Question

A planet of mass 1.000 × 10²⁶ kg, has a moon of mass 2.100 × 10²² kg and orbital radius 3.550 × 10⁵ km. The orbit of the moon is assumed to be circular.

Determine the distance, from the centre of the planet, the point at which the resultant gravitational field is zero.

Answer 1

$$G\frac{M}{x^2}=G\frac{m}{(R-x)^2}\\\frac{10^4}{x^2}=\frac{2.1}{(3.55-x)^2}\\x=3.499\cdot10^5\ km$$