Re: Couple Old Style Space Opera questions...

Nyrath the nearly wise wrote:

Of course this does remind one of the situation in
Larry Niven's novels THE INTEGRAL TREES and
THE SMOKE RING.

And Niven had this to say in his essay BIGGER THAN WORLDS:

To his credit, he only suggested it as a mathematical possibility (but then what _wouldn't_ be a mathematical possibility?), but the idea is pretty much dead on arrival.

He talks about putting the megashell around the "heart of a galaxy," so let's take him to mean the central bulge, and we can use the disk and halo for construction material, and use the Milky Way as a baseline example.

The Milky Way Galaxy contains about 2 x 10^11 solar masses (4 x 10^41 kg) of visible material, 4 x 10^11 stars, and its total mass (stars, gas, and dust) is about 6 x 10^11 solar masses (1 x 10^42 kg). So that's a hard limit on what we have to work with. (We'll ignore dark matter since it's probably not going to be helpful for construction projects.) The total luminosity of the Galaxy is about 1.4 x 10^10 solar luminosities (5 x 10^36 W).

As a rough cutoff, let's leave 10% of the Galaxy's visible mass and luminosity for our "heart," and we'll build the shell around that. (The details, as we'll soon find out, don't really matter.) That means that our heart will have mass M = 4 x 10^40 kg and luminosity L = 5 x 10^35 W.

We want to choose a radius r for our shell so that it receives something like the normal insolation that we get here on Earth, which is I = 1400 W/m^2. The relationship is

I = L/(4 pi r^2),

so the radius of our shell will be r = 5 x 10^15 m, or about half a light-year -- and that volume has to contain 4 x 10^10 stars! Even if you were to back up and use the entire luminosity of the Galaxy (5 x 10^36 W), that would leave you with a radius of 2 x 10^16 m, or only about 2 ly (containing 4 x 10^11 stars). In other words, this thing isn't going to be nearly as big as he thinks it is -- either that or it's going to be really, really dim.

What's the gravitational acceleration at the surface of our shell of radius r?

a = G M/r^2

or, for our 10% heart, about 0.1 m/s^2 at the surface. That causes a bit of a problem for what he's talking about.

The thickness of the shell isn't a problem for the size it turns out to have to have, since we have 1 x 10^8 kg/m^2 with which to construct all 3 x 10^32 m^2 of it.

What about the atmosphere? If we want Earth-like pressures -- 100 kPa -- at the surface of the shell, then that means the areic mass of the atmosphere must be p_0/a = 1 x 10^6 kg/m^2, so its total mass is 3 x 10^38 kg. Again, not a problem for what turns out to be such a tiny shell.

Now what about the type of shell _Niven_ was talking about? A really, really huge one? He talks about "a surface area of tens of millions of light-years [sic]." To convert that to something that makes sense and that he meant light-years squared, let's (slightly arbitrarily) choose the surface area to be 3 x 10^7 ly^2 = 3 x 10^39 m^2. So the radius would be 1 x 10^19 m, or about 1500 ly.

How bright would it be? Even using the Galaxy's entire luminosity (5 x 10^36 W), the insolation at the radius of the sphere would be 2 mW/m^2; that's almost a million times dimmer than the solar insolation on Earth. For reference, that's dimmer than the full moon alone.

How much construction material would we have to work with? Using the whole mass of the galaxy (4 x 10^41 kg), that's an areic mass of 100 kg/m^2. That doesn't seem horrible, but what about the mass of the atmosphere?

Being conservative and putting the whole Galaxy's mass inside the shell, at that distance the gravitational acceleration would be 3 x 10^-7 m/s^2. Doing the same magic with a surface pressure of 100 kPa, that's an areic atmosphere mass of 4 x 10^11 kg/m^2, or a total mass of 1 x 10^51 kg -- that's about three billion galaxies' worth, approaching the total number of known galaxies in the observable Universe.

In other words, I think Niven's imagination leaped before it looked.

--
Erik Max Francis && max@xxxxxxxxxxx && http://www.alcyone.com/max/
San Jose, CA, USA && 37 20 N 121 53 W && AIM, Y!M erikmaxfrancis
We have always been space travelers.
-- Carl Sagan, 1934-1996
.

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