Golden Moon

[jee_c2]

I would lie to sketch an extremely futuristic idea about how we could create usable living space on/in the Moon in the far future.

First list the problems:
- low gravity
- no atmosphere
- no shielding against radiation
- 28 day long Moon day
- no usable soil

Basic idea: mine most parts of the Moon, leave the most upper layer in the proper width, leave pillars to hold it*, take the mined material, transform it either chemical, mechanical or nuclear way to make it denser**. Collect the dense material in the remaining core. Fill the created empty layer with proper atmosphere. Cover the Moon surface with computer controlled mirrors (isru, not that it matters much on this scale of work). Dig holes, create tunnels, where the collected light can enter the Moon inner space in a controlled way. Make elevators from the surface to the inner Moon surface.

What do we get?
Gravity - solved (about same mass, smaller radius) on the inner Moon surface.
Atmosphere - check, inside (* actually it helps keeping the outer shell - I read about it here: Shell worlds -> https://forum.nasaspaceflight.com/index.php?topic=49788.0)
Radiation shielding - the outer shell do it
Too long Moon day - controlled light can solve it
Soil - sorry, that has to be solved somehow

Almost ridiculous to ask it, but how could we do it?
I imagine machines, which can replicate themself (call them Neumann machines). These can cover the Moon surface with controlled direction mirrors. Actually this controlled flow of energy can be used to drive these machines even at Moon sunset.
The similar mining, digging machines start to create tunnels under the Moon sutrface. Here notice: we can start using it already by filling it with Moon air (this is a question, since we got O2, but unfortunately no N2.. other inert gas from local resource? .. )
So this whole mining phase is gradual, and produce usable spaces while ongoing.
The machines are fed with solar energy directed to them, lead to them.
And the big question: how to transform the material, how to compress it? I tried to find some chemical solution, but I'm not expert on that field at all, so even though I 've found what is the composition of the Moon (other on the surface, in the crust and in the mantle, in the core), I haven't found a proper chemical réaction, that produce the needed density material. As it can be seen next, it is not even possible..

** What is the needed density?

First, let's try a target inner Moon gravity equal to the Earth surtface gravity (~9.81m/s2).

Take Moon sutface gravity simply as 1/6 g.
M - Moon (as now)
M' - inner Moon (the targeted compressed sphere)

g_M = 1/6 g_E = f*m_M / r_M²

g_M' = g_E = f*m_M / r_M²

r_M' = 1/SQRT(6)*r_M


ρ_M = 3.34 g/cm²
ρ_M' = ρ_M*V_M/V_M' = ρ_M* r_M³ / r_M'³ = ρ_M * SQRT(6)³ = 14.69 g/cm³

What are at least so dense?
i.e.:
ρ_Berkelium = 14.78 g/cm³
ρ_Gold = 19.32 g/cm³
ρ_Platinum = 21.45 g/cm³

We can see, that probably neither chemical nor mechanical way is suitable for achieving this level of density (correct me, if I'm wrong). That leads to nuclear transformation, which really seems probelmatic.. (some kind of nuclear reactor? could not really imagine how)

Also, note, we need to transform the Moon actual material into ... gold (or something similarly dense). The golden inner Moon.
We just fall back to the old alchemist question: how to produce gold from another material (atoms), aka transmutation..
Also this reminds me the planet builder planet Magrathea from the HHGTTG, where they produced golden or platinum planets. Given the above calculations, az least -assuming normal Earth like gravity - those planets were not too big...

What would be the habitable surface area of the inner Moon?

r_M' = 1/SQRT(6)*r_M = 723km (note, even so the radius is bigger, we still have to mine and transform the material inside the Moon's partial melt mantle and in the fluid outer core and in the core also..)
A = 6568753 km², which is about 2/3 of the area of the USA.
Of course it is "easy" to leave a lot of different layers (100m high i.e.) in that range of proper g, multiplying the habitable area. The light distribution could be solved in mirror channels in the pillars from the original surface (remember, it is almost totally covered with computer controlled mirrors, so light collection can be done).

I hope you enjoyed this thought experiment as much as I did, when wandering through the different aspects of this imagined, far future Luna engineering project!

To be realistic, it is almost certainly better to build habitable rings, torroids in space, instead of processing almost the whole amount of lunar material..

[TrevorMonty]

Transforming other elements into gold etc won't increase gravity, still have same mass (quantity of atoms) on moon regardless if its H or Au. Only way to increase gravity is add extra mass to moon. Not enough asteriods in solar system to even get close to earth mass.

If you want earth gravity, live on earth or Venus (0.91g). The alternative is artifical gravity from centrifigal force, which is why Oneil Cylinders are such popular concept for space colonies. If we have capability to transform moon as you suggested, then building a few thousand Oneil colonies from asteriods shouldn't be problem.

[jee_c2]

Transforming other elements into gold etc won't increase gravity, still have same mass (quantity of atoms) on moon regardless if its H or Au. Only way to increase gravity is add extra mass to moon. Not enough asteriods in solar system to even get close to earth mass.

If you want earth gravity, live on earth or Venus (0.91g). The alternative is artifical gravity from centrifigal force, which is why Oneil Cylinders are such popular concept for space colonies. If we have capability to transform moon as you suggested, then building a few thousand Oneil colonies from asteriods shouldn't be problem.

I'm sorry, you misunderstand the idea a bit. The point is, you concentrate ("compress") the mass of the Moon in a smaller sphere at it's center (the inner Moon). On it's surface, the gravity will be higher. On the crust of the original Moon (on the remaining outer shell), the gravity will remain the same, of course.

I totally agree, O'Neill Cylinders are a way better and realistic solution for more habitable space. The Golden Moon is rather a thought experiment, not a real proposal. Perhaps it is better for a Kardashev II type civilization (ok, somewhere between level I and level II)

[TrevorMonty]

Compressing moon mass won't increase gravity.

[ppnl]

No but compressing the mass thus reducing radius will increase surface gravity. Think of the surface gravity of a neutron star with the mass of the moon.



Not that compressing the moon is a real option. I mean that's really, REALLY doing it the hard way.

[TrevorMonty]

No but compressing the mass thus reducing radius will increase surface gravity. Think of the surface gravity of a neutron star with the mass of the moon.



Not that compressing the moon is a real option. I mean that's really, REALLY doing it the hard way.

Have do some research but seems it would as more of mass will be directly under your feet. On earth alot of mass is around us not directly underneath, land in distant doesn't contribute to gravity under foot. Would concentrated moon give equivalent of 1g?.

[jee_c2]

Compressing moon mass won't increase gravity.

When talking about gravity, it's a bit shortening the phrase. Actually, I meant gravitational acceleration.
You are right, the original mass causing the gravitational force would not change, the smaller radius of the body would allow you to go closer to it's center, thus experiencing higher gravitational acceleration (caused by the same mass).

[tbellman]

Have do some research but seems it would as more of mass will be directly under your feet. On earth alot of mass is around us not directly underneath, land in distant doesn't contribute to gravity under foot. Would concentrated moon give equivalent of 1g?.

Whether the mass is directly under your feet or not, does not matter.  At the same distance from the center of gravity (CoG) of a certain mass, the gravity is the same regardless of if the mass is concentrated in a small point, spread out in a large sphere, or is concentrated in a large, thin spherical shell (as long as the distance from the CoG is larger than the radius of the sphere).

If the Earth was suddenly compressed into a black hole (radius ca 8.9 mm), you would still experience 9.8 m/s² of gravity at the distance of 6370 km from it.  Then you would start falling down towards the black hole, and be subject to higher and higher gravity, as you get closer, until when you reach the "surface", gravity is high enough to prevent even light from escaping.  Despite not adding any mass to the black hole, just because you get closer to its CoG.  (Of course, you would be in free fall, so you wouldn't feel the higher gravity; until you get close enough that tidal effect start stretching you...)

Similarly, compressing the Moon to higher density, allows you to get closer to the CoG while still being "outside" of all its mass, and thus gives you higher gravity.  If you insist on building a 1000 km high tower on jee_c2's compressed moon and staying at its top, you would still only be subject to 1/6 g, but descending to the base of that tower will allow you to experience a full 1g.

[lamontagne]

You might inject a few small black holes into the moon.  These would eventually eat most of it, allowing you to build a shell world with a much smaller radius around the black holes.  Radiation from the black holes would provide power for a long time, I expect.
The only 'real' way I know to create denser material.
The shell world would probably need to be a dynamically supported structure, similar to a Lofstrom loop, as there is no way normal matter could stand up to the new gravity. Without a dynamic structure the Moon would entirely crumple into the black hole(s).

You could spin up the dynamic structure so that it turns on itself in a day.

Alternatively, you can turn the moon into 'Scree'  and build a mini Ringworld, more on the scale of a Culture Orbital.  Probably simpler than trying to keep it spherical.

[Twark_Main]

Absurdly ambitious, yet perfectly compatible with the laws of physics. I love it.

You might inject a few small black holes into the moon.  These would eventually eat most of it, allowing you to build a shell world with a much smaller radius around the black holes.  Radiation from the black holes would provide power for a long time, I expect.

You mean radiation from the hot collapsing gas, or Hawking radiation? Because according to this handy Hawking radiation calculator, the latter will be absurdly small, on the order of a few dozen femtowatts.

This provides a mildly interesting algebra exercise: what is the mass of black hole required to achieve Earth-like radiant balance (250 W/m²) at a radius with a local gravity of 1 g?


Also, this idea really belongs in Advanced Advanced Concepts.


Edit: Someone check my math. I get m = 25 billion tonnes and d = 26 meters. So... I invented the Little Prince planet.

[ChrisWilson68]

No but compressing the mass thus reducing radius will increase surface gravity. Think of the surface gravity of a neutron star with the mass of the moon.



Not that compressing the moon is a real option. I mean that's really, REALLY doing it the hard way.

Have do some research but seems it would as more of mass will be directly under your feet. On earth alot of mass is around us not directly underneath, land in distant doesn't contribute to gravity under foot. Would concentrated moon give equivalent of 1g?.

All the people telling you that the same mass in a smaller radius will give a higher surface gravitational acceleration are correct.  Your objections are based on a misunderstanding of physics.

One of the things that's normally taught in an introductory physics class is that if you have a spherical shell and the mass in that shell is uniformly distributed throughout the shell, then everywhere outside the shell the gravity is exactly as if that same amount of mass was a point mass at the center of the shell.  Strangely enough, anywhere inside the shell, there's exactly no gravitational effect from the mass of the shell at all.  This can be proven with calculus and Newton's law of gravitation.

Since it's true of a single shell, it's also true of arbitrarily many shells inside each other with a common center.  Since you can slice up a sphere into lots of shells, it's true of a sphere too.

That's really handy because as long as mass is uniformly distributed at each layer of a sphere, you can just do your calculations for spherical bodies as if all their mass was concentrated at their centers.  That's super convenient.  It doesn't even matter if they are denser toward the center.

Anyway, since gravitational attraction is proportional to the square of the distance between two objects, the force due to gravity between a person on the surface of the planet and the entire planet is proportional to the square of the radius of the planet.  Cut the radius in half and you increase the force of gravity on the surface by a factor of 4.  Of course the volume is proportional to the cube of the radius, so that means you need to increase the density by a factor of 8 to increase the surface gravity by a factor of 4.

And that sets off an alarm bell for me, because the surface of the Moon today has less than a quarter of the gravity of the surface of the Earth.  So the density of the Moon would have to be more than 8 times greater.  But the original poster said the current density of the Moon is 3.34 g/cm3 and calculated a target density of 14.69 g/cm3.  But 3 times 8 is 24, so the density would have to be more than 24 g/cm3.

Lets see where the original poster went wrong.  Ah, the original poster multiplied 3.34 g/cm3 times the square root of 6 cubed to get 14.69 g/cm3.  But actually the square root of 6 cubed is itself 14.69 (actually, 14.6969..., so it should be rounded to 14.70 if we're going with only two decimals of precision).  The OP forgot to multiply by 3.34.  So the real required density would be 49.09 g/cm3.

So, gold isn't going to cut it.  Even Osmium, the densest material at standard temperature and pressure ranges only has a density of 22 g/cm3.

So the title of this thread is wrong.  It can't be Golden Moon.  It has to be Unobtainium Moon.

[rakaydos]

So, gold isn't going to cut it.  Even Osmium, the densest material at standard temperature and pressure ranges only has a density of 22 g/cm3.

So the title of this thread is wrong.  It can't be Golden Moon.  It has to be Unobtainium Moon.

Sounds like Osmium would be enough to get Mars gravity or better?

[Steve G]

Until that glorious day when we master the mysteries of gravity and develop Star Trek-like artificial gravity, we're going to be stuck with the ambient gravity of planetary bodies and all its shortcomings.

[lamontagne]

Absurdly ambitious, yet perfectly compatible with the laws of physics. I love it.

You might inject a few small black holes into the moon.  These would eventually eat most of it, allowing you to build a shell world with a much smaller radius around the black holes.  Radiation from the black holes would provide power for a long time, I expect.

You mean radiation from the hot collapsing gas, or Hawking radiation? Because according to this handy Hawking radiation calculator, the latter will be absurdly small, on the order of a few dozen femtowatts.

This provides a mildly interesting algebra exercise: what is the mass of black hole required to achieve Earth-like radiant balance (250 W/m²) at a radius with a local gravity of 1 g?


Also, this idea really belongs in Advanced Advanced Concepts.


Edit: Someone check my math. I get m = 25 billion tonnes and d = 26 meters. So... I invented the Little Prince planet.

I was thinking of the radiation from the gas, but hadn't excluded the Hawkins radiation.  Great calculator for the Hawkins radiation.

[ChrisWilson68]

Absurdly ambitious, yet perfectly compatible with the laws of physics. I love it.

You might inject a few small black holes into the moon.  These would eventually eat most of it, allowing you to build a shell world with a much smaller radius around the black holes.  Radiation from the black holes would provide power for a long time, I expect.

You mean radiation from the hot collapsing gas, or Hawking radiation? Because according to this handy Hawking radiation calculator, the latter will be absurdly small, on the order of a few dozen femtowatts.

This provides a mildly interesting algebra exercise: what is the mass of black hole required to achieve Earth-like radiant balance (250 W/m²) at a radius with a local gravity of 1 g?


Also, this idea really belongs in Advanced Advanced Concepts. :)


Edit: Someone check my math. I get m = 25 billion tonnes and d = 26 meters. So... I invented the Little Prince planet. 8)

I was thinking of the radiation from the gas, but hadn't excluded the Hawkins radiation.  Great calculator for the Hawkins radiation.

It's not Hawkins radiation, it's Hawking radiation.  As in Steven Hawking.

[Barley]

ρ_M = 3.34 g/cm²
ρ_M' = ρ_M*V_M/V_M' = ρ_M* r_M³ / r_M'³ = ρ_M * SQRT(6)³ = 14.69 g/cm³

I fear you have dropped a factor of ρ_M.
Sqrt(6)^3 = 6^1.5 = 14.69

3.34 g/cm³ * sqrt(6)^3 = 3.34 * 14.69 g/cm³ = 49.09 g/cm³

[jee_c2]

...
Lets see where the original poster went wrong.  Ah, the original poster multiplied 3.34 g/cm3 times the square root of 6 cubed to get 14.69 g/cm3.  But actually the square root of 6 cubed is itself 14.69 (actually, 14.6969..., so it should be rounded to 14.70 if we're going with only two decimals of precision).  The OP forgot to multiply by 3.34.  So the real required density would be 49.09 g/cm3.
...

Indeed , I made that failure while entering it in the calculator. Barley also pointed out this. Thank you for the correction!

Too bad, than the Golden Moon is lost..

Unless ... we decrease the required gravitational acceleration on the Inner Moon. Like Mars gravity (about 0.38g), as rakaydos mentioned? (which would make Bobby or Alex feel comfortable on the Inner Moon )

ro_M' = m_M / V_M'
g_M' = f*m_M/r_M'²

g_M'/ g_M = r_M2/r_M'2

V_M' = r_M'³* CV
V_M = r_M³ * CV
r_M/r_M' = SQRT(g_M'/g_M)

ro_M'/ro_M = V_M / V_M' = r_M³ / r_M'³ = SQRT(g_M'/g_M)³ = (g_M'/g_M)^(3/2)

ro_M'= ro_M * (g_M'/g_M)^(3/2) = 3.4 * (3.71/1.62)^(3/2) = 11.78 g/cm³ (or kg/dm³)

A bit more, than the density of the lead, but less, than palladium, less than mercury. So to answer rakaydos, yes, Mars gravity is reachable.

Well, if the whole plan is ambitious, then we should consider using the black holes (or I'm not sure if neutron condensate could exists the stable way outside of the strange environment of the neutron stars.. Because that is also really dense..
I have ideas of solving the density problem with smaller black holes (as lamontagne also proposed), I will come back with it.

[ChrisWilson68]

Well, if the whole plan is ambitious, then we should consider using the black holes (or I'm not sure if neutron condensate could exists the stable way outside of the strange environment of the neutron stars.. Because that is also really dense..
I have ideas of solving the density problem with smaller black holes (as lamontagne also proposed), I will come back with it.

Coming up with a small black hole might be even more ambitious than using nuclear reactors to transmute most of the mass of the moon into gold (which is already, of course, extremely ambitious).  It's not clear that there is a way to make these small black holes other than taking the black hole that results from the end of life of a sufficiently-large star and then waiting until enough of it has evaporated that it's moon-mass or smaller.  We're talking waiting a really, really long time.  A trillion times the current age of the universe doesn't even begin to get there.

I have to wonder -- if we have the massive resources to do any of this, why not just build a new planet from scratch that has the properties we're looking for?  It sounds a lot easier than producing these small (but not too small that they evaporate away quickly) black holes or transmuting a Moon's-mass of other elements to gold in nuclear reactors.

[Twark_Main]

I have to wonder -- if we have the massive resources to do any of this, why not just build a new planet from scratch that has the properties we're looking for?  It sounds a lot easier...

Meh, nowadays all the galaxy's fashionable heptillionaires have their own custom planets. If you really want to flex some coin, you need to up your game.

[edzieba]

It would probably take less energy to turn the Moon into a mini Globus Cassus than to try and transmute the majority of its mass into transuranics.