#### What is the minimum energy required to launch a satellite of mass m from the surface of a planet of mass M and radius R in a circular orbit at an altitude of 2R?

I came across this question and couldn't answer it

Anonymous

0

I came across this question and couldn't answer it

Krishna

0

A satellite is a moon, planet or machine that orbits a planet or star. Most satellites are launched into space on rockets.

To launch a satellite into orbit you required to change the mechanical energy. You will increase potential energy and kinetic energy.

So, Total energy = Kinetic energy + potential energy

kinetic energy = \frac{1}{2} mv^2

v = \sqrt{\frac{GM}{R}}

= \frac{1}{2} m (\sqrt{\frac{GM}{R}})^2

= \frac{GMm}{2R}

The kinetic energy at altitude 2 R = \frac{GMm}{6R}

The gravitational potential energy at altitude 2 R = - \frac{GMm}{3R}

Where m = mass of an satellite, M = mass of the planet. R = radius of the planet. G = regularly occurring gravitational consistent.

Energy at altitude of 2R = P.E +K.E.

= - \frac{GMm}{3R} + \frac{GMm}{6R}

= \frac{5GMm}{6R}

The energy also depends on whether you launch the satellite against or in the direction of the rotation of the earth. bot it is not required now.