$A$ satellite is in an elliptical orbit around a planet $P.$ It is observed that the velocity of the satellite when it is farthest from the planet is $6$ times less than that when it is closest to the planet. The ratio of distances between the satellite and the planet at closest and farthest points is $......$

An artificial satellite is placed into a circular orbit around the Earth at such a height that it always remains above a definite place on the surface of the Earth. Its height from the surface of the Earth is ........... $km$.

The orbit of a geo-stationary satellite is circular. The time period of the satellite depends on:
$(i)$ mass of the satellite
(ii) mass of the earth
(iii) radius of the orbit
(iv) height of the satellite from the surface of the earth
Which of the following is correct?

$A$ satellite is in an elliptic orbit around the Earth with an aphelion of $6R$ and a perihelion of $2R$,where $R = 6400 \, km$ is the radius of the Earth. Find the eccentricity of the orbit. Find the velocity of the satellite at apogee and perigee. What should be done if this satellite has to be transferred to a circular orbit of radius $6R$? $(G = 6.67 \times 10^{-11} \, SI \text{ units and } M = 6 \times 10^{24} \, kg)$

If due to air drag,the orbital radius of a satellite decreases from $R$ to $R - \Delta R$,where $\Delta R << R$,the expression for the change in orbital velocity $\Delta v$ is (mass of Earth is $M$):

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