Abstract
In this paper we use the Jacobian integral of the circular restricted three-body problem to establish a testing function of a moving testing particle when it moves like a planet. This function determines whether or not the particle will stay in a definite region (which may be called “stable region”, SR). By means of checking with an electronic computer, we can find that the SR of quasicircular orbit of retrograde planet motion is much less than the SR of direct planet motion. It is the reason why the existence of a retrograde planet is very rare.
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References
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Chia-ho, W. Why we have not yet found a retrograde planet in the solar system?. Appl Math Mech 11, 421–428 (1990). https://doi.org/10.1007/BF02016372
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DOI: https://doi.org/10.1007/BF02016372