The periodic time of a satellite revolving above Earth's surface at a height equal to $R$ (where $R$ is the radius of the Earth) is given by (where $g$ is the acceleration due to gravity at Earth's surface):

Three identical bodies of equal mass $M$ each are moving along a circle of radius $R$ under the action of their mutual gravitational attraction. The speed of each body is

Write the equation and value of the orbital periodic time of a satellite revolving very close to the surface of the Earth.

The time period of revolution of a satellite orbiting very close to a planet of radius $R$ is $T$. What is the period of revolution around another planet,whose radius is $3R$ but having the same density?

$A$ spaceship orbits around a planet at a height of $20 \, km$ from its surface. Assuming that only the gravitational field of the planet acts on the spaceship, what will be the number of complete revolutions made by the spaceship in $24 \, hours$ around the planet? [Given: Mass of planet $= 8 \times 10^{22} \, kg$, Radius of planet $= 2 \times 10^6 \, m$, Gravitational constant $G = 6.67 \times 10^{-11} \, N \cdot m^2/kg^2$]

$A$ geostationary satellite is orbiting the earth at a height of $6R$ from the earth's surface ($R$ is the earth's radius). What is the period of rotation of another satellite at a height of $2.5R$ from the earth's surface?