Gravitational force on an astronaut from a nearby massive torus

[srecko97]

Homework Statement

There are a big object and an astronaut in space. How do we calculate the gravitational force between them. I enclose a photo. I have given the mass of an astronaut, the dimensions of this giant ring and density of the ring. There is also a mistake in the photo. The astronaut is not 2*R away, but only 1*R away from the top of the ring.

2. Relevant equation
F=G*m*M/r²

The Attempt at a Solution

I do not know how to start solivng it. I know how to calculate the force between a point and a thin ring and between a point and a thin circle... but this homework is really hard for me. I would be greatful if I got any key ideas or maybe some beginnings of solution. Help me please!

 

[vela]

What's the difference between a "thin ring" and a "thin circle"? To me, they mean the same thing, but you apparently think of them differently, so I'm looking for a bit of clarification in what you meant by those terms.

 

[jtbell]

And when you say you "know how to calculate the force" between a point and one of those those two objects, does that mean you simply know the formulas, or that you know how to derive them from F = GMm/r² via integration?

 

[srecko97]

I meant circle as a 2 dimensional shape with surface and ring as a curve. Yes, i know how to derive these formlas via integration, but this problem seems much harder.

 

[Cutter Ketch]

I meant circle as a 2 dimensional shape with surface and ring as a curve. Yes, i know how to derive these formlas via integration, but this problem seems much harder.

Much harder? If you know how to integrate to get the force for a single slice then you just need to integrate all the slices in the third dimension.

 

[vela]

I meant circle as a 2 dimensional shape with surface and ring as a curve. Yes, i know how to derive these formlas via integration, but this problem seems much harder.

Disk might be a better word to use than circle.

As Cutter has implied, if you really understand how to derive the other results, solving this problem should be relatively straightforward. I'm guessing you were shown the derivation for the ring and possibly how that result was used to get the formula for the disk. You want to do essentially the same thing here. Try deriving the result for a cylinder without the hole in the middle. Show us what you've tried so far.

 

[srecko97]

Thanks

 

[redivider]

wow I was doing the same problem, check my thread maybe it helps. Also this isn't a torus. That would be way more fun though.

 

[srecko97]

Thanks, redivider. I know it is not a torus, but one of the administrators obviously thinks so, as the title was changed.