In the solar system,which quantity is conserved?

$A$ rocket is fired vertically upwards from the surface of the Earth with a velocity $V$. If $R$ is the radius of the Earth,what is the maximum height attained by the rocket?

An object is propelled vertically to a maximum height of $4 R$ from the surface of a planet of radius $R$ and mass $M$. The speed of the object when it returns to the surface of the planet is

What is the change in the gravitational potential energy of an object when it moves away from the Earth and when it comes closer to the Earth?

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 $km/s$.

Energy required to move a body of mass $m$ from an orbit of radius $2R$ to $3R$ is