Low energy method for changing the inclinations of orbiting satellites using weak stability boundaries and a computer process for implementing same
First Claim
1. A method of changing an inclination of an object 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 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 steps of:
- (a) implementing a forward targeting process by varying velocity magnitude VE, and flight path angle γ
E for convergence of first target variables at the WSB or the WSB orbit, the first target variables including radial distance, rL, and inclination iL ;
(b) iterating step (a) until sufficient convergence to obtain the operational ballistic capture transfer from the earth or the earth orbit to a weak lunar capture in the WSB or the WSB orbit;
(c) performing an inclination change at the WSB or the WSB orbit;
(d) implementing the forward targeting process by varying velocity magnitude VL, and flight path angle γ
L for convergence of second target variables at the earth or the earth orbit from the WSB or the WSB orbit, the second target variables including radial distance, rE, and inclination iE including the inclination change performed in step (c); and
(e) iterating step (d) until sufficient convergence to obtain the operational ballistic ejection transfer from the WSB or the WSB orbit to the earth or the earth orbit at the inclination change.
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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°. This yields a savings of approximately 13% in Delta-V as compared to the standard approach which could translate into a significant increase of payload or perhaps a smaller launch vehicle. This may have applications to commercial satellite launches for the Iridium or Teledesic networks and others.
28 Citations
19 Claims
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1. A method of changing an inclination of an object 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 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 steps of:
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(a) implementing a forward targeting process by varying velocity magnitude VE, and flight path angle γ
E for convergence of first target variables at the WSB or the WSB orbit, the first target variables including radial distance, rL, and inclination iL ;(b) iterating step (a) until sufficient convergence to obtain the operational ballistic capture transfer from the earth or the earth orbit to a weak lunar capture in the WSB or the WSB orbit; (c) performing an inclination change at the WSB or the WSB orbit; (d) implementing the forward targeting process by varying velocity magnitude VL, and flight path angle γ
L for convergence of second target variables at the earth or the earth orbit from the WSB or the WSB orbit, the second target variables including radial distance, rE, and inclination iE including the inclination change performed in step (c); and(e) iterating step (d) until sufficient convergence to obtain the operational ballistic ejection transfer from the WSB or the WSB orbit to the earth or the earth orbit at the inclination change. - View Dependent Claims (2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13)
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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 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 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:
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(a) generating the BCT using a forward targeting process by varying velocity magnitude VE, and flight path angle γ
E for convergence of first target variables at the WSB or the WSB orbit, the first target variables including radial distance, rL, and inclination iL ;(b) traveling from the earth or the earth orbit to a weak lunar capture in the WSB or the WSB orbit using the operational ballistic capture transfer; (c) optionally performing an inclination change at the WSB or the WSB orbit; (d) generating the BET using the forward targeting process by varying velocity magnitude VL, and flight path angle γ
L for convergence of second target variables at the earth or the earth orbit from the WSB or the WSB orbit, the second target variables including radial distance, rE, and inclination iE 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. - View Dependent Claims (15, 16)
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17. 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 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 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, wherein the computer implements the sequential or non-sequential functions of:
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(a) generating the BCT using a forward targeting process by varying velocity magnitude VE, and flight path angle γ
E for convergence of first target variables at the WSB or the WSB orbit;(b) generating the BET using the forward targeting process by varying velocity magnitude VL, and flight path angle γ
L 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 the earth or the earth orbit to a weak lunar capture in the WSB or the WSB orbit using the operational ballistic capture transfer, and navigating the object 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.
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18. A computer program memory, storing computer instructions to generate an operational ballistic capture transfer for an object emanating substantially at earth or earth orbit to arrive at the moon or moon orbit using a computer, the computer instructions including:
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(a) generating a forward targeting process by varying velocity magnitude VE, and flight path angle γ
E for convergence of first target variables at a weak stability boundary WSB or a WSB orbit, the first target variables including radial distance, rL, and inclination iL ;(b) iterating step (a) until sufficient convergence to obtain the operational ballistic capture transfer from the earth or the earth orbit to a weak lunar capture in the WSB or the WSB orbit; (c) generating the forward targeting process by varying velocity magnitude VL, and flight path angle γ
L for convergence of second target variables at the earth or the earth orbit from the WSB or the WSB orbit, the second target variables including radial distance, rE, and inclination iE ; and(e) iterating step (d) until sufficient convergence to obtain the operational ballistic ejection transfer from the WSB or the WSB orbit to the earth or the earth orbit at the inclination change.
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19. 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:
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(a) generating a ballistic capture transfer (BCT) using a forward targeting process by varying velocity magnitude VE, and flight path angle γ
E, for convergence of first target variables at a weak stability boundary 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 operational ballistic capture transfer; (c) optionally performing an inclination change at the WSB or the WSB orbit; (d) generating a ballistic ejection transfer (BET) using the forward targeting process by varying velocity magnitude VL, and flight path angle γ
L for convergence of second target variables at the earth or the earth orbit from the WSB or the WSB orbit; 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.
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Specification