Question

Define the period of revolution of a satellite. Derive an expression for the period of revolution of a satellite in a circular orbit.

Answer 1

Hint: Period of revolution of satellite in circular orbit around earth is inversely proportional to its orbital speed. The period of a satellite is nothing but the time takes it to make one full orbit around an object or earth. The period of the Earth as it travels around the sun is one year If we want to know the satellite’s speed and the radius at which it orbits we can find out its period.

Complete answer:
The speed of a satellite around an object using the equation is written as
$v = \sqrt {\dfrac{{G{m_2}}}{r}} $
Where v is the speed of the satellite.
r is the radius of the orbit.
the satellite travels in a circular orbit is given by.
${2\pi r}$
Where r is the radius of the orbit then the period T it means the orbital speed must be.
$\dfrac{{2\pi r}}{T}$
It gives,
$\sqrt {\dfrac{{G{m_2}}}{r}} = \dfrac{{2\pi r}}{T}$
solve this for the period of the satellite then we can write $v = \dfrac{{2\pi r}}{T}$
For the period of satellite
$\dfrac{{2\pi r}}{v}$
This is the equation of period of revolution in a uniform circular motion.
Where r is the radius of orbit and v is the speed of the satellite.

Additional information:
When the satellite travels in the orbits it stays in position because the centripetal force on the satellite balances the gravitational attractive force of the earth.
Centripetal force acts on the satellite balances the gravitational force of the earth, remember this balance does not depend upon the mass and size of the satellite.

Note:
The time in which a body rotates once on its axis is called period of revolution, The period of a satellite is the time it takes it to make one full orbit around an object. We know that The period of the earth as it travels around the sun is one year. We have to know these terms to solve this question.