A satellite of mass $m$ is in a circular orbit of radius $2R_E$ around the earth. The energy required to transfer it to a circular orbit of radius $4R_E$ is (where $M_E$ and $R_E$ is the mass and radius of the earth respectively)

A satellite of mass $m$, initially at rest on the earth, is launched into a circular orbit at a height equal to the radius of the earth. The minimum energy required is

Asatellite of mass $5\,M$ orbits the earth in a circular orbit. At one point in its orbit, the satellite explodes into two pieces, one of mass $M$ and the other of mass $4M.$ After the explosion the mass $M$ ends up travelling in the same circular orbit, but in opposite direction. After explosion the mass $4M$ is in

A rocket of mass $M$ is launched vertically from the surface of the earth with an initial speed $V$. Assuming the radius of the earth to be $R$ and negligible air resistance, the maximum height attained by the rocket above the surface of the earth is

Two satellites $A$ and $B$, having ratio of masses $3 : 1$ are in circular orbits of radius $r$ and $4r$. Calculate the ratio of total mechanical energy of $A$ and $B$.