$A$ spaceship moves from the Earth to the Moon and back. The greatest energy required for the spaceship is to overcome the difficulty in:

The potential energy of a satellite is $-8 \times 10^9 \ J$. What is its binding energy (escape energy)?

$A$ certain object is projected vertically from the surface of the earth of radius $R$ with a velocity equal to half the escape velocity. The maximum height attained by the object will be

$A$ spaceship of mass $2 \times 10^4 \, kg$ is launched into a circular orbit close to the Earth's surface. The additional velocity to be imparted to the spaceship in the orbit to overcome the gravitational pull will be $......$ (given $g = 10 \, m/s^2$ and radius of Earth $R = 6400 \, km$).

$A$ boy can jump to a height $h$ on the surface of a planet. If the density of the planet is $d$,what should be its radius $R$ so that the boy can escape from the gravitational pull of the planet?

The velocity with which a projectile must be fired so that it escapes Earth's gravitation does not depend on