Old News: Dyson Sphere Revisited
Oct. 24th, 2003 05:20 pm![[personal profile]](https://www.dreamwidth.org/img/silk/identity/user.png){kind=small}
swestrupI was googling for some old articles that I had long ago posted to usenet, and it occurred to me that some of the ones that I find more interesting could be reposted here. So, here's a debate I started on a variational design for a dyson sphere:
You can see the whole archived discussion thread here.
Several years ago, I decided to design a Dyson Sphere as a thought experiment. For those unfamiliar with the term, a Dyson Sphere is the name given to a structure that completely surrounds a star, and allows a *very* advanced technological race to use all of the energy intercepted from the star. Some authors, such as Bob Shaw, have proposed that a large solid shell (made of an uspecified material) with a radius just in excess of 1 A.U. and englobing a Sol type sun would provide an ideal living environment for humans. The surface area of the inner side of a Dyson sphere is mind-bogglingly huge and would provide plenty of living space for a long time to come.
It was this latter type that I attempted to design. Right from the start I ran into problems. The net gravitational attraction from a spherical shell cancels at all points within the shell. Therefor there would be no gravity to hold down an atmosphere (or people, for that matter). Rather than blithely assuming that a race that could build a Dyson Sphere would be able to control gravity, I attempted to find another solution. If the sphere were spun, then a centrifugal force would radiate out from the axis (bad terminology, I know, but its late) and could provide a 1g force at the equator. Unfortunately, the force would not be normal to the surface. Folks living at an internal lattitude of 45 degrees would feel a diminished force, at 45 degrees to the surface. Those at the poles would feel no gravity at all (which is good considering that it would be at 90 degrees to the surface...)
Now, it occured to me that a large enough mass, affixed to each pole, and carefully distributed, would add a compensating gravitational force that would combine with the centrifugal force to provide a net force of 1g at the surface, and normal to the surface. I have been unable to calculate that mass distribution, or even to prove that it exists. I do have some worries that a perfect solution would require a shape with an asymptote, but I have hope that a 'close enough' answer can be found by modifying a perfect answer.
So, in summary, I am trying to find the function describing the outer surface of a rotating object, which has a spherical inner surface, such that the vector sum of the 'centrifugal' force and the gravitational force generated by the mass of the object is, at every point on the inner sphere, of constant magnitude, and normal to the inner surface. The axis of rotation of the object passes through the center of the sphere. In addition, the point on the outer surface closest to the center of the inner sphere must be at least as far from that center as the surface of the sphere. (The shell has no area of negative width). Assume either a constant density for the shell, or one that varies, as you wish. I have some hope that, if there is no solution for an object of constant density, that there is one for an object of varying density.
I'll be glad to provide any clarification to the problem that is asked for.
You can see the whole archived discussion thread here.
Several years ago, I decided to design a Dyson Sphere as a thought experiment. For those unfamiliar with the term, a Dyson Sphere is the name given to a structure that completely surrounds a star, and allows a *very* advanced technological race to use all of the energy intercepted from the star. Some authors, such as Bob Shaw, have proposed that a large solid shell (made of an uspecified material) with a radius just in excess of 1 A.U. and englobing a Sol type sun would provide an ideal living environment for humans. The surface area of the inner side of a Dyson sphere is mind-bogglingly huge and would provide plenty of living space for a long time to come.
It was this latter type that I attempted to design. Right from the start I ran into problems. The net gravitational attraction from a spherical shell cancels at all points within the shell. Therefor there would be no gravity to hold down an atmosphere (or people, for that matter). Rather than blithely assuming that a race that could build a Dyson Sphere would be able to control gravity, I attempted to find another solution. If the sphere were spun, then a centrifugal force would radiate out from the axis (bad terminology, I know, but its late) and could provide a 1g force at the equator. Unfortunately, the force would not be normal to the surface. Folks living at an internal lattitude of 45 degrees would feel a diminished force, at 45 degrees to the surface. Those at the poles would feel no gravity at all (which is good considering that it would be at 90 degrees to the surface...)
Now, it occured to me that a large enough mass, affixed to each pole, and carefully distributed, would add a compensating gravitational force that would combine with the centrifugal force to provide a net force of 1g at the surface, and normal to the surface. I have been unable to calculate that mass distribution, or even to prove that it exists. I do have some worries that a perfect solution would require a shape with an asymptote, but I have hope that a 'close enough' answer can be found by modifying a perfect answer.
So, in summary, I am trying to find the function describing the outer surface of a rotating object, which has a spherical inner surface, such that the vector sum of the 'centrifugal' force and the gravitational force generated by the mass of the object is, at every point on the inner sphere, of constant magnitude, and normal to the inner surface. The axis of rotation of the object passes through the center of the sphere. In addition, the point on the outer surface closest to the center of the inner sphere must be at least as far from that center as the surface of the sphere. (The shell has no area of negative width). Assume either a constant density for the shell, or one that varies, as you wish. I have some hope that, if there is no solution for an object of constant density, that there is one for an object of varying density.
I'll be glad to provide any clarification to the problem that is asked for.
-- Opinions expressed herein are the sole property of | Stirling G. Westrup this poster; illegally retained opinions will be | UUCP: stirling@ozrout.uucp surgically removed. | BIX: swestrup
