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General equation of motion with gravitational field

  1. Jun 1, 2014 #1
    I was studying the equations of free fall and of launch when I realize that those equations are spetial case of a object in motion through of a gravitational field. So exist some general equation that describe the motion (the trajetory*) of the object through of the field (using initial values like moment, velocity, position, direction, mass, gravity, distance, etc)?

    * Illustration:

    Attached Files:

  2. jcsd
  3. Jun 1, 2014 #2


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    There certainly are...this is just the central force problem (actually it's the Kepler problem) in Newtonian mechanics. You need 12 initial value data, 2 initial positions, and 2 initial velocities (each of which have 3 components).

    See here: http://en.wikipedia.org/wiki/Kepler_problem
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