Initially, a satellite of $100 \ kg$ is in a circular orbit of radius $1.5 R_E$. This satellite can be moved to a circular orbit of radius $3 R_E$ by supplying $\alpha \times 10^6 \ J$ of energy. The value of $\alpha$ is . . . . . . .
(Take Radius of Earth $R_E = 6 \times 10^6 \ m$ and $g = 10 \ m/s^2$)

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

If the radius of an orbiting satellite is decreased,then its kinetic energy

$A$ satellite of mass $m$,revolving around the Earth of radius $r$,has kinetic energy $E$. Its angular momentum is:

Two satellites $A$ and $B$ having masses in the ratio $4: 3$ are revolving in circular orbits of radii $3r$ and $4r$ respectively around the earth. The ratio of total mechanical energy of $A$ to $B$ is.

$A$ launching vehicle carrying an artificial satellite of mass $m$ is set for launch on the surface of the earth of mass $M$ and radius $R$. If the satellite is intended to move in a circular orbit of radius $7R$,the minimum energy required to be spent by the launching vehicle on the satellite is ($G$ is the gravitational constant).