Escape Velocity and Satellites

If we ask our
self why the moon not fall on the earth? Why the earth and the planets are orbiting
the sun, what force is keeping them in orbit?

This question was
answered by Newton’s Law of Universal Gravitation.

“Any two objects
attract each other with a gravitational force, proportional to the product of
their masses and inversely proportional to the square of the distance between
them.

1.
If Earth
is a uniform sphere with mass 𝑀 the gravitational force between Earth and the body near the earth
is:

𝐹=𝐺 (𝑀𝑚 )/𝑟^2

2.
If the
body is far from the Earth, the gravitational potential energy is:

𝐹(r) = -𝐺 (𝑀𝑚)/𝑟^2

3.
If the
body’s initial kinetic energy is equal to the potential energy at the Earth’s
surface, it means their total energy will be zero. So the velocity is called
the Escape Velocity.

4.
The Satellites
are usually put into orbit around the Earth. If the tangential speed high
enough, so the satellite put into orbit around the Earth. It
does not return to Earth, but not so high that it escapes Earth’s gravity
altogether.