Question

A planet Mars has a mass of 6.4x10²³ kg and its moon, Phobos has a mass of 9.6x10¹⁵kg. The garvitational force between Mars and Phobos is 4.6x10¹⁵ N. Find the radius of the orbit between Mars and Phobos?

Answer 1

$F=G\frac{M_mM_f}{r^2}\to r=\sqrt{\frac{GM_mM_f}{F}}=$

$=\sqrt{\frac{6.67\cdot10^{-11}\cdot 6.4\cdot10^{23}\cdot 9.6\cdot10^{15}}{4.6\cdot 10^{15}}}=9.44\cdot10^6(m)=9440(km)$