Suppose the law of gravitational attraction suddenly changes and becomes an inverse cube law i.e. $F \propto {1\over r^3}$, but still remaining a central force. Then

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 ……… $\times 10^{3}\, m / s$

A satellite $A$ of mass $m$ is at a distance of $r$ from the centre of the earth. Another satellite $B$ of mass $2m$ is at a distance of $2r$ from the earth's centre. Their time periods are in the ratio of

Explain Kepler’s first (Law of Orbits) law for planetary motion.

A planet revolving in elliptical orbit has

$(A)$ a constant velocity of revolution.

$(B)$ has the least velocity when it is nearest to the sun.

$(C)$ its areal velocity is directly proportional to its velocity.

$(D)$ areal velocity is inversely proportional to its velocity.

$(E)$ to follow a trajectory such that the areal velocity is constant.

Choose the correct answer from the options given below