Dynamics and Control

, Volume 4, Issue 4, pp 383–394 | Cite as

Minimum fuel lunar trajectories for a low-thrust power-limited spacecraft

  • Oded M. Golan
  • John V. Breakwell
Article

Abstract

Minimum fuel trajectories from a low Earth parking orbit to a low Moon orbit are obtained for a low-thrust power-limited spacecraft with thrust acceleration levels of the order of 10−3G. The trajectories are found by matching an Earth spiral to a Moon spiral at some intermediate distance. Results are given for the planar case and for the three dimensional case where the Moon orbit is polar.

Keywords

Dimensional Case Planar Case Acceleration Level Intermediate Distance Minimum Fuel 

Nomenclature

H

Hamiltonian function

P

power

U

gravity potential

M

Jacobian matrix

a

thrust acceleration

h

angular momentum

i

inclination angle

m

mass of the spacecraft

n

angular rate of the Earth-Moon system

r

radius

t

time

v

velocity

π

angular coordinate in the orbit plane

λ

adjoint variable (Lagrange multiplier)

μe, μm

gravity coefficient of Earth, Moon

σ

state

ω

right ascension of the node

\([\overrightarrow ]\),\(\widehat{[ ]}\)

vector and a unit vector

[]o, []f

variable evaluated at initial, final time

[]1, []2

quantity related to body 1,2 (interchangeably the Earth and the Moon)

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References

  1. 1.
    Golan, O. M., and Breakwell, J. V., “Minimum fuel trajectories for a low-thrust power-limited mission to the moon and to lagrange pointsl 4 andl 5,” inAAS/AIAA Astrodynamics Specialist Conference, stowe, Vermont, August, 1989.Google Scholar
  2. 2.
    Breakwell, J. V., and Rauch, H. E., “Asymptotic matching in power-limited interplanetary transfers,” inSpace Flight Mechanics Specialist Symposium, AAS Science and Technology Series, Vol. 11, 1967.Google Scholar
  3. 3.
    Bryson, A. E., Jr., and Ho, Y.-C.,Applied Optimal Control, Hemisphere Publishing Corporation, 1975.Google Scholar
  4. 4.
    Battin, R. H.,An Introduction to the Mathematics and Methods of Astrodynamics. AIAA Education Series, American Institute of Aeronautics and Astronautics, 1987.Google Scholar
  5. 5.
    Szebehely, R.,Theory of Orbits, the Restricted Problem of Three Bodies, Academic Press, 1967.Google Scholar

Copyright information

© Kluwer Academic Publishers 1994

Authors and Affiliations

  • Oded M. Golan
    • 1
  • John V. Breakwell
    • 1
  1. 1.Department of Aeronautics and AstronauticsStanford UniversityStanfordUSA

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