Calculating the Net Force on a Spherical Shell Around the Sun

[~angel~]

I am beyond lost with the question, so any help would be greatly appreciated.

Consider a solid, rigid spherical shell with a thickness of 100 m and a density of 3900 kg/m^3. The sphere is centered around the sun so that its inner surface is at a distance of 1.5×1011 m from the center of the sun. What is the net force that the sun would exert on such a Dyson sphere were it to get displaced off-center by some small amount?

Now this is one question which i have no idea how to approach. Any hints would be great.

Thank you

 

[SpaceTiger]

You should only need to work out one component of the force, since by symmetry the other two should cancel. You can then integrate that component of force over the surface area of the sphere. Since they say it's a small displacement, I'm guessing you'll have to do a first-order Taylor expansion somewhere along the line, but you should probably show some work before I go any further.

 

[~angel~]

Ok...I haven't really covered that stuff in class yet...I'll wait a few days to see if I learn anything about it.

 

[ramollari]

I would think this is an integration problem to determine the net gravitation on a Dyson shell, so unless I'm mistaken it is quite straightforward.

 

[jdstokes]

Hi Komal

It appears to me that if the sphere is perturbed slightly, then it will drift with uniform velocity until it collides with the star. This is a consequence of the fact that there is not net gravitational force between a spherical shell and a point mass located inside the shell. There is quite a lengthy proof of this result on pp. 456--8 of Y & F.

 

[learningphysics]

Hi Komal

It appears to me that if the sphere is perturbed slightly, then it will drift with uniform velocity until it collides with the star. This is a consequence of the fact that there is not net gravitational force between a spherical shell and a point mass located inside the shell. There is quite a lengthy proof of this result on pp. 456--8 of Y & F.

Yes, I believe this is the correct answer. 0 force.

 

[dark_angel]

Hi Komal

It appears to me that if the sphere is perturbed slightly, then it will drift with uniform velocity until it collides with the star. This is a consequence of the fact that there is not net gravitational force between a spherical shell and a point mass located inside the shell. There is quite a lengthy proof of this result on pp. 456--8 of Y & F.

lol, that wasnt me, this is me

 

[SpaceTiger]

This is a consequence of the fact that there is not net gravitational force between a spherical shell and a point mass located inside the shell.

Yes, of course, I totally overlooked that.

My method would have equated to rederiving that theorem, so I don't recommend that you do that.

 

[~angel~]

Hi Komal

It appears to me that if the sphere is perturbed slightly, then it will drift with uniform velocity until it collides with the star. This is a consequence of the fact that there is not net gravitational force between a spherical shell and a point mass located inside the shell. There is quite a lengthy proof of this result on pp. 456--8 of Y & F.

lol. I'm not Komal...hehehe. Thnaks for your help...all of you.

 

[jdstokes]

lol. I'm not Komal...hehehe. Thnaks for your help...all of you.

Oh right. Who are you mate?

 

[~angel~]

Im a bit confused with the second part.

What is the net gravitational force F_out on a unit mass located on the outer surface of the Dyson sphere described in Part A?

Don't you use F = G*m_1*m_2/r^2? So, you can find out the mass of the sun, you can find out the mass of the sphere from the density and everything. Would r^2 = 1.500000001E11?

I keep on getting the wrong answer. Any help would be great.

 

[~angel~]

Never mind
I got the answer.