Question

A planetMars has a mass of 6.4X10^23 kg and its moon, Phobos has a mass o fee 9.6X10^15 kg. The gravitational force between Mars and Phobos is 4.6X10^15 N. Find the radius of the orbit between Mars and Phobos.

Answer 1

From the Newton's law of universal gravitation, we get:

$$F=\dfrac{GM_MM_F}{R^2},$$ $$R=\sqrt{\dfrac{GM_MM_F}{F}},$$ $$R=\sqrt{\dfrac{6.67\cdot10^{-11}\ \dfrac{Nm^2}{kg^2}\cdot6.4\cdot10^{23}\ kg\cdot9.6\cdot10^{15}\ kg}{4.6\cdot10^{15}\ N}}=9438.6\ km.$$