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Finding the (Newtonian) movement equation of an object in a gravitational field

  1. Dec 27, 2011 #1
    This is a problem I've been looking to solve for some time.

    1. The problem statement, all variables and given/known data
    You must find a movement equation for an object in a gravitational field knowing traditional formulas of force and acceleration of gravity (see below).


    2. Relevant equations

    absolute value of the acceleration at a distance 'r' from the centre of gravity of an object with mass 'm'

    [itex]g=G\frac{m}{r^{2}}[/itex]

    'r' as a movement equation

    [itex]r=r(t)[/itex]
    [itex]r''(t)=-g[/itex]


    3. The attempt at a solution

    [itex]r''(t)=-G\frac{m}{r(t)^{2}}[/itex]
    [itex]r''(t)r(t)^{2}=-Gm[/itex]

    I don't really know what to do next. It seems that r(t) has at least one constant term and it's of degree>2 if it's a polynomial (as acceleration changes). I know nothing more than that.
     
  2. jcsd
  3. Dec 27, 2011 #2
    It might help to rewrite as
    [tex] \frac{d^2r}{dt^2}r^2 = -Gm [/tex]
    After this you should use a relationship you know linking position, velocity and acceleration mathematically.
     
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