The distances of two planets $A$ and $B$ from the sun are $r_A$ and $r_B$ respectively. Given that $r_B = 100 r_A$. If the orbital speed of planet $A$ is $v$,then the orbital speed of planet $B$ is:

Which of the following statements is correct in respect of a geostationary satellite?

The mean radius of Earth is $R$,and its angular speed on its axis is $\omega$. What will be the radius of orbit of a geostationary satellite?

Given below are two statements:
Statement $I$: $A$ satellite is moving around the Earth in an orbit very close to the Earth's surface. The time period of revolution of the satellite depends upon the density of the Earth.
Statement $II$: The time period of revolution of the satellite is $T = 2\pi\sqrt{\frac{R_e}{g}}$ (for a satellite very close to the Earth's surface), where $R_e$ is the radius of the Earth and $g$ is the acceleration due to gravity.
In the light of the above statements, choose the correct answer from the options given below:

$A$ geostationary satellite is taken to a new orbit such that its distance from the centre of the earth is doubled. Find the time period of this satellite in the new orbit.

The orbital velocity of an artificial satellite in a circular orbit very close to the Earth is $v$. The velocity of a geostationary satellite orbiting in a circular orbit at an altitude of $3R$ from the Earth's surface will be