Two satellites $P$ and $Q$ go round a planet in circular orbits having radii $3R$ and $R$ respectively. If the speed of satellite $P$ is $2V$,what will be the speed of satellite $Q$?

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?

Does the orbital velocity of a planet depend on its mass?

If $g \propto \frac{1}{R^3}$ (instead of $\frac{1}{R^2}$),then the relation between the time period $T$ of a satellite near the Earth's surface and the radius $R$ will be:

Which fact is represented by the pictures of an astronaut floating in a satellite?

$A$ 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: