Question

Mars has two moons, Phobos and Deimos. Phobos orbits at 6000 km above the surface of Mars, closer than any other moon in the solar system, once every 7.66 hours. (Radius of Mars = 3389 km). You want to put an artificial satellite (the Mars Reconnaissance Orbiter in this case) into a circular orbit at a height of 300 km above the surface of Mars. This process, called orbital insertion, requires the orbiter to speed up or slow down to the correct speed. Based on what you know about Phobos, what speed will the orbiter need for this orbit? (Give your answer in meters per second).

Answer 1

The centripetal force (provided by gravitational force) of a satellite in circular speed is given by

Now, for Phobos

The period of Phobos is

So, the speed of Phobos is

That gives us

Now for our satellite

So, the speed of the satellite must be 3412.9 m/s.