Answer:
[tex]v=\sqrt{\frac{GM}{R}}[/tex]
Explanation:
The only force that keeps the satellite in circular orbit is the force of gravity. This force therefore must provide the centripetal force that keeps the satellite in circular motion, so we can write:
[tex]G\frac{Mm}{R^2}=m\frac{v^2}{R}[/tex]
where:
G is the gravitational constant
M is the mass of the planet
m is the mass of the satellite
R is the radius of the orbit
v is the orbital speed of the satellite
We see that the mass of the satellite simplifies from the formula, as well as one radius R:
[tex]G\frac{M}{R}=v^2[/tex]
And so, we find an expression for the orbital speed of the satellite:
[tex]v=\sqrt{\frac{GM}{R}}[/tex]
