How Does Gravitational Potential Influence Kinetic Energy in Satellite Launches?

[koujidaisuki76]

There is a graph saying that at r=1.0 is the center of the moon..

A satellite of mass 1500 kg is launched from the surface of the planet. Determine the minimum kinetic energy at launch the satellite must have so that it can reach the surface of the moon.

The surface of the moon is r= 0.96.
mass of the planet is 2398800599 kg


To find minimum kinetic energy would you use:

-GMm/r or GMm/2r ?

And wouldn't finding the potential energy equal the kinetic energy?
why or why not caus ei get two different answers

 

[member 553083]

To find the minimum kinetic energy, you would use GMm/2r. This is because the formula for kinetic energy (KE) is 1/2 mv^2, and the formula for gravitational potential energy (PE) is GMm/r. To calculate the minimum KE required to reach the moon's surface, you would subtract the PE at the planet's surface (GMm/r) from the PE at the moon's surface (GMm/2r). This is because the KE must be equal to the difference in PE between the two locations. Therefore, the minimum kinetic energy required to reach the moon's surface is GMm/2r - GMm/r = GMm/2r. It is true that the KE must equal the difference in PE between the two locations. However, the KE and PE are not necessarily equal to each other as they represent different forms of energy. The KE represents the energy of motion, whereas the PE represents the energy stored in an object due to its position relative to other objects.