The kinetic energies of a planet in an elliptical orbit about the Sun,at positions $A, B$ and $C$ are $K_A, K_B$ and $K_C$,respectively. $AC$ is the major axis and $SB$ is perpendicular to $AC$ at the position of the Sun $S$ as shown in the figure. Then

If a planet revolves around the sun with an angular velocity $(\omega)$ and distance $(r)$,then the areal velocity of the planet is proportional to which of the following?

The time period of a satellite of Earth is $24 \text{ hours}$. If the separation between the Earth and the satellite is decreased to one-fourth of the previous value, then its new time period will become: (in $\text{ hours}$)

The time period of a satellite of earth is $24 \ hours$. If the separation between the earth and the satellite is decreased to one-fourth of the previous value,then its new time period will become $....... \ hours$.

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.

An artificial satellite of mass $m$ is moving along an elliptical path around the earth. The areal velocity of the satellite is proportional to