$A$ satellite of $10^3 \text{ kg}$ mass is revolving in a circular orbit of radius $2R$. If $\frac{10^4 R}{6} \text{ J}$ of energy is supplied to the satellite,it would revolve in a new circular orbit of radius: (use $g = 10 \text{ m/s}^2$,$R = \text{radius of earth}$) (in $R$)

$A$ 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).

The total energy of a circularly orbiting satellite 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.

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 $2R$ is

$A$ satellite is orbiting the Earth. If its orbital radius is reduced to half of its initial value,then the percentage change in its total energy is: (in $\%$)