# Calculating the Net Force on a Spherical Shell Around the Sun

• ~angel~
In summary, the conversation involves discussing a question about a solid, rigid spherical shell surrounding the sun and the net force that the sun would exert on it if it were displaced off-center. The conversation includes suggestions for solving the problem, a proof of a relevant theorem, and confusion about identities of the participants. Ultimately, the question is resolved with the correct answer being found.
~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

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.

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.

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.

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.

jdstokes said:
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.

jdstokes said:
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

jdstokes said:
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.

jdstokes said:
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.

~angel~ said:
lol. I'm not Komal...hehehe. Thnaks for your help...all of you.

Oh right. Who are you mate?

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.

Never mind

## What is the formula for calculating the net force on a spherical shell around the sun?

The formula for calculating the net force on a spherical shell around the sun is F = GMm/r^2, where G is the gravitational constant, M is the mass of the sun, m is the mass of the object, and r is the distance between the object and the center of the sun.

## How do you determine the direction of the net force on a spherical shell around the sun?

The direction of the net force on a spherical shell around the sun is always towards the center of the sun. This is because gravity is an attractive force and the sun's mass is concentrated at its center.

## What factors affect the net force on a spherical shell around the sun?

The net force on a spherical shell around the sun is affected by the mass of the object, the mass of the sun, and the distance between the object and the center of the sun. The net force also depends on the direction of the force, which is always towards the center of the sun.

## Can the net force on a spherical shell around the sun ever be zero?

Yes, the net force on a spherical shell around the sun can be zero. This would occur if the object is in a state of constant motion, such as orbiting the sun at a constant distance and speed. In this case, the gravitational force is balanced by the centripetal force, resulting in a net force of zero.

## How does the net force on a spherical shell change as the distance from the sun increases?

The net force on a spherical shell around the sun decreases as the distance from the sun increases. This is because the force of gravity decreases with distance according to the inverse square law. Therefore, the closer an object is to the sun, the stronger the net force will be.

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