$A$ particle moves in a circular orbit of radius $r$ under a central attractive force $F = -\frac{k}{r^2}$,where $k$ is a constant. The time period of its motion shall be proportional to

Define the periodic time (orbital period) of a satellite.

Assertion $A$: An astronaut inside a massive spaceship orbiting around the Earth will experience a finite but small gravitational force.
Reason $R$: The centripetal force necessary to keep the spaceship in orbit around the Earth is provided by the gravitational force between the Earth and the spaceship.

The time period $T$ of a satellite is related to the density $(\rho)$ of the planet around which it is orbiting close to the surface as:

If the mass of a satellite is doubled and the time period remains constant,the ratio of the orbital radii in the two cases will be:

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 $6 \times 10^{4} \ m/s$,the speed at the farthest point is ......... $\times 10^{3} \ m/s$.