The maximum and minimum distances of a comet from the Sun are $1.6 \times 10^{12}\, m$ and $8.0 \times 10^{10}\, m$ respectively. If the speed of the comet at the nearest point is $6 \times 10^{4}\, ms ^{-1},$ the speed at the farthest point is ……… $\times 10^{3}\, m / s$

What does not change in the field of central force

India's Mangalyan was sent to the 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 $a_e = 1.5 \times 10^{11}\, m$, that of Mars orbit $a_m= 2.28 \times 10^{11}\, m$, taken Kepler's laws give the estimate of time for Mangalyan to reach Mars from Earth to be close to …….. $days$.

A star like the sun has several bodies moving around it at different distances. Consider that all of them are moving in circular orbits. Let $r$ be the distance of the body from the centre of the star and let its linear velocity be $v$, angular velocity  $\omega $, kinetic energy $K $, gravitational potential energy $U$, total energy $E$ and angular momentum $l$. As the radius $r$ of the orbit increases, determine which of the  abovequantities increase and which ones decrease.

A satellite $S$ moves around a planet $P$ in an elliptical orbit as shown in figure. The ratio the speed of the satellite at point $a$ to that at point $b$ is