Find the kinetic energy required to project an object of mass $m$ from the surface of the Earth to infinity.

The escape velocity from the moon's surface is less than that on the earth's surface,because:

The escape velocity from the surface of Earth of mass $M$ and radius $R$ is $V_{e}$. The escape velocity from the surface of a planet whose mass and radius are $3$ times that of the Earth will be:

$A$ rocket is launched with velocity $10 \ km/s$. If the radius of the Earth is $R$,then the maximum height attained by it will be: (in $R$)

The ratio of the kinetic energy required to be given to a satellite to escape from the Earth's surface to the kinetic energy required to be given to the same satellite to revolve around the Earth in an orbit just above the Earth's surface is ...........

$A$ spaceship is stationed on Mars. How much energy must be expended on the spaceship to launch it out of the solar system? Mass of the spaceship $= 1000 \; kg$,mass of the Sun $= 2 \times 10^{30} \; kg$,mass of Mars $= 6.4 \times 10^{23} \; kg$,radius of Mars $= 3395 \; km$,radius of the orbit of Mars $= 2.28 \times 10^{8} \; km$,$G = 6.67 \times 10^{-11} \; N m^{2} kg^{-2}$.