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

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?

The period of a satellite in a circular orbit of radius $R$ is $T$, the period of another satellite in a circular orbit of radius $4R$ is

The fig. shows the motion of a planet around the un in an elliptical orbit with sun at the  focus. The shaded areas can be assumed to be equal. If $t_1$ and $t_2$ represent the  time taken for the planet to move from $A$ to $B$ and $C$ to $D$ respectively, then

A star like the sun has several bodies moving around it at different distances. Consider that all of them are moving in circular orbits. Let $r$ be the distance of the body from the centre of the star and let its linear velocity be $v$, angular velocity  $\omega $, kinetic energy $K $, gravitational potential energy $U$, total energy $E$ and angular momentum $l$. As the radius $r$ of the orbit increases, determine which of the  abovequantities increase and which ones decrease.