### Abstract

This paper presents a comparison between an analytical approximation to a spacecraft transfer from a low Earth orbit to a highly elliptical Molniya orbit with an optimal solution. In this paper, a spacecraft is transferred from low Earth orbit to the final mission orbit by using various initial thrust accelerations ranging from 10 ^{-1} to 10 ^{-2} m/sec ^{2}. An approximate analytical method using a blended control that satisfy some basic physical constraints on the orbit transfer and comparing these results to the exact optimal case found using a well known trajectory optimization software. The comparison between the analytical data and the numerical data showed that the percent error between the two is small, there is about a 13% percent difference in propellant usage for the initial thrust acceleration of 10 ^{-1} m/sec ^{2} and 10 ^{-2} m/sec ^{2}. The factor that affected the results of both solutions is that in the analytical method, the radius of perigee was held constant while with the numerical solution the radius of perigee was free. This difference indicates that while the analytical solution was closely related to numerical solution, it can be improved by doing another analytical analysis with the radius of perigee free.

Original language | English (US) |
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Title of host publication | Collection of Technical Papers - AIAA/AAS Astrodynamics Specialist Conference |

Pages | 763-782 |

Number of pages | 20 |

State | Published - Dec 1 2004 |

Event | Collection of Technical Papers - AIAA/AAS Astrodynamics Specialist Conference - Providence, RI, United States Duration: Aug 16 2004 → Aug 19 2004 |

### Publication series

Name | Collection of Technical Papers - AIAA/AAS Astrodynamics Specialist Conference |
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Volume | 2 |

### Other

Other | Collection of Technical Papers - AIAA/AAS Astrodynamics Specialist Conference |
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Country | United States |

City | Providence, RI |

Period | 8/16/04 → 8/19/04 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Engineering(all)

### Cite this

*Collection of Technical Papers - AIAA/AAS Astrodynamics Specialist Conference*(pp. 763-782). [AIAA-2004-5090] (Collection of Technical Papers - AIAA/AAS Astrodynamics Specialist Conference; Vol. 2).

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*Collection of Technical Papers - AIAA/AAS Astrodynamics Specialist Conference.*, AIAA-2004-5090, Collection of Technical Papers - AIAA/AAS Astrodynamics Specialist Conference, vol. 2, pp. 763-782, Collection of Technical Papers - AIAA/AAS Astrodynamics Specialist Conference, Providence, RI, United States, 8/16/04.

**An analytical approach for continuous-thrust, LEO-Molniya transfers.** / Spencer, David Bradley; Acon-Chen, Felix.

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

TY - GEN

T1 - An analytical approach for continuous-thrust, LEO-Molniya transfers

AU - Spencer, David Bradley

AU - Acon-Chen, Felix

PY - 2004/12/1

Y1 - 2004/12/1

N2 - This paper presents a comparison between an analytical approximation to a spacecraft transfer from a low Earth orbit to a highly elliptical Molniya orbit with an optimal solution. In this paper, a spacecraft is transferred from low Earth orbit to the final mission orbit by using various initial thrust accelerations ranging from 10 -1 to 10 -2 m/sec 2. An approximate analytical method using a blended control that satisfy some basic physical constraints on the orbit transfer and comparing these results to the exact optimal case found using a well known trajectory optimization software. The comparison between the analytical data and the numerical data showed that the percent error between the two is small, there is about a 13% percent difference in propellant usage for the initial thrust acceleration of 10 -1 m/sec 2 and 10 -2 m/sec 2. The factor that affected the results of both solutions is that in the analytical method, the radius of perigee was held constant while with the numerical solution the radius of perigee was free. This difference indicates that while the analytical solution was closely related to numerical solution, it can be improved by doing another analytical analysis with the radius of perigee free.

AB - This paper presents a comparison between an analytical approximation to a spacecraft transfer from a low Earth orbit to a highly elliptical Molniya orbit with an optimal solution. In this paper, a spacecraft is transferred from low Earth orbit to the final mission orbit by using various initial thrust accelerations ranging from 10 -1 to 10 -2 m/sec 2. An approximate analytical method using a blended control that satisfy some basic physical constraints on the orbit transfer and comparing these results to the exact optimal case found using a well known trajectory optimization software. The comparison between the analytical data and the numerical data showed that the percent error between the two is small, there is about a 13% percent difference in propellant usage for the initial thrust acceleration of 10 -1 m/sec 2 and 10 -2 m/sec 2. The factor that affected the results of both solutions is that in the analytical method, the radius of perigee was held constant while with the numerical solution the radius of perigee was free. This difference indicates that while the analytical solution was closely related to numerical solution, it can be improved by doing another analytical analysis with the radius of perigee free.

UR - http://www.scopus.com/inward/record.url?scp=19644372464&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=19644372464&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:19644372464

SN - 1563477149

SN - 9781563477140

T3 - Collection of Technical Papers - AIAA/AAS Astrodynamics Specialist Conference

SP - 763

EP - 782

BT - Collection of Technical Papers - AIAA/AAS Astrodynamics Specialist Conference

ER -