Abstract
A translunar communication station is to be kept close to a nominal unstable periodic ‘Halo’ orbit, visible at all times from Earth. The analytically computed nominal orbit is not perfect, requiring an average control acceleration of about 10−6 g's for tight control. An adjustable quadratic combination of position deviation and control acceleration is minimized to provide an (adjustable) control law with period feedback gains and a periodic bias. The average control acceleration can be reduced to less than 10−8 g's with an error settling time of less than 21/2 months. The resulting limiting motion provides, in turn, an improved nominal, permitting the same low control cost with much tighter control, corresponding to settling times of the order of one day.
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References
Farquhar, R. W.: 1970, NASA TR R-346.
Farquhar, R. W. and Kamel, Ahmed A.: AIAA Paper No. 72-935,AIAA Astrodynamics Conf., Palo Alto, Calif.
Nishimura, T.: 1972,J. Spacecraft 9, No. 7.
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Breakwell, J.V., Kamel, A.A. & Ratner, M.J. Station-keeping for a translunar communication station. Celestial Mechanics 10, 357–373 (1974). https://doi.org/10.1007/BF01586864
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DOI: https://doi.org/10.1007/BF01586864