Question

Two solid spherical planets of equal radii $R$ have masses $4M$ and $9M$. Their centres are separated by a distance $6R$. A projectile of mass $m$ is sent from the planet of mass $4M$ towards the heavier planet. If the distance $r$ of the point from the lighter planet where the gravitational force on the projectile is zero is $kR$, then calculate $k$.

Answer 1

The gravitational force on projectile of mass $m$ at a distance $r$ from a planet of mass $4M$ is zero.

$\therefore \frac{G\left(4M\right)m}{r^2}=\frac{G\left(9M\right)m}{(6R-r{)}^2}$

Or $4(6R-r{)}^2=9r^2$

Or $2(6R-r)=3r$

Or $r=2.4R$