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Orbit derivation

  1. Apr 10, 2006 #1
    Hey everyone,
    I need to prove something explictly, problem is, i dont know where to start.
    In orbits, we can show that the motion of 2 bodies interacting with each other only by central forces can be reduced to a an equivalent one-body problem. This is by using a Lagrangian, and by introducing an 'equivalent' mass.
    The question is to show that this is possible even if these bodies are in an external uniform gravitational field.
    I dont know where to start. I cant see how a gravitational field will affect the Lagrangian, because a graviatational field will just affect the potential energy term. This isnt really solving it explicity though...
    any ideas where to start?
    Cheers
     
  2. jcsd
  3. Apr 10, 2006 #2
    If I'm following your argument correctly, you've made the correct connection. The process by which the coordinates are modified to produce an equivalent one body problem do not depend on a specific form of a potential, so the process will still go through. All you should have to do to prove the process is possible is to input the change of variables into the Lagrangian explicitly.

    -Dan
     
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