The time period $T$ of a satellite is related to the density $(\rho)$ of the planet around which it is orbiting close to the surface as:

$A$ planet revolves around the Sun in an elliptical orbit. When it is closest to the Sun,its distance from the Sun is $d_1$ and its velocity is $v_1$. When it is farthest from the Sun,its distance from the Sun is $d_2$. What is its velocity at that point?

Consider a binary star system of star $A$ and star $B$ with masses $m_{A}$ and $m_{B}$ revolving in a circular orbit of radii $r_{A}$ and $r_{B}$,respectively. If $T_{A}$ and $T_{B}$ are the time periods of star $A$ and star $B$,respectively,then -

Let us assume that our galaxy consists of $2.5 \times 10^{11}$ stars, each of one solar mass. How long will a star at a distance of $50,000 \; ly$ from the galactic centre take to complete one revolution? Take the diameter of the Milky Way to be $10^{5} \; ly$.

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 a circular equatorial orbit of radius $r = 7000 \, km$ around the Earth. If it is transferred to a circular orbit of double the radius $(2r)$,then its angular momentum will: