Abstract
Numerical and analytical comparisons are made between three methods of obtaining stability information on satellite motion using the model of the restricted problem of three bodies. Kuiper's (1961) and Szebehely's (1978) approximate results are compared with computer solutions obtained by successive iterations. The three methods show close agreement regarding the maximum values of the orbital radii for stability. The lowest result and therefore the most conservative estimate is obtained by the simplest formula, ρmax=(μ/81)1/3 where ϱ is the ratio of the satellite's orbital radius to the distance between the primaries with massesm 1>m 2 and μ is the mass-ratio given bym 2/(m 1+m 2).
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References
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Szebehely, V., McKenzie, R. Comparison between stability limits for satellite motion. Celestial Mechanics 18, 391–394 (1978). https://doi.org/10.1007/BF01230351
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DOI: https://doi.org/10.1007/BF01230351