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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$\begingroup$ 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? $\endgroup$– Brandon EnrightJun 11, 2014 at 23:40
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1 Answer
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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.
answered Jul 24, 2013 at 12:00
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$\begingroup$ 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. $\endgroup$– govJul 24, 2013 at 12:04
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$\begingroup$ The attractive body(earth) has to be spherical, or else you couldn't use $\frac {GMm}{r^2}$ for the gravitational attraction. $\endgroup$ Jul 24, 2013 at 12:04
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$\begingroup$ 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). $\endgroup$ Jul 24, 2013 at 16:23
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$\begingroup$ I thought about that, but then there would be no significance of the velocity, as $\frac Mr \to 0$ $\endgroup$ Jul 24, 2013 at 16:29