Astronomy and Astrophysics – Astrophysics
Scientific paper
Jan 2012
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2012ap%26ss.tmp...44k&link_type=abstract
Astrophysics and Space Science, Online First
Astronomy and Astrophysics
Astrophysics
Robe'S Restricted Problem, Equilibrium Solution, Stability, Buoyancy Force
Scientific paper
In the problem of 2+2 bodies in the Robe's setup, one of the primaries of mass m^{*}1 is a rigid spherical shell filled with a homogeneous incompressible fluid of density ρ 1. The second primary is a mass point m 2 outside the shell. The third and the fourth bodies (of mass m 3 and m 4 respectively) are small solid spheres of density ρ 3 and ρ 4 respectively inside the shell, with the assumption that the mass and the radius of third and fourth body are infinitesimal. We assume m 2 is describing a circle around m^{*}1. The masses m 3 and m 4 mutually attract each other, do not influence the motion of m^{*}1 and m 2 but are influenced by them. We also assume masses m 3 and m 4 are moving in the plane of motion of mass m 2. In the paper, the equations of motion, equilibrium solutions, linear stability of m 3 and m 4 are analyzed. There are four collinear equilibrium solutions for the given system. The collinear equilibrium solutions are unstable for all values of the mass parameters μ,μ 3,μ 4. There exist an infinite number of non collinear equilibrium solutions each for m 3 and m 4, lying on circles of radii λ,λ' respectively (if the densities of m 3 and m 4 are different) and the centre at the second primary. These solutions are also unstable for all values of the parameters μ,μ 3,μ 4, φ, φ'. Such a model may be useful to study the motion of submarines due to the attraction of earth and moon.
Aggarwal Rajiv
Kaur Bhavneet
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