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Justinjah91

KSP EDU Energy Sphere values seem off

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Hello,

I am a TA for a university physics lab. We are trying to see if KSP EDU can be used in our lab sections to discuss gravity and orbits, but the potential energy that is given on the energy spheres seems to be incorrect. According to pretty much everyone in physics, orbital potential energy is given by

U = -GMm/r

Where G is the gravitational constant, M is the mass of the planet, m is the mass of the orbiting body, and r is the distance from the center of the planet. I'm ok with the negative not being present in game, as a negative volume sphere would be rather hard to depict. Unfortunately, the energy sphere says that, at an apoapsis of 8,600,000 m from the center of kerbin, the potential energy is 120,000 kJ. When I calculate the potential energy, I get 8,833,106 KJ. Can anyone explain why this is happening?

 

Thanks

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Hello,

Actually the whole formula for gravitational potential energy is 

U = -G \frac{m_1 M_2}{r}\ + K, where K is an arbitrary constant that can be used to define where we consider the zero potential to be.

Usually "pretty much everyone in physics" uses 0 for K meaning that gravitational potential energy will only be approaching zero at infinity (infinite distance from the main body), which makes sense since there is not limit to the reach for the force of gravity (it just gets weaker and weaker the longer the distance). It also makes calculations easier since you don't need to include the constant K everywhere.

However for the purpose of visualizing how kinetic energy is converted to potential energy and back with the energy spheres we consider potential energy to be zero at the surface of the main body (K = GMm / R, where R is the radius of the main body). Otherwise we could not really draw a sphere to visualize it since it would always be negative for finite distances.

I am actually now making changes to the energy spheres UI for the next update of KerbalEdu to add an option to set K = 0 (potential zero at infinity). It will make the potential energy sphere not show, but you will be able to demonstrate the values it gets when it is calculated the usual way.

 

Edited by MarkZero

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Now i also want to make this note about the energy spheres. If you set the "Reference frame:" to surface or launch altitude the kinetic energy sphere will use speed relative to surface for calculating the kinetic energy. This will give you "wrong" values in orbit and at great heights and might even make the energy sum seem to change. You should only use these options when at low altitudes and speeds where the craft can be considered to be moving along with the surface of the body.

Edited by MarkZero

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