Circular Orbits
 
What is the velocity of a satellite in a circular orbit?
 
A body traveling on a circular path is accelerated toward the center of the circle. This acceleration is known as centripetal acceleration. The formula for centripetal acceleration is:


a = v ² / r


The formula for centripetal force is:


Fc = mv ² / r


The force acting on a satellite is the force of gravity. For a satellite in a circular orbit, we can write:


Fc = Fg


mv ²/ r = GMm / r ²

v ² = GM / r



Weight
 
The force of gravity between the Earth and a body on its surface is the weight of the body. What is the weight of a one kilogram body on the surface of the Earth?
 
The value of GM for the Earth is 399 trillion meters cubed per seconds squared. The mean radius of the Earth is 6,371,000 meters. The weight of a one kilogram body on the surface of the Earth is:

W = GMm / r ² = 399 × 1012 m ³ ∕ s ² × 1 kg ÷ 6,371,000 ² m ² = 9.8 kg m / s ²


 One kg m / s ² is known as a newton.




Kinetic Energy

The formula for kinetic energy is:

KE = ½ mv ²

 They get this formula by integrating the formula for force.


 
Gravitational Potential Energy
 
The formula for gravitational potential energy is:

GPE = − GMm / r

They get this formula by integrating the formula for the force of gravity.
 
If a one kilogram body falls one meter near the surface of the Earth, the kinetic energy of the body goes up ten joules. What is the change in gravitational potential energy of the body?

The gravitational potential energy of a one kilogram body on the surface of the Earth is:

GPE = − 399 × 1012 m ³ ∕ s ² × 1 kg ÷ 6,371,000 m = − 62,627,531 J
 
The gravitational potential energy of a one kilogram body at a height of one meter is:
 
GPE = − 399 × 1012 m ³ ∕ s ² × 1 kg ÷ 6,371,001 m = − 62,627,521 J

If a one kilogram body falls one meter near the surface f the Earth, the change in gravitational potential energy is:
ΔGPE = − 62,627,531 J − − 62,627,521 J = − 10 J

 
Mechanical Energy
 
Mechanical energy is equal to kinetic energy plus gravitational potential energy. The formula for mechanical energy is:

ME = ½ mv ² − GMm / r

 The mechanical energy of a one kilogram body at rest on the surface of the Earth is −63 million joules.



Elastic Potential Energy
 
A stretched spring has energy. The energy a stretched spring has is called elastic potential energy. The formula for elastic potential energy is:

EPE  = ½ kx ²

They get this formula by integrating the formula for restoring force.



Conclusion

They're going backwards. The start with force and integrate to get energy. I start with energy and take the derivative to get the derivative of energy.

There's no such thing as force. Force is a bunch of baloney.

Also, they have negative energy. They have negative energy because they don't know that energy is the opposite of bond strength.