Image Credit: NASA Ames/Dana Berry

A satellite orbits the Moon in a circular orbit. The radius of the Moon is 1.74×10^6 m , the mass of the Moon is 7.35×10^22 kg. Calculate the speed of a satellite in a circular orbit, very near the Moon’s surface.

###### Solution.

The gravitational force between the satellite and the Moon is in the radial direction and its magnitude is given by the Newton’s equation

F=G*M*m/R^2

where G is the gravitational constant equals 6.67×10−11 m^3kg^−1s^-2, M and m are the masses of the Moon and the satellite respectively and R is the radius of the orbit (radius of the Moon).

In case of the circular motion the net force equals mass times acceleration, where acceleration could be calculated by v^2/R.

Thereby,

F=m*a=m*v^2/R.

Based on the last formula and the Newton’s equation we should get

G*M*m/R^2=m*v^2/R

or

v=√(G*M/R)

Finally,

v=√(G*M/R) = √(6.67×10−11*7.35×10^22/1.74×10^6) = 1678.54 m/s .