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Please bear with me, as I'm not in the field of physics, this question may seem a bit simple.

The scenario is the following;

A specific stable orbit radius of a small body, say a satellite, to large body, say a planet, is known.

My questions then are;

  1. Is the velocity of said body a single value, or is there an interval of possible velocities?
  2. What are the determining factors for the value/interval of velocit(y/ies)? (Assuming the orbit radius stays constant, and is stable)
    • The masses of the two bodies?
    • Orbit radius?
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1 Answer

up vote 2 down vote accepted

If we assume a circular orbit, the equation relevant to your question is given by the equality of gravitational to centripetal force:

$$G\frac{mM}{r^2}=\frac{mv^2}{r},$$

where $m$ is the mass of the satellite, $M$ the mass of the planet, $G$ the gravitational constant, $r$ the distance between the centers of mass of both bodies and $v$ the tangential velocity. You can solve this equation for $v$ and end up at

$$v=\sqrt{G\frac{M}{r}}.$$

As you can see, there is one solution to this equation. It is determined by two variables: the mass of the planet and the radius.

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Is the gravitational constant based upon the mass of the planet, or? –  Skeen Aug 3 '13 at 0:07
    
No, it is an universal empirical constant. For more detail see en.wikipedia.org/wiki/Gravitational_constant –  Frederic Brünner Aug 3 '13 at 0:09
    
Ah, alright, thanks, accepting answer. –  Skeen Aug 3 '13 at 0:19
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