Co-Orbital Motion with Slowly Varying Parameters |
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| Authors: | Bruno Sicardy Véronique Dubois |
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| Institution: | (1) Observatoire et Université, de Paris, Bat. 10, LESIA, F-92195 Meudon Cédex Principal, France;(2) Université de Nantes Laboratoire de Géophysique et Planétologie, BP 92208, F-44322 Nantes, Cédex 3, France ( |
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| Abstract: | We consider the dynamics of a test particle co-orbital with a satellite of mass m
s which revolves around a planet of mass M
0  m
s with a mean motion n
s and semi-major axis a
s. We study the long term evolution of the particle motion under slow variations of (1) the mass of the primary, M
0, (2) the mass of the satellite, m
s and (3) the specific angular momentum of the satellite J
s. The particle is not restricted to small harmonic oscillations near L
4 or L
5, and may have any libration amplitude on tadpole or horseshoe orbits. In a first step, no torque is applied to the particle, so that its motion is described by a Hamiltonian with slowly varying parameters. We show that the torque applied to the satellite, as measured by  s = js/(n
s
J
s) induces an distortion of the phase space which is entirely described by an asymmetry coefficient  = s/ , where = m
s/M. The adiabatic invariance of action implies furthermore that the long term evolution of the particle co-orbital motion depends only on the variation of m
s
a
s with time. Applying a constant torque to the particle, as measured by s = js/(n
s
J
p) is then merely equivalent to replacing = s/ by = (s – p)/. However, if the torque acting on the particle exhibits a radial gradient, then the action is no more conserved and the evolution of the particle orbit is no more controlled by m
s
a
s only. We show that even mild torque gradients can dominate the orbital evolution of the particle, and eventually decide whether the latter will be pulled towards the stable equilibrium points L
4 or L
5, or driven away from them. Finally, we show that when the co-orbital bodies are two satellites with comparable masses m
1 and m
2, we can reduce the problem to that of a test particle co-orbital with a satellite of mass m
1 + m
2. This new problem has then parameters varying at rates which are combinations, with appropriate coefficients, of the changes suffered by each satellite. |
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| Keywords: | co-orbital motion adiabatic invariant |
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