The orbital velocity of an artificial satellite in a circular orbit just above the earth's surface is $v$. For a satellite orbiting at an altitude of half the earth's radius above the surface,the orbital velocity is:

The distance between the centre of the Earth and the Moon is $384000 \, km$. If the mass of the Earth is $6 \times 10^{24} \, kg$ and $G = 6.67 \times 10^{-11} \, N m^2/kg^2$,the orbital speed of the Moon is nearly ......... $km/s$.

$A$ satellite of mass $m$ is revolving around the Earth of mass $M$ in an orbit of radius $r$ with constant angular velocity $\omega$. The angular momentum of the satellite is ($G$ = gravitational constant).

The ratio of kinetic energy of a planet at perigee and apogee during its motion around the sun in an elliptical orbit of eccentricity $e$ is ..........

What is the ratio of the time periods of a satellite $A$ of mass $m$ at a distance $r$ from the center of the Earth and a satellite $B$ of mass $2m$ at a distance $2r$ from the center of the Earth?

$A$ 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 $= 6.67 \times 10^{-11} \ Nm^2 \ kg^{-2}$)