# How would the rotational and orbital mechanics differ on a torus-shaped planet as compared to a spherical planet?

I am making the attempt to develop some computational models of Star systems and I was wondering how the a torus shaped planet would compare to a traditional spherical planet in the context of rotational and orbital motion.

• This reminds me of this video youtu.be/UrLey-pX7Bc – BioPhysicist Sep 16 '18 at 0:56
• – anna v Sep 16 '18 at 3:45
• I really wonder why this is not regarded as mainstream physics, since point masses moving in classical fields is about as mainstream as anything can be. And there is a biggish literature in astrophysics on orbits related to massive torii in AGNs, so torus shaped mass distributions are also mainstream. – Anders Sandberg Sep 16 '18 at 20:15
• I think this is not non-mainstream but is too broad as it's basically asking us to re-derive a significant portion of Newtonian mechanics in a different gravitational system. Even the answer given basically says, "there are changes, take a look at my blog" where the post is quite lengthy. – Kyle Kanos Jan 28 '19 at 11:19
• Related meta post: physics.meta.stackexchange.com/q/11037 – user191954 Jan 28 '19 at 12:35

Near the surface and for short distances projectile motion will look fairly terrestrial. Thrown things follow parabolas. As the trajectories get longer the above effects will matter. The Coriolis acceleration $\mathbf{a}=2\mathbf{v}\times\mathbf{\Omega}$ will tend to tilt and twist the trajectory. Along the poles $\mathbf{\Omega}$ and gravity as aligned, and the trajectory will be tilted and twisted. Closer to the equators the twisting gets more asymmetric.