Physics: Gravitation

Example.

This does not depend on r. Thus, the potential due to a uniform spherical shell is constant throughout the cavity of the shell.

Figure (11.10) shows graphically the variation of potential with the distance from the centre of the shell.

Gravitational Potential at a Point Due to the Earth

Outside the earth: The work done in bringing a body of mass $m$ from infinity to a point at a distance $r$ from the centre of earth is $W=-\frac{G M m}{r}$ for $r>R$.

Hence, gravitational potential, $V=\frac{W}{m}=\frac{-G M m / r}{m}=\frac{-G M}{r}, r>R$

Inside the earth:

\textbf{Solution}

Let the speed of the instrument package be v when it grazes the surface of the planet.

Solutions: