a negligible maneuver and optionally performing an inclination change at the WSB or the WSB orbit and ejecting therefrom; and

(c) traveling using a second transfer from the WSB or the WSB orbit to at least one of the first heavenly body or the first heavenly body orbit and a second heavenly body or a second heavenly body orbit at a predetermined arbitrary altitude and optionally at the inclination change,

wherein the first transfer comprises an operational ballistic capture transfer (BCT), and wherein said traveling step (a) further comprises the step of traveling using the BCT from the first heavenly body or the first heavenly body orbit to the weak capture in the weak stability boundary (WSB) or the WSB orbit associated with said first heavenly body by implementing a forward targeting process by varying parameters for said method until convergence of target variables at the WSB or the WSB orbit.

12. 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, non-sequential or sequence independent steps of:

(a) traveling using a first transfer from a first heavenly body or a first heavenly body orbit to a weak capture in a weak stability boundary (WSB) or WSB orbit associated with said first heavenly body;

(b) performing at least a negligible maneuver and optionally performing an inclination change at the WSB or the WSB orbit and ejecting therefrom; and

(c) traveling using a second transfer from the WSB or the WSB orbit to at least one of the first heavenly body or the first heavenly body orbit and a second heavenly body or a second heavenly body orbit at a predetermined arbitrary altitude and optionally at the inclination change,

wherein the first transfer comprises an operational ballistic capture transfer (BCT), and wherein said traveling step (a) further comprises the step of traveling using the BCT from the first heavenly body or the first heavenly body orbit to the weak capture in the weak stability boundary (WSB) or the WSB orbit associated with said first heavenly body by implementing a forward targeting process by varying the at least two spherical parameters for convergence of target variables at the WSB or the WSB orbit, while maintaining at least one classical variable used in said forward targeting process substantially fixed.

13. 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, non-sequential or sequence independent steps of:

(a) traveling using a first transfer from a first heavenly body or a first heavenly body orbit to a weak capture in a weak stability boundary (WSB) or WSB orbit associated with said first heavenly body;

(b) performing at least a negligible maneuver and optionally performing an inclination change at the WSB or the WSB orbit and ejecting therefrom; and

(c) traveling using a second transfer from the WSB or the WSB orbit to at least one of the first heavenly body or the first heavenly body orbit and a second heavenly body or a second heavenly body orbit at a predetermined arbitrary altitude and optionally at the inclination change,

wherein the first transfer comprises an operational ballistic capture transfer (BCT), and wherein said traveling step (a) further comprises the step of traveling using the BCT from the first heavenly body or the first heavenly body orbit to the weak capture in the weak stability boundary (WSB) or the WSB orbit associated with said first heavenly body by implementing a forward targeting process by varying velocity magnitude V_E, and flight path angle γ

_E for convergence of target variables at the WSB or the WSB orbit, the target variables including radial distance, r_M, and inclination i_M.

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, non-sequential or sequence independent steps of:

(a) traveling using a first transfer from a first heavenly body or a first heavenly body orbit to a weak capture in a weak stability boundary (WSB) or WSB orbit associated with said first heavenly body;

(b) performing at least a negligible maneuver and optionally performing an inclination change at the WSB or the WSB orbit and ejecting therefrom; and

(c) traveling using a second transfer from the WSB or the WSB orbit to at least one of the first heavenly body or the first heavenly body orbit and a second heavenly body or a second heavenly body orbit at a predetermined arbitrary altitude and optionally at the inclination change,

wherein the first transfer comprises an operational ballistic capture transfer (BCT), and wherein said traveling step (a) further comprises the step of traveling using the first transfer from the first heavenly body or the first heavenly body orbit to the weak capture in the weak stability boundary (WSB) or the WSB orbit associated with said first heavenly body by implementing a forward targeting process comprising a second order Newton algorithm, and wherein the second order Newton algorithm utilizes two control variables including velocity magnitude V_E, and flight path angle γ

_E that are varied to achieve WSB conditions at the second heavenly body or the second heavenly body orbit using two target variables including radial distance, r_M, and inclination i_M.

15. A method according to claim 14, wherein the velocity magnitude V_E, and the flight path angle γ

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

16. A method according to claim 14, wherein the velocity magnitude V_E, and the flight path angle γ

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

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

_E.

17. 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, non-sequential or sequence independent steps of:

(a) traveling using a first transfer from a first heavenly body or a first heavenly body orbit to a weak capture in a weak stability boundary (WSB) or WSB orbit associated with said first heavenly body;

(b) performing at least a negligible maneuver and optionally performing an inclination change at the WSB or the WSB orbit and ejecting therefrom; and

(c) traveling using a second transfer from the WSB or the WSB orbit to at least one of the first heavenly body or the first heavenly body orbit and a second heavenly body or a second heavenly body orbit at a predetermined arbitrary altitude and optionally at the inclination change,

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.

18. 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, non-sequential or sequence independent steps of:

(a) traveling using a first transfer from a first heavenly body or a first heavenly body orbit to a weak capture in a weak stability boundary (WSB) or WSB orbit associated with said first heavenly body;

(b) performing at least a negligible maneuver and optionally performing an inclination change at the WSB or the WSB orbit and ejecting therefrom; and

(c) traveling using a second transfer from the WSB or the WSB orbit to at least one of the first heavenly body or the first heavenly body orbit and a second heavenly body or a second heavenly body orbit at a predetermined arbitrary altitude and optionally at the inclination change,

wherein the second transfer comprises an operational ballistic ejection transfer (BET), and wherein said traveling step (c) further comprises the step of traveling using the BET from the weak capture in the weak stability boundary (WSB) or the WSB orbit to the at least one of the first heavenly body or the first heavenly body orbit and the second heavenly body or the second heavenly body orbit by implementing a forward targeting process by varying second parameters for said method until convergence of second target variables at the WSB or the WSB orbit.

19. A method according to claim 18, wherein the second target variables are decoupled from at least one of the first heavenly body or the first heavenly body orbit and angular second heavenly body elements.

20. A satellite placed in orbit at least one of an inclination and an altitude using a computer implemented or computer assisted process, comprising the sequential, non-sequential or sequence independent steps of:

(a) traveling using a first Hohmann transfer from a first heavenly body or a first heavenly body orbit to a weak capture in a weak stability boundary (WSB) or WSB orbit associated with said first heavenly body;

(b) performing at least a negligible maneuver and optionally performing an inclination change at the WSB or the WSB orbit and ejecting therefrom; and

(c) traveling using a second Hohmann transfer from the WSB or the WSB orbit to at least one of the first heavenly body or the first heavenly body orbit and a second heavenly body or a second heavenly body orbit at a predetermined arbitrary altitude and optionally at the inclination change,

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.

21. A satellite placed in orbit at least one of an inclination and an altitude using a computer implemented or computer assisted process, comprising the sequential, non-sequential or sequence independent steps of:

(a) traveling using a first transfer from a first heavenly body or a first heavenly body orbit to a weak capture in a weak stability boundary (WSB) or WSB orbit associated with said first heavenly body;

(b) performing at least a negligible maneuver and optionally performing an inclination change at the WSB or the WSB orbit and ejecting therefrom; and

(c) traveling using a second transfer from the WSB or the WSB orbit to at least one of the first heavenly body or the first heavenly body orbit and a second heavenly body or a second heavenly body orbit at a predetermined arbitrary altitude and optionally at the inclination change,

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.

22. A satellite placed in orbit at least one of an inclination and an altitude using a computer implemented or computer assisted process, comprising the sequential, non-sequential or sequence independent steps of:

(a) traveling from the earth or the earth orbit to a weak lunar capture in a weak stability boundary (WSB) or WSB orbit using at least one of an operational ballistic capture transfer (BCT) and 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 and optionally at the inclination change using at least one of an operational ballistic ejection transfer (BET) and a second Hohmann transfer,

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.