$A$ 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:

$A$ planet is moving around the sun in an elliptical orbit at different positions $A, B, C, D$. The maximum kinetic energy of the planet is at position:

$A$ remote-sensing satellite of Earth revolves in a circular orbit at a height of $0.25 \times 10^6 \, m$ above the surface of Earth. If Earth's radius is $6.38 \times 10^6 \, m$ and $g = 9.8 \, m s^{-2}$,then the orbital speed of the satellite is ...... $km s^{-1}$.

$A$ satellite revolving around a planet in a stationary orbit has a time period of $6 \text{ hours}$. The mass of the planet is one-fourth the mass of the Earth. What is the radius of the orbit of the satellite? (Given: Radius of the geostationary orbit for Earth is $4.2 \times 10^4 \text{ km}$)

$A$ body moves in a circular orbit of radius $R$ under the action of a central force. The potential due to the central force is given by $V(r) = kr$ ($k$ is a positive constant). The period of revolution of the body is proportional to:

If a satellite is shifted towards the Earth,then the time period of the satellite will be: