I just read about an Alderson disk. It's a big DVD in space with a star in the hole in the middle. The DVD in big and people can live on the surface because on the surface of such a big DVD, not near to the edges, the gravitational field is like an infinite flat plane. How massive would a 2 AU DVD be?

First, I needed to derive the gravitational field of an infinite plane, having forgotten it from before.

Start off being geometric. On an infinite plane, the field lines will emanate from the plane perpendicular to the plane. We can imagine a closed surface being a cylinder, perpendicular to the plane.

Now analogising to electrostatics, we can use a version of Gauss's Law. Gauss's Law is:
S (E.dA) = q/e0
Analogising, for gravitics, we get:
S (g.dA) = m/k
where k is some physical constant.

Okay, we know the result for a point mass and a sphere as the Gaussian surface.
We have a field of strength g over a surface area of 4pi*r², where the lines are perpendicular to the surface at all points. So:
4pi*r²*g = m/k
This means that:
g = 1/4pik * m/r².
Compare this to ULG:
k = 1/4piG
So
S (g.dA) = 4piGm

So, if we know replace our sphere of radius r with the point masss m at its centre and instead move to our cylinder, through the plane. Because the field lines are parallel to the curved surface of the cylinder, the dot product g.dA is 0 for the curved surface. Therefore, we only worry about the discs at the end, of radius r, to which the field lines are perpendicular.

Therefore,

2pi*r²*g = 4piGm
=>
g = 2GM/r²

But the m enclosed in the cylinder has an area of pi*r² and an area density of s.

So
m = pi*r²*s
g = 2pi*G*s

So to get an Earth surface gravity environment, we want g=10m/s².

Therefore, we want a surface density of 2.4e10 kg/m². At 2AU, the disc would be 6.8e33 kg.

That's heavy!

Let's say we built it out of depleted uranium (because that's the kind of guy I am). The density of uranium is 22kg/m³. Therefore, the thickness of the disc would have to be 1 million metres!

I think this idea is an non starter.

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2 good 2 need 4 engines

I agree. We've got some pretty large speculative structures in OA but none of this kind. It has so many problems that even ultratechnology couldn't solve them.

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