$A$ 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:

If the orbital period of a satellite becomes $8$ times, then by how many times does its orbital radius increase (in $times$)?

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 motion of satellites in the solar system is an example of which of the following?

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 $= R$)

$A$ satellite $S_1$ of mass $m$ is moving in an orbit of radius $r$. Another satellite $S_2$ of mass $2m$ is moving in an orbit of radius $2r$. The ratio of the time period of satellite $S_2$ to that of $S_1$ is