### Abstract

Minimizing the amount of fuel needed to place a satellite into Earth orbit and then inserting it into its operational altitude is an important driver of space mission analysis and design. This paper analyzes the velocity changes required to transfer satellites initially in Earth orbit to the Sun-Earth triangular Lagrange points and estimates the minimum velocity changes needed for station keeping at those points after the satellite's two-body motion around the Sun has been gravitationally perturbed. Times of flight required by each insertion and station keeping scenario investigated are also analyzed. Analytical, co-orbital rendezvous equations for an elliptical Earth orbit are derived as a function of Earth true anomaly and solved numerically due to their transcendental nature. These equations predict that total, minimum velocity changes are comparable to the solution of Lambert's problem for various times of flight. When these velocity change results are compared to the velocity changes required to transfer a satellite from Earth orbit to the planets, it can be concluded that a transfer from Earth orbit to the Sun-Earth L_{4} and L_{5} Lagrange points is comparable to a transfer from the Earth to Venus or the Earth to Mars. Station keeping velocity changes and times of flight are investigated by solving Lambert's problem for various initial conditions. The investigation shows that the minimum velocity changes needed to station keep a satellite positioned at L_{4} or L_{5} are in general inversely proportional to the corresponding times of flight needed to implement the station keeping maneuvers and directly proportional to the perturbation time elapsed when the maneuvers are commenced.

Original language | English (US) |
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Title of host publication | American Astronautical Society - Space Flight Mechanics 2007 - Advances in the Astronautical Sciences, Proceedings of the AAS/AIAA Space Flight Mechanics Meeting |

Pages | 1961-1985 |

Number of pages | 25 |

State | Published - Dec 1 2007 |

Event | 17th Annual Space Flight Mechanics Meeting - Sedona, AZ, United States Duration: Jan 28 2007 → Feb 1 2007 |

### Publication series

Name | Advances in the Astronautical Sciences |
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Volume | 127 PART 2 |

ISSN (Print) | 0065-3438 |

### Other

Other | 17th Annual Space Flight Mechanics Meeting |
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Country | United States |

City | Sedona, AZ |

Period | 1/28/07 → 2/1/07 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Aerospace Engineering
- Space and Planetary Science

### Cite this

*American Astronautical Society - Space Flight Mechanics 2007 - Advances in the Astronautical Sciences, Proceedings of the AAS/AIAA Space Flight Mechanics Meeting*(pp. 1961-1985). (Advances in the Astronautical Sciences; Vol. 127 PART 2).

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*American Astronautical Society - Space Flight Mechanics 2007 - Advances in the Astronautical Sciences, Proceedings of the AAS/AIAA Space Flight Mechanics Meeting.*Advances in the Astronautical Sciences, vol. 127 PART 2, pp. 1961-1985, 17th Annual Space Flight Mechanics Meeting, Sedona, AZ, United States, 1/28/07.

**Sun-Earth triangular Lagrange point orbit insertion and satellite station keeping.** / Benavides, Julio Cesar; Spencer, David Bradley.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

TY - GEN

T1 - Sun-Earth triangular Lagrange point orbit insertion and satellite station keeping

AU - Benavides, Julio Cesar

AU - Spencer, David Bradley

PY - 2007/12/1

Y1 - 2007/12/1

N2 - Minimizing the amount of fuel needed to place a satellite into Earth orbit and then inserting it into its operational altitude is an important driver of space mission analysis and design. This paper analyzes the velocity changes required to transfer satellites initially in Earth orbit to the Sun-Earth triangular Lagrange points and estimates the minimum velocity changes needed for station keeping at those points after the satellite's two-body motion around the Sun has been gravitationally perturbed. Times of flight required by each insertion and station keeping scenario investigated are also analyzed. Analytical, co-orbital rendezvous equations for an elliptical Earth orbit are derived as a function of Earth true anomaly and solved numerically due to their transcendental nature. These equations predict that total, minimum velocity changes are comparable to the solution of Lambert's problem for various times of flight. When these velocity change results are compared to the velocity changes required to transfer a satellite from Earth orbit to the planets, it can be concluded that a transfer from Earth orbit to the Sun-Earth L4 and L5 Lagrange points is comparable to a transfer from the Earth to Venus or the Earth to Mars. Station keeping velocity changes and times of flight are investigated by solving Lambert's problem for various initial conditions. The investigation shows that the minimum velocity changes needed to station keep a satellite positioned at L4 or L5 are in general inversely proportional to the corresponding times of flight needed to implement the station keeping maneuvers and directly proportional to the perturbation time elapsed when the maneuvers are commenced.

AB - Minimizing the amount of fuel needed to place a satellite into Earth orbit and then inserting it into its operational altitude is an important driver of space mission analysis and design. This paper analyzes the velocity changes required to transfer satellites initially in Earth orbit to the Sun-Earth triangular Lagrange points and estimates the minimum velocity changes needed for station keeping at those points after the satellite's two-body motion around the Sun has been gravitationally perturbed. Times of flight required by each insertion and station keeping scenario investigated are also analyzed. Analytical, co-orbital rendezvous equations for an elliptical Earth orbit are derived as a function of Earth true anomaly and solved numerically due to their transcendental nature. These equations predict that total, minimum velocity changes are comparable to the solution of Lambert's problem for various times of flight. When these velocity change results are compared to the velocity changes required to transfer a satellite from Earth orbit to the planets, it can be concluded that a transfer from Earth orbit to the Sun-Earth L4 and L5 Lagrange points is comparable to a transfer from the Earth to Venus or the Earth to Mars. Station keeping velocity changes and times of flight are investigated by solving Lambert's problem for various initial conditions. The investigation shows that the minimum velocity changes needed to station keep a satellite positioned at L4 or L5 are in general inversely proportional to the corresponding times of flight needed to implement the station keeping maneuvers and directly proportional to the perturbation time elapsed when the maneuvers are commenced.

UR - http://www.scopus.com/inward/record.url?scp=55849106349&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=55849106349&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:55849106349

SN - 9780877035411

T3 - Advances in the Astronautical Sciences

SP - 1961

EP - 1985

BT - American Astronautical Society - Space Flight Mechanics 2007 - Advances in the Astronautical Sciences, Proceedings of the AAS/AIAA Space Flight Mechanics Meeting

ER -