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.