It's sad, at one time I used to be able to do the full integration by parts for proving that a solid surfaced Dyson Sphere simply could not work. The whole 'no gravity outward to remain upon the inner surface and consequently fall into the center sun' thing. (it was a classical charged body proof taught to us in our EE course)
These days, I'm lucky to remember SOH-CAH-TOA without saying it out-loud.
Doing it coordinate by coordinate is the hard way anyway; the easy proof is to use Gauss's Theorem plus spherical symmetry. (But Gauss's Theorem is really just a very generalized statement about integration by parts.)
But doesn't that lead to spherical cows getting strewn across the landscape? And they're useless as livestock due to the complexity involved with figuring out how to optimally stack them in the cow barn (plus it's impossible to milk their perfectly smooth udders).
I think it's safe to assume that a Dyson sphere is a sphere without worrying about it being a slippery slope to spherical cows.
On the other hand, I now have the reverse image of a giant cow showing up on galaxy's doorstep, and after it's brought in it starts firing off Nicoll-Dyson laser blasts while a quintillion Trojans pour out and proceed to ransack the galaxy.
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It's sad, at one time I used to be able to do the full integration by parts for proving that a solid surfaced Dyson Sphere simply could not work. The whole 'no gravity outward to remain upon the inner surface and consequently fall into the center sun' thing. (it was a classical charged body proof taught to us in our EE course)
These days, I'm lucky to remember SOH-CAH-TOA without saying it out-loud.
no subject
no subject
But doesn't that lead to spherical cows getting strewn across the landscape? And they're useless as livestock due to the complexity involved with figuring out how to optimally stack them in the cow barn (plus it's impossible to milk their perfectly smooth udders).
no subject
no subject
no subject
On the other hand, I now have the reverse image of a giant cow showing up on galaxy's doorstep, and after it's brought in it starts firing off Nicoll-Dyson laser blasts while a quintillion Trojans pour out and proceed to ransack the galaxy.