The radius of the Martian orbit around the Sun is about $4$ times the radius of the orbit of Mercury. The Martian year is $687$ Earth days. What is the length of $1$ year on Mercury?

$A$ 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 ..........

Draw the areal velocity versus time graph for Mars.

The figure shows the orbit of a planet $P$ around the sun $S.$ $AB$ and $CD$ are the minor and major axes of the ellipse,respectively.
If $t_1$ is the time taken by the planet to travel along the path $ACB$ and $t_2$ is the time taken to travel along the path $BDA,$ then:

$A$ 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:

Describe the model and theory of planetary motions presented in the earliest of times.