[Agemegos]

Let's dirty up the back of an envelope.

We're looking up into the sky to see a bubble-wrapped moon. So let's check the figures for bubble-wrapping The Moon.

The purpose of this bubble-wrapping is to keep an atmosphere in where none belongs, which means that the air tends to go outward, which means that the pressure is greater than the weight of the air. The atmosphere enclosed pushes upward on the envelope and tends to support it. The envelope doesn't nave to support its own weight. That's good: it tells us that we don't need to worry about buckling. It also tells us that the bubble is supported by air pressure inside it, not hung off sky-hooks. That's terrific.

In order that the bubble stay where it is (as opposed to sink lower down and compress the atmosphere further, or bulge out and let the pressure drop, we need the weight of the envelope plus tension in the envelope to be equal to the unbalanced pressure of the atmosphere. We'll take the pressure above the envelope to be negligible, and the atmosphere below the envelope to be no more than 25% oxygen (to prevent a fire hazard) and no less than 10 kPa pp(O2) (so that it will support human respiration). That gives us an unbalanced pressure of at least 40 kPa on the envelope.

The surface gravity on the Moon is about 1.5 N/kg, so to provide the necessary compression to the envelope contents by weight alone would require 40000 N/m^2 divided by 1.5 N/kg = 27 tonnes per square metre. The density of the envelope material would be somewhere between that of polythene and that of diamond so that means an envelope thickness of about 8 to 28 metres. If you make it any thicker than that of reasonable material and you would have to support it somehow (perhaps with a denser atmosphere, though there are limits to that), and if you make it any thinner you will need tension in the envelope to hold it down. How transparent is 8 metres of diamondoid? How transparent is 28 metres of polythene?

The Moon's surface area is 3.8 * 10^7 square kilometres, which is 3.8 * 10^13 square metres. At 27 tonnes per square metre that is 10^15 tonnes. One quadrillion tonnes of transparent wrapping material.

Okay, so let's see how much tension will help.

A great circle of the Moon has a length of 1.1 * 10^7 m and an area of 9.5 * 10^13 m^2. With a pressure of 40 kPa that's about 3.8 * 10^17 N spread around 1.1 * 10^7 metres. Call it 3.4 * 10^10 N/m. The tensile strength of polythene is about 25 MPa and that of diamond about 60 GPa. A polythene envelope would need to be at least 1.4 kilometres thick to withstand the pressure (and then its weight would make the tension irrelevant). But 0.57 m of diamondoid could do it.

Allowing an order of magnitude for safety in the tension element (tearing would be catastrophic) we're in the region of a 3.6-metre thick diamondoid envelope restraining the air 40% by weight and 60% by tension, massing a total of 400 trillion tonnes. The structure is supported by an atmosphere of at least 0.4 bar contained within it: without that there it will collapse.


As is always the case with self-supporting structures, the real engineering difficulty is in getting the envelope and air into place without having both in place to support or constrain each other while you get them into place. I do not fancy building a centring for this dome.