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There is no such thing as "gravitational kinetic energy". Kinetic energy is energy contained in movement, and it doesn't make any difference, for the energy contents, whether an object was accelerated by gravity or by any other means. All you need to know is the object's speed and mass. "Gravitational energy" basically refers to the potential energy which an object has as a result of the gravitational field.

Answer2:

Gravitational "kinetic" energy is mv2 equal to mGM/r the potential energy or scalar energy. This gives v2 = GM/r, and the orbit frequency w2 = GM/r3.

Gravitational Energy also has vector energy cP= cmV, creating a Quaternion Energy. cP is the so-called "Dark Energy":

Total Energy E = -mGM/r + cP = [-mu/r, mcV]

The force is the first derivative:

F = [d/dr, Del] m[-u/r, cV] = m[u/r2 - cDel.V, cdV/dr -Del u/r + cDelxV]

F = mcv/r[v/c - cos(V), -1V + v/c 1R + sin(V) 1H]

Conservation of Gravitational Energy occurs at v/c= cos(V) = 1 and V is parallel to R. v/c = cos(V) is the redshift, v/c is the Gravitational Fine Structure Constant.

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Q: What is Gravitational Kinetic energy?
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