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:

An artificial satellite is placed into a circular orbit around the Earth at such a height that it always remains above a definite place on the surface of the Earth. Its height from the surface of the Earth is ........... $km$.

$A$ satellite is placed in a circular orbit around the Earth at an altitude of $1000 \,km$. The time period of the satellite in minutes is approximately (mass of the Earth $= 6 \times 10^{24} \,kg$, radius of the Earth $= 6.4 \times 10^6 \,m$, $G = 6.67 \times 10^{-11} \,Nm^2 \,kg^{-2}$).

The orbital velocity of an artificial satellite in a circular orbit just above the Earth's surface is $v$. For a satellite orbiting at an altitude of half of the Earth's radius,the orbital velocity is

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.

$A$ comet orbits the Sun in a highly elliptical orbit. Does the comet have a constant $(a)$ linear speed,$(b)$ angular speed,$(c)$ angular momentum,$(d)$ kinetic energy,$(e)$ potential energy,$(f)$ total energy throughout its orbit? Neglect any mass loss of the comet when it comes very close to the Sun.