$A$ 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).

$A$ planet is revolving around the Sun as shown in the figure. The radius vectors joining the Sun and the planet at points $A$ and $B$ are $90 \times 10^6 \text{ km}$ and $60 \times 10^6 \text{ km}$,respectively. The ratio of velocities of the planet at the points $A$ and $B$ when its velocities make angles $30^{\circ}$ and $60^{\circ}$ with the major axis of the orbit is:

If the gravitational constant $G$ is decreasing with time,what will remain unchanged for a satellite orbiting around the Earth?

What are the conditions necessary for a satellite to appear stationary? What is the direction of rotation of a geostationary satellite?

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

$A$ planet moves around the sun in an elliptical orbit with the sun at one of its foci. The physical quantity associated with the motion of the planet that remains constant with time is