Write an equation of potential energy of satellite. Why the potential energy of the satellite comes negative ?

The escape speed of a projectile on the earth's surface is $11.2\; km s ^{-1} .$ A body is projected out with thrice this speed. What is the speed (in $km/s$) of the body far away from the earth? Ignore the presence of the sun and other planets.

How much energy will be necessary for making a body of 500 kg escape from the earth $[g = 9.8\,m/{s^2}$, radius of earth $ = 6.4 \times {10^6}\,m]$

The gravitational potential energy of a body of mass $‘m’$ at the earth’s surface $ – mg{R_e}$. Its gravitational potential energy at a height ${R_e}$ from the earth’s surface will be (Here ${R_e}$ is the radius of the earth)

A particle of mass $'\mathrm{m}'$ is projected with a velocity $v=\mathrm{kV}_{\mathrm{e}}(\mathrm{k}\,<\,1)$ from the surface of the earth.

$\left(\mathrm{V}_{\mathrm{e}}=\right.\text { escape velocity) }$

The maximum height above the surface reached by the particle is :