Kepler discovered

How will you 'weigh the sun',that is estimate its mass? The mean orbital radius of the earth around the sun is $1.5 \times 10^{8} \text{ km}$.

$A$ 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:

Two planets $A$ and $B$ of equal mass have periods of revolution $T_{A}$ and $T_{B}$ such that $T_{A} = 2 T_{B}$. These planets are revolving in circular orbits of radii $r_{A}$ and $r_{B}$ respectively. Which of the following is the correct relationship between their orbital radii?

The distances of two planets from the Sun are $10^{11} \ m$ and $10^{10} \ m$ respectively. Find the ratio of their orbital periods.

$A$ 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: