Two planets $A$ and $B$ of equal mass are having their period of revolutions $T_{A}$ and $T_{B}$ such that $T_{A}=2 T_{B}$. These planets are revolving in the circular orbits of radii $I_{A}$ and $I_{B}$ respectively. Which out of the following would be the correct relationship of their orbits?

A spherical asteroid having the same density as that of earth is floating in free space. A small pebble is revolving around the asteroid under the influence of gravity near the surface of the asteroid. What is the approximate time period of the pebble?

Every planet revolves around the sun in an elliptical orbit :

$A.$ The force acting on a planet is inversely proportional to square of distance from sun.

$B.$ Force acting on planet is inversely proportional to product of the masses of the planet and the sun

$C.$ The centripetal force acting on the planet is directed away from the sun.

$D.$ The square of time period of revolution of planet around sun is directly proportional to cube of semi-major axis of elliptical orbit.

Choose the correct answer from the options given below :

A satellite moves round the earth in a circular orbit of radius $R$ making one revolution per day. A second satellite moving in a circular orbit, moves round the earth once in $8$ days. The radius of the orbit of the second satellite is

The time period of a satellite of earth is $5$ hours. If the separation between the earth and the satellite is increased to four times the previous value, the new time period will become ……… $hours$