The escape velocity of a rocket launched from the surface of the earth:

$A$ body is projected vertically from the Earth's surface with a velocity equal to half the escape velocity. The maximum height reached by the body is ($R =$ radius of the Earth).

If the radius of a planet is $R$ and its density is $\rho$,the escape velocity from its surface will be

The kinetic energy needed to project a body of mass $m$ from the earth's surface (radius $R$) to infinity is:

$A$ body of mass $m$ is situated at a distance equal to $2R$ ($R$ is the radius of the Earth) from the Earth's surface. The minimum energy required to be given to the body so that it may escape out of the Earth's gravitational field is:

The mass and radius of the earth and moon are $M, R$ and $m, r$ respectively. The distance between their centers is $d$. The minimum velocity with which a particle of mass $m_0$ should be projected from the midpoint between them so that it could reach infinity is