$A$ satellite is to revolve around the Earth in a circle of radius $8000\, km$. The speed at which this satellite must be projected into an orbit will be......... $km/s$.

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 ......... $km/s$.

The mean radius of the earth is $R$,its angular speed on its own axis is $\omega$,and the acceleration due to gravity at the earth's surface is $g$. The cube of the radius of the orbit of a geostationary satellite will be

The maximum and minimum distances of a comet from the sun are $8 \times 10^{12} \, m$ and $1.6 \times 10^{12} \, m$. If its velocity when nearest to the sun is $60 \, m/s$,what will be its velocity in $m/s$ when it is farthest?

Two particles of equal mass $m$ move in a circle of radius $r$ under the action of their mutual gravitational attraction. The speed of each particle will be ($G=$ Universal gravitational constant).

Two satellites of masses $m_1$ and $m_2$ $(m_1 > m_2)$ are revolving around the Earth in circular orbits of radii $r_1$ and $r_2$ $(r_1 > r_2)$ respectively. Which of the following statements is true regarding their speeds $v_1$ and $v_2$?