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What is a formula for velocity of a spacecraft in a circular orbit?

Also, on side note, is there a formula or I can find it from equation of motion?

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closed as off-topic by Colin McFaul, DavePhD, Brandon Enright, Chris White, John Rennie Jun 12 '14 at 6:02

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Your question seems to be under-defined. What are you asking? Is this just a homework-like question or is there some underlying concept to your question? – Brandon Enright Jun 11 '14 at 23:40
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. – udiboy1209 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 Oman Jul 24 '13 at 16:23
I thought about that, but then there would be no significance of the velocity, as $\frac Mr \to 0$ – udiboy1209 Jul 24 '13 at 16:29

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