Detection by MEGNO of the gravitational resonances between a rotating ellipsoid and a point mass satellite |
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Authors: | Email author" target="_blank">A?CompèreEmail author A?Lema?tre N?Delsate |
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Institution: | (1) Institute of Astronomy, University of Vienna, Türkenschanzstrasse 17, A-1180 Vienna, Austria |
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Abstract: | Nowadays the scientific community considers that more than a third of the asteroids are double. The study of the stability
of these systems is quite complex, because of their irregular shapes and tumbling rotations, and requires a full body–full
body approach. A particular case is analysed here, when the secondary body is sufficiently small and distant from the primary
to be considered as a point mass satellite. Gravitational resonances (between the revolution of the satellite and the rotation
of the asteroid) of a small body in fast or slow rotation around a rigid ellipsoid are studied. The same model can be used
for the motion of a probe around an irregular asteroid. The gravitational potential induced by the primary body is modelled
by the MacMillan potential. The stability of the satellite is measured thanks to the MEGNO indicator (Mean Exponential Growth
Factor of Nearby Orbits). We present stability maps in the plane
(\fracbd, \fraccd){\left(\frac{b}{d}, \frac{c}{d}\right)} where d, b, and c are the three semi-axes of the ellipsoid shaping the asteroid. Special stable conic-like curves are detected on these maps
and explained by an analytical model, based on a simplification of the MacMillan potential for some specific resonances (1
: 1 and 2 : 1). The efficiency of the MEGNO to detect stability is confirmed. |
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