If a particle of mass $m$ is moving in a horizontal circle of radius $r$ with a centripetal force $(-k/r^2)$,the total energy is

For a satellite moving in an orbit around the earth,the ratio of kinetic energy to potential energy is

$A$ 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 $R_E$ are the mass and radius of the Earth,respectively).

$A$ 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 $R$)

$A$ particle of mass $m$ moves in a horizontal circle of radius $r$ under the influence of a centripetal force given by $F = -k/r^2$,where $k$ is a constant. Calculate the total energy of the particle.

$A$ 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).