Stable orbit
Overview
| Difficulty | Intermediate (2/4) |
| Topics | Newton's 2nd Law, Circular motion, Centripetal acceleration |
A satellite is located at a distance \(R\) from the center of a planet with mass \(M\), initially at rest relative to the planet.
Calculate the velocity \(v\) that must be given to the satellite so that it maintains a circular orbit around the planet.
If the velocity is too low, the satellite will fall onto the planet. If the velocity is too high, the satellite will escape the planet's gravitational field.
Relevant Equations
\[a_n = \frac{v^2}{R}\]
\[m\vec{a} = \sum \vec{F_i}\]
\[F = G\frac{mM}{R^2}\]
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