Question

Find the orbital speed v for a satellite in a circular orbit of radius R.Express the orbital speed in terms of G, M, and R.

Answer 1

Answer:$V=\sqrt{G\frac{M}{R}}$  

The velocity of a satellite describing a circular orbit is constant and defined by the following expression:

$V=\sqrt{G\frac{M}{R}}$     (1)

Where:

$G$ is the gravity constant

$M$ the mass of the massive body around which the satellite is orbiting

$R$ the radius of the orbit (measured from the center of the planet to the satellite).

Note this orbital speed, as well as orbital period, does not depend on the mass of the satellite. It depends on the mass of the massive body.

In addition, this orbital speed is constant because at all times both the kinetic energy and the potential remain constant in a circular (closed) orbit.