$A$ 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 $24 \ hours$. If the separation between the earth and the satellite is decreased to one-fourth of the previous value,then its new time period will become $....... \ hours$.

The time period of a satellite of the 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 ......... $hours$.

$A$ planet moves around the sun. At a given point $P$,it is closest to the sun at a distance $d_1$ and has a speed $v_1$. At another point $Q$,when it is farthest from the sun at a distance $d_2$,its speed will be:

$A$ 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 $dab$.

$A$ satellite is launched into a circular orbit of radius $R$ around Earth,while a second satellite is launched into a circular orbit of radius $1.02 R$. The percentage difference in the time periods of the two satellites is: