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Unformatted text preview: The Restricted three-body problem Although the three-body problem is not generally soluble algorithmically, we can tell much about the behaviour in restricted situations. The usual "restricted" three-body problem assumes that the third body (the motion of which we are interested in) is small in comparison to the other bodies as in the example above, but here the two main bodies are comparable in size and we look at the motion of the third in the frame rest of the two-body system (which must be a rotating frame where the bodies rotate about their common centre of gravity). So, taking axes centred on the centre of gravity of the system, containing bodies mass m 1 and m 2 , a rotating frame in which m 1 and m 2 are fixed, we have a small body m very small compared to m 1 and m 2 and m 2 , at position distance r 1 from m 1 and r 2 from m 2 : The energy equation, given that m is at (eta, epsilon) in this frame, is given by: where the first term is the kinetic energy, the second the energy due to the centrifugal force and...
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This note was uploaded on 12/15/2011 for the course AST AST1002 taught by Professor Emilyhoward during the Fall '10 term at Broward College.
- Fall '10