IngentaConnect Co-Orbital Motion with Slowly Varying Parameters

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 M₀ 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, M₀, (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 L₄ or L₅, 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 $\epsilon_{\rm s}=\dot{J}_{\rm s}/(n_{\rm s}J_{\rm s})$ induces an distortion of the phase space which is entirely described by an asymmetry coefficient alpha = epsi _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_sa_s with time. Applying a constant torque to the particle, as measured by $\epsilon_{\rm p}=\dot{J}/(n_{\rm s}J_{\rm s})$ is then merely equivalent to replacing alpha = epsi _s/ by alpha = ( epsi _s - epsi _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_sa_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 L₄ or L₅, or driven away from them. Finally, we show that when the co-orbital bodies are two satellites with comparable masses m₁ and m₂, we can reduce the problem to that of a test particle co-orbital with a satellite of mass m₁ + m₂. This new problem has then parameters varying at rates which are combinations, with appropriate coefficients, of the changes suffered by each satellite.

Keywords: co-orbital motion; adiabatic invariant

Language: English

Document Type: Research article

Affiliations: 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 (veronique.dubois@chimie.univ-nantes.fr)

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