Two satellites,$A$ and $B,$ have masses $m$ and $2m$ respectively. $A$ is in a circular orbit of radius $R,$ and $B$ is in a circular orbit of radius $2R$ around the earth. The ratio of their kinetic energies,$K.E._A / K.E._B ,$ is

$A$ satellite of mass $1000 \ kg$ is launched to revolve around the earth in an orbit at a height of $270 \ km$ from the earth's surface. Kinetic energy of the satellite in this orbit is . . . . . . $\times 10^{10} \ J$. (Mass of earth $= 6 \times 10^{24} \ kg$,Radius of earth $= 6.4 \times 10^6 \ m$,Gravitational constant $= 6.67 \times 10^{-11} \ Nm^2 \ kg^{-2}$)

The weight of an astronaut,in an artificial satellite revolving around the earth,is

An artificial satellite is moving around the Earth in a circular orbit with a speed equal to one-fourth the escape speed of a body from the surface of the Earth. The height of the satellite above the Earth's surface is ............ ($R$ is the radius of the Earth). (in $R$)

Assuming that the earth is revolving around the sun in a circular orbit of radius $R$,the angular momentum is directly proportional to $R^{n}$. The value of $n$ is

$A$ satellite of mass $m$ is revolving close to the surface of a planet of density $d$ with time period $T$. The value of the universal gravitational constant $G$ in terms of $d$ and $T$ is given by: