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Periodic and Secular Solutions in the Restricted Three–Body Problem under the Effect of Zonal Harmonic Parameters |
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PP: 1659-1669 |
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Author(s) |
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Elbaz I. Abouelmagd,
M. S. Alhothuali,
Juan L. G. Guirao,
H. M. Malaikah,
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Abstract |
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| The aim of the present work is to study the periodic structure of the restricted three–body problem considering the effect of
the zonal harmonics J2 and J4 for the more massive body. We show that the triangular points in the restricted three–body problem have
long or short periodic orbits in the range 0 m < mc. We also present a graphical analysis for the variations of the angular frequencies
for the long and short periodic orbits computing explicitly the expressions of the lengths of the semi–major and semi–minor axes and
determining the orientations of the principal axes for the ellipses that represent periodic orbits. Moreover, the secular solution when
m = mc is stated and it is proved that the triangular points have periodic orbits in this case too. This model has special significance in
space missions either to place telescopes or for dispatching satellites and exploring vehicles. |
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