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The Restricted thre1

The Restricted thre1 - The Restricted three-body problem...

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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:

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