Hi
Geopotential U is the gravitational potential of the Earth without taking into account the rotation of the Earth whereas gravity's potential ##U_T## considers the rotation of the earth such as :
##U_T = U + \frac{1}{2}\omega ^2r^2cos(\psi)^2## (with common spherical coordinates)
However, for a satellite, the potential of the Earth undergone by the satellite is ##U## and not ##U_T##.
My question : why?
In fact, I agree the satellite does not belong the the surface of the Earth but it seems that the geopotential ##U## does not consider the rotation of the Earth ? It would say that the rotation of the Earth does not affect the gravitational force of the Earth on the satellite ?
Geopotential U is the gravitational potential of the Earth without taking into account the rotation of the Earth whereas gravity's potential ##U_T## considers the rotation of the earth such as :
##U_T = U + \frac{1}{2}\omega ^2r^2cos(\psi)^2## (with common spherical coordinates)
However, for a satellite, the potential of the Earth undergone by the satellite is ##U## and not ##U_T##.
My question : why?
In fact, I agree the satellite does not belong the the surface of the Earth but it seems that the geopotential ##U## does not consider the rotation of the Earth ? It would say that the rotation of the Earth does not affect the gravitational force of the Earth on the satellite ?
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