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Newtonian physics: torque on a planet sun system
imagine 2 bodies in space. one is the sun, the other is the planet. they are perfectly rigid and spherical. these 2 bodies are separated quite far apart. Imagine the non-uniform gravitational field the planet experiences. due to its non-uniform nature, gravitation force do not act exactly at the planet's center of mass (the position should be a little bit closer to the sun than the center of mass).
Consider this: when the earth spin at a non-zero inclination angle, the gravitation pull would result in a net torque on the planet, which results in precession.
i have worked out a approximation of this torque (10 page paper..). what i did was basicaly directly integrating over the whole sphere (the planet) while using some reasonable approximations in between. however, no one has ever validate it nor do i know if it is mathmetically correctly or has been discovered before...
any comments or inputs are appreciated. if you are interested, i can post my project.
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