The orbital speed of a satellite revolving around a planet in a circular orbit is $v_0$. If its speed is increased by $10 \%$,then ..........

$A$ planet revolves around the Sun in an elliptical orbit. When it is closest to the Sun,its distance from the Sun is $1.6 \times 10^{12} \ m$ and its velocity is $60 \ m/s$. What is its velocity in $m/s$ when it is farthest from the Sun,given its distance is $8 \times 10^{12} \ m$?

The angular momentum of a planet of mass $M$ moving around the sun in an elliptical orbit is $\overrightarrow{L}$. The magnitude of the areal velocity of the planet is:

Assuming that the earth is revolving around the sun in a circular orbit of radius $R$,the angular momentum is directly proportional to $R^{n}$. The value of $n$ is

$A$ 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: $M = 6 \times 10^{24} \ kg$,$R = 6400 \ km$,$T = 24 \ h$,$G = 6.67 \times 10^{-11} \ N \cdot m^2/kg^2$.

What is the period of revolution of an Earth satellite? Ignore the height of the satellite above the surface of the Earth.
Given:
$(1)$ The value of gravitational acceleration $g = 10 \ ms^{-2}$.
$(2)$ Radius of Earth $R_E = 6400 \ km$. Take $\pi = 3.14$.