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.
The gravitational force between the satellite and the Moon is in the radial direction and its magnitude is given by the Newton’s equation
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.
Based on the last formula and the Newton’s equation we should get
v=√(G*M/R) = √(6.67×10−11*7.35×10^22/1.74×10^6) = 1678.54 m/s .