In planetary motion,the areal velocity of the position vector of a planet depends on the angular velocity $\omega$ and the distance of the planet from the sun $r$. The correct relation for areal velocity is:

$A$ 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:

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.

$A$ geostationary satellite is taken from one orbit to another orbit,whose distance from the centre of the Earth is $2$ times that of the earlier orbit. The time period in the second orbit is how many hours?

If $A$ is the areal velocity of a planet of mass $M$,its angular momentum is

$A$ satellite moves in a circle around the earth. The radius of this circle is equal to one half of the radius of the moon's orbit. The satellite completes one revolution in