Potential energy of a satellite having mass $m$ and rotating at a height of $6.4 \times 10^6 \ m$ from the Earth's surface is

$A$ body of mass $2M$ is split into four masses $\{m, M-m, m, M-m\}$,which are placed at the corners of a square of side $d$ as shown in the figure. The ratio $\frac{M}{m}$ for which the gravitational potential energy of the system is maximum is $x:1$. The value of $x$ is ..... .

Four particles $A, B, C$ and $D$ each of mass $m$ are kept at the corners of a square of side $L$. Now the particle $D$ is taken to infinity by an external agent,keeping the other particles fixed at their respective positions. The work done by the gravitational force acting on the particle $D$ during its movement is ..........

The gravitational potential energy of a body of mass $m$ at the earth's surface is $-mgR_e$. Its gravitational potential energy at a height $R_e$ from the earth's surface will be (Here $R_e$ is the radius of the earth).

Taking the gravitational potential at a point at an infinite distance away as zero,the gravitational potential at a point $A$ is $-5 \, unit$. If the gravitational potential at a point at an infinite distance away is taken as $+10 \, units$,the potential at point $A$ is ......... $unit$.

The mass of the earth is $6.00 \times 10^{24} \ kg$ and that of the moon is $7.40 \times 10^{22} \ kg$. The gravitational constant is $G = 6.67 \times 10^{-11} \ N \cdot m^2/kg^2$. The potential energy of the system is $-7.79 \times 10^{28} \ J$. The mean distance between the earth and the moon is: