The maximum and minimum distances of a comet from the sun are $8 \times 10^{12} \, m$ and $1.6 \times 10^{12} \, m$. If its velocity when nearest to the sun is $60 \, m/s$,what will be its velocity in $m/s$ when it is farthest?

$A$ satellite is to be placed in an equatorial geostationary orbit around the Earth for communication.
$(a)$ Calculate the height of such a satellite.
$(b)$ Find out the minimum number of satellites that are needed to cover the entire Earth,so that at least one satellite is visible from any point on the equator.
Given: $M = 6 \times 10^{24} \ kg$,$R = 6400 \ km$,$T = 24 \ h$,$G = 6.67 \times 10^{-11} \ N \cdot m^2/kg^2$.

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 distance of a geostationary satellite from the centre of the earth (Radius $R = 6400 \ km$) is nearest to (in $R$)

The radius of a planet is $R$. $A$ satellite revolves around it in a circle of radius $r$ with angular velocity $\omega_0$. The acceleration due to gravity on the planet's surface is

Which fact is represented by the pictures of an astronaut floating in a satellite?