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Missing mass in gravitational force

  1. Apr 19, 2013 #1
    This is a really dumb question but I can't seem to make sense out of this...

    For a conservative force, we have [itex]\vec{F}=-\nabla \phi[/itex], where [itex]\phi[/itex] stands for the potential. So let's take the gravitational potential, given by:
    [tex]\phi=-G_N \frac{M}{r}.[/tex]
    Then, by the previous formula: [itex]\vec{F_g}=-G_N \frac{M}{r^2}\hat{e_r}[/itex]...but this is the expression for the gravitational field (force per unit mass) not the gravitational force... What am I doing wrong?


    Thank you very much.
     
  2. jcsd
  3. Apr 19, 2013 #2

    WannabeNewton

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    Science Advisor

    No, ##a = -\nabla \phi##. ##F = -\nabla \phi## holds for a unit test mass. You are confusing the potential ##\phi## with the potential energy ##U## for which it is true that ##F = -\nabla U##. Whenever you have doubts like this, just check units. ##\phi## has units of Joules/kg so ##\nabla \phi## has units of Joules/(kg*m) = N*m/(kg*m) = N/kg = m/s^2
     
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