The moon and the planets

, Volume 26, Issue 4, pp 371–382 | Cite as

Trojan-type orbits in the system of two gravitational centers with variable masses and separation

  • B. B. Djakov
  • B. I. Reznikov


Trojan type orbits in the system of two gravitational centers with variable separation are studied within the framework of the restricted problem of three bodies. The backward numerical integration of the equations of motion of the bodies starting in the triangular libration pointsL4 andL5 (reverse problem) finds the breakdown of librations as the separation decreases because of the mass gain of the smaller component and an approach of the body of negligible, mass to the latter up to the distance below its sphere of action with a relative velocity approximately equal to the escape one on this sphere. The breakdown of librations aboutL5 occurs under the mass gain of the smaller component considerably larger than in the case ofL4 and implications are made for the asymmetry of the number of librators aboutL4 andL5 in the solar system (Greeks and Trojans). Other parameters of the libration motion near 1/1 commensurability are obtained, namely, the asymmetry of the libration amplitudes about the triangular points as well as the values of periods and amplitudes within the limits of those for real Trojan asteroids. Trojans could be supposedly, formed inside the Proto-jupiter and escape during its intensive mass loss.


Mass Loss Solar System Relative Velocity Mass Gain Variable Mass 
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Copyright information

© D. Reidel Publishing Co. 1982

Authors and Affiliations

  • B. B. Djakov
    • 1
  • B. I. Reznikov
    • 1
  1. 1.Ioffe Physico-Technical InstituteAcademy of Sciences of the U.S.S.R.LeningradU.S.S.R.

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