The figure shows the motion of a planet around the sun in an elliptical orbit with the sun at the focus. The shaded areas are 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:

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

Which of the following quantities does not depend upon the orbital radius of the satellite?

India's Mangalyaan was sent to Mars by launching it into a transfer orbit $EOM$ around the Sun. It leaves the Earth at $E$ and meets Mars at $M$. If the semi-major axis of Earth's orbit is $a_e = 1.5 \times 10^{11} \, m$ and that of Mars' orbit is $a_m = 2.28 \times 10^{11} \, m$, using Kepler's laws, estimate the time taken for Mangalyaan to reach Mars from Earth in days.

The ratio of the distances of two planets from the sun is $1.38$. The ratio of their period of revolution around the sun is

Suppose a planet goes around the Sun with a linear speed twice as fast as that of the Earth. What will be its orbit size compared to that of the Earth? (Radius of Earth $= R$)