What is the minimum energy required to launch a satellite of mass $m$ from the surface of the Earth of mass $M$ and radius $R$ to an altitude of $2R$?

An object is projected vertically upward from the earth's surface with a velocity $u = \sqrt{Rg}$,where $R$ is the radius of the earth and $g$ is the acceleration due to gravity on the earth's surface. Find the maximum height reached by the object.

$A$ body is thrown from the surface of the earth with velocity $V \ m/s$. The maximum height above the earth's surface up to which it will reach is ($R =$ radius of earth,$g =$ acceleration due to gravity).

Two stars each of one solar mass $\left(=2 \times 10^{30} \; kg\right)$ are approaching each other for a head-on collision. When they are at a distance of $10^{9} \; km$,their speeds are negligible. What is the speed with which they collide? The radius of each star is $10^{4} \; km$. Assume the stars remain undistorted until they collide. (Use $G = 6.67 \times 10^{-11} \; N \cdot m^{2}/kg^{2}$)

In the solar system,which quantity is conserved?

An asteroid is moving directly towards the centre of the Earth. When at a distance of $10 R$ ($R$ is the radius of the Earth) from the Earth's centre,it has a speed of $12 \; km/s$. Neglecting the effect of Earth's atmosphere,what will be the speed of the asteroid when it hits the surface of the Earth? (Escape velocity from the Earth is $11.2 \; km/s$). Give your answer to the nearest integer in $km/s$.