Let kinetic energy of a satellite is $x$, then its time of revolution $T$ is proportional to ..............

The mean radius of the earth's orbit round the sun is $1.5 \times {10^{11}}$. The mean radius of the orbit of mercury round the sun is $6 \times {10^{10}}\,m$. The mercury will rotate around the sun in

The figure shows the motion of a planet around the sun in an elliptical orbit with sun at the focus. The shaded areas $A$ and $B$ are also shown in the figure which can be assumed to be equal. If ${t_1}$ and ${t_2}$ represent the time for the planet to move from $a$ to $b$ and $d$ to $c$ respectively, then

What does not change in the field of central force

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 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 ......... $hours$