$A$ satellite $A$ of mass $m$ is at a distance of $r$ from the centre of the earth. Another satellite $B$ of mass $2m$ is at a distance of $2r$ from the earth's centre. Their time periods are in the ratio of:

The period of a planet around the sun is $8$ times that of earth. The ratio of the radius of the planet's orbit to the radius of the earth's orbit is:

$A$ planet is revolving around the sun in an elliptical path as shown. The orbital velocity of the planet will be minimum at:

$A$ planet revolves around the Sun in an elliptical orbit,where the semi-major axis $a$ is double the semi-minor axis $b$ $(a = 2b)$. The Sun is at the focus. Given that the planet takes $24$ hours to travel through the path $bed$ as shown in the figure,find the time taken by the planet to travel along the path $dab$.

$A$ planet of mass $m$ moves around the sun of mass $M$ in an elliptical orbit. The maximum and minimum distances of the planet from the sun are $r_1$ and $r_2$ respectively. The time period of the planet is proportional to ..........

An earth satellite $X$ is revolving around the earth in an orbit whose radius is one-fourth of the radius of the orbit of a communication satellite. The time period of revolution of $X$ is ..........