Physics - Gravitation Question with Solution | TestHub

A spaceship is sent to investigate a planet of mass ${\mathrm{m}}_{\mathrm{P}}$ and radius ${\mathrm{r}}_{\mathrm{P}}$. While hanging motionless in space at a distance $5r_p$ from the centre of the planet, the ship fires an instrument package with speed $v_0$. The package has mass ${\mathrm{m}}_{\mathrm{i}}$ which is much smaller than the mass of the spacecraft. The package is launched at an angle $\theta$ with respect to a radial line between the centre of the planet and the spacecraft. Find the value of $(\sin \theta {)}^{-1}$ so that package just graze the surface of the planet. [Take : $\frac{{\mathrm{Gm}}_{\mathrm{P}}}{{\mathrm{Rv}}_0^2}=\frac{10}{9}$ ]