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What is a formula for velocity of a spacecraft in a circular orbit? Actually, is there a formula or I can find it from equation of motion?

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up vote 2 down vote accepted

It is $\sqrt{\frac {GM}{r}}$ , where $M$ is the mass of the body(Earth) the spacecraft is revolving around, $r$ is the distance from the center of that body(Earth), and $G$ is the universal gravitational constant.

This can be easily derived from equating centripetal acceleration and gravitational attraction, i.e. $$\frac {mv^2}{r} = \frac {GMm}{r^2}$$

Note: this is only applicable for spherical bodies.

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For attractive body or moving body? In this case, moving body is spacecraft. I don't know if it has to be spherical. Attractive body is the Earth. –  gov Jul 24 '13 at 12:04
The attractive body(earth) has to be spherical, or else you couldn't use $\frac {GMm}{r^2}$ for the gravitational attraction. –  udiboy Jul 24 '13 at 12:04
It's also a good approximation around non-spherical attractors as long as the orbital radius is large compared to the size of the attractor (i.e. you approximate the attractor as a point mass). –  Kyle Jul 24 '13 at 16:23
I thought about that, but then there would be no significance of the velocity, as $\frac Mr \to 0$ –  udiboy Jul 24 '13 at 16:29
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