Originally posted by mtthw
Oh, it's a plausible argument. I just have a sneaking suspicion that I can't get away with just neglecting the rest of the torus like that (it's a long way away, but there's so much of it!). I'd have to do the calculation to be sure - integrate round the torus. Maybe later 🙂
One thing about MIR and others, it's not gravitational instabilies that kill that kind of orbit, it's dust and upper atmoshperic gasses gradually slowing down the craft, especially big ones with relatively low mass, ISS is in the same boat. If it was in orbit around the moon, the same orbit would last a whole lot longer due to less dust and air. If there was no gas there would be no instability except for the pertubutions of external masses like the sun, etc. Another thing that perturbs orbits is something called "Mascons", concentrations of higher or lower density mass under the surface of a planet or moon. That is being traced now with a pair of satellites called GRACE. Two craft in constant touch by laser where they know their positions with respect to one another within one micron or so. Mass concentrations cause the orbit of the leading craft first encountering it to get slightly closer and that change is position is charted somewhat like an atomic force microscope except this is one humunous microscope, eh.
What led me to think about toroid shaped planets and such was thinking about the idea (scientifically impossible with present day technology) of drilling a hole straight through the earth, evacuating the hole and using it as a transportation system, just drop a craft into the hole which is in vacuum, it gets acellerated starting with one G and dropping to zero at the exact center of the earth, then negative G's until you reach the other end with exactly zero velocity and just clamp on to a stop, get out and new passengers get on and back down the hole you go. Free transport (at least after you spend the trillions of dollars for the tunnel🙂 Now I was thinking what if you did not stop at the end, just let it cycle down and back up forever. How long would it do that, what forces would act on it to slow it down and then end up like a dampened wave, stopping eventually in the center of the earth.
So thinking about that, I mentally stretched out the tunnel to approximate a toroid shape. I think the same thing would happen. If you had a craft at some altitude, it would acellerate to the center and then decellerate and reach the other side of the toroid with zero velocity. So then I figured, what if it was coming in with a pretty large velocity, could it be a stable orbit? I think it would have to be a very large ellipse because the curved nature of the orbit would mean it would need to intersect the center of the toroid but that leaves the curve favoring one side of the torous. Which probably means instability. That's what I have been struggling with.