EXERCISE

A satellite $S$ is moving in an elliptical orbit around the earth. The mass of the satellite is very small compared to the mass of the earth, then :

Find the gravitational potential $\left(V\right)$ and intensity $\left(E\right)$ at a point at a distance $r$ from the centre of a uniform ring of radius $a$.

Find the gravitational potential $\left(V\right)$ and intensity $\left(E\right)$ at a point at a distance $r$ from the centre of a hollow sphere of radius $R$, where $r$ varies from $0$ to $\infty$.

Find the gravitational potential $\left(V\right)$ and intensity $\left(E\right)$ at a point at a distance $r$ from the centre of a solid sphere of radius $R$, where $r$ varies from $0$ to $\infty$.

Find the gravitational potential $\left(V\right)$ and intensity $\left(E\right)$ at a point at a distance $r$ from the centre of Show graphically the variations of $V$ and $E$ with $r$.

Explain why planets or satellites move round the sun or the earth. Explain why the sun or earth does not lose energy in revolving the planets or the satellites.

Derive Kepler's laws from Newton's law of gravitation.

Explain how we may get the values of the mass and mean density of the earth and the mass of the sun from laws of gravitation.