A satellite of mass $m$ is revolving around the earth in a circular orbit of radius $\mathrm{r}.$ Write the expressions for the kinetic energy and the total energy of this satellite. Why is the total energy negative?

 A satellite of mass $m$ is revolving around the earth in a circular orbit of radius $\mathrm{r}.$ What will be escape velocity for this satellite?

A satellite of mass $m$ is revolving around the earth in a circular orbit of radius $r$. Show that this satellite obeys Kepler's third law, according to which, the ratio of the cube of its orbit's radius to the square of its period of revolution is constant.

A rocket projected upward with a velocity $\mathrm{v}$ reaches a height $\mathrm{h}$ which is not negligible in comparison to the radius ${\mathrm{R}}_{\mathrm{e}}$ of the earth. Derive the expression for $\mathrm{h}$ in terms of $\mathrm{v}, {\mathrm{R}}_{\mathrm{e}} \mathrm{and} \mathrm{g}.$ Calculate $\mathrm{v}$ when $\mathrm{h}={\mathrm{R}}_{\mathrm{e}}$

A rocket projected upward with a velocity $\mathrm{v}$ reaches a height $\mathrm{h}$ which is not negligible in comparison to the radius ${\mathrm{R}}_{\mathrm{e}}$ of the earth. Derive the expression for $\mathrm{h}$ in terms of $\mathrm{v}, {\mathrm{R}}_{\mathrm{e}} \mathrm{and} \mathrm{g}.$ Calculate $\mathrm{v}$ when $\mathrm{h}=\infty$