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Space is pretty expensive to get to, and there's a shocking lack of things in it. A planet made of gold sounds like a treasure worth the trip! How far would such a thing have to be away from Earth in order for it not to be economical to retrieve it?

Assume:

  • current technology. Developing is fine as long as it's not blatantly unphysical (no EmDrive)
  • a single launch
  • a solid gold planet of equivalent mass to the Moon.
  • a fixed price for gold

A tolerably exact answer to this question may be difficult; alternately a reasonable upper bound may be presented. I believe the most appropriate measure of "distance" would be in terms of delta-v.

Kaia Leahy
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    I'm not sure what you mean by "a single launch". Do you mean that every launch must be able to pay its way immediately upon completion (which would have made e.g. Apollo impossible, but would work fine for most modern probes), that the whole gold planet must be retrieved in one go, or what? – Nathan Tuggy Jun 23 '17 at 00:22
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    Have you tried to answer this question for yourself? The answer is not likely to be of broad interest. – Russell Borogove Jun 23 '17 at 00:26
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    answering this question requires rough but a couple of calculations, which requires time. Would you share what you actually want to find out? I mean, let's assume we have found out it is.. X a.e. Okay and now? :-) – J. Doe Jun 23 '17 at 00:29
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    @NathanTuggy Pay its way immediately upon completion. A US court settled the value of Apollo moon rocks at $50,800 per gram, which exceeds the current spot price of gold by a large margin; ergo getting gold from the Moon with a Saturn V would be a waste of time. At that price, even a solid gold planet in LEO sounds like a dubious proposition. – Kaia Leahy Jun 23 '17 at 03:27
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    +1 for "no EmDrive". Seriously, I think it's an interesting question and an answer would be meaningful. There is a lot of both noise & news about mining asteroids. If it turns out that a simpler mission — bringing pure gold back from the moon — is not economical, it would immediately put the whole concept of deep-space mining and refining of asteroids for profit in a new and stark light. I'm really interested seeing a ballpark answer to this question! – uhoh Jun 23 '17 at 03:36
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    @RussellBorogove Whether or not space mining is a viable proposition under any terms is an open question (and will be until it's actually accomplished). The question of what resources would be valuable to mine in space was considered an appropriate question for this forum, I have no idea why a question about a specific resource would be less so. I think that it is a useful concept. Retrieving anything from e.g. Pluto would be difficult now, retrieving stuff from the Moon would be difficult fifty years ago, and interstellar commerce may never be possible. – Kaia Leahy Jun 23 '17 at 03:47
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    If a $US 1E+08, 1E+06 kg rocket could get 1E+04 kg to the moon and bring back 1E+02 kg of gold worth US 4E+06, hmm.... Better start looking for asteroids covered knee-deep in square meter sheets of defect-free graphene or pure Vantablack. – uhoh Jun 23 '17 at 03:48
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    Farther away mostly means longer time per delivery. It doesn't change the price/economy of things very much. The size of rocket and payload is dictated mostly by getting to orbit and landings on the Earth and that other planet. Moon is not significantly closer than Mars in terms of minimal delta-v, just availability of optimal transfer windows and transfer time. – jkavalik Jun 23 '17 at 12:24
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    Don't forget, that the value of something is based on the supply and usefulness. If we are able to bring tons of gold back from the Moon, the supply will go way up, so the value will go way down. Even if you can go there, get the gold, and bring it back for 1% of what it would cost today, the supply would increase so much that the price of gold would crash. Simply, it would never be economically viable to get that much gold. – Cody Jun 23 '17 at 16:00
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    @Cody That's sort of the underlying theme of this, that there's very few extraterrestrial resources worth the trouble to retrieve, even assuming more-than-optimal conditions. – Kaia Leahy Jun 23 '17 at 16:31
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    @uhoh Water is one of the first commodities asteroid miners hope to extract. How many times Have I gone over notions like mass fractions, delta V budgets, and Tsiolkovsky's rocket equation? Your comment is frustrating to say the least. – HopDavid Jun 23 '17 at 17:04
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    @HopDavid you're reading some context into my comment that isn't there. I'm talking about mining and refining valuable metals (thus the words "mining and refining" in the comment). One doesn't refine water, right? The question is about bringing metal back to the Earth, right? My goodness, if you have a strong point, leave your own comment or post an answer, don't go after someone else's comment out of context as a way to work a "how many times have had to tell you....' zinger in somewhere. Let's keep the focus on the question and its topic. If you'd like to talk about water, ask/answer! – uhoh Jun 23 '17 at 18:33
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    @HopDavid if you think you've made a good post about the need for finding sources of water beyond Earth, and/or how the term "mining" might be misunderstood as it applies to space, please leave a helpful link to it here. Note, the OP does state "single launch" in the question, and since the body described is made of gold, there is no water. I think my order of magnitude numbers turn out to be not so far off (on a log scale) considering the question as asked. If I'm missing something and you in fact see a way to get more much more gold back considering the constraints of the question, tell me – uhoh Jun 23 '17 at 19:43
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    Gold has very little intrinsic value -- in space or on earth. – Erik Jun 24 '17 at 02:46
  • For a celestial object to have the same mass as the Moon, but be composed of solid gold, its diameter would be 968 km, which is slightly larger than Ceres. Its gravity would be 5.228 m/s2 & the escape velocity from it would be 3.182 km/s. – Fred Jul 07 '23 at 04:56

3 Answers3

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Given your constraints I can't see it being worthwhile, period, even if it were our own moon. Lets throw some numbers at it:

Current cost to deliver a kilogram of payload to the moon: \$1.2 million. Price of a kilogram of gold: \$40k. In other words, for every kilogram you land on the target you need to bring back 30kg of gold just to pay your launch costs, not even considering the cost of what you landed.

Oops, look at the Apollo landers. Their ascent stages were mostly fuel. In other words, you're paying well over $1.2 million to lift a kilogram of anything off the moon. In reality it's a lot more brutal than that as the density means you're closer in. The escape velocity goes up by 1/3, increasing both the cost of landing and takeoff.

In other words, bringing gold home the moon by rocket isn't remotely worthwhile even if it's free for the taking.

Now, I hear squawking about proposed lunar and asteroid mining—surely the numbers can't be right?? The key is by rocket—if you want to make money mining extraterrestrial bodies you'll have to come up with some better means of bringing the stuff home.

Now, such methods have been known for some time. Take an electric motor, unwrap it and make it very long. Instead of turning something round and round it sends it off at a high speed. While I am not aware of anyone building one powerful enough to toss stuff off your gold moon it's simply a case of building bigger. (Note: We do not use such a system for launch from Earth due to the atmosphere. Scaling the motor is fine, building a system that can survive the shockwaves and heating is quite problematic.) Your crew lands, and starts tossing packages of gold somewhere. Since the launch only costs electricity the cost is quite cheap. (After the package has been boosted to the required speed it's released from the booster. The rest of the track has reversed polarity and stops the booster. Take it back to the start and throw another package.)

However, that's a lot more equipment than you're going to deliver with a single launch—which is why I said your constraints mean it's not worth doing.

Nathan Tuggy
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Loren Pechtel
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  • So generally it seems that we can say that rocket chemistry being what it is, the breakeven point is likely to be in high earth orbit? And didn't Heinlein do electric lunar catapults in The Moon Is A Harsh Mistress? But surely there are limits even to catapults? Would mining Pluto be possible? – Kaia Leahy Jun 23 '17 at 05:15
  • For mining Moon-sized bodies, yes. Bodies with negligible gravity are easier to exploit. – Russell Borogove Jun 23 '17 at 07:11
  • Pluto is going to be far less cost effective, sethrin. Look at the cost of getting all the way out there with even something like Voyager, which didn't even need to slow down and stop there. – Rory Alsop Jun 23 '17 at 08:15
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    To illustrate it, SLS and Orion without the solid boosters literally cost their mass in gold to develop (1,000 tons). Orion could bring home a couple of tons of payload. – LocalFluff Jun 23 '17 at 12:49
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    +1 for pointing out that the setup in the question is not necessarily a good guideline for the viability of space mining. – called2voyage Jun 23 '17 at 13:28
  • @sethrin So long as you don't have to deal with a pesky atmosphere planetary-based catapults can be built powerful enough to reach any other planet, your only limit is accuracy and how you catch the stuff. Manned catapults are more problematic but a track wrapped around the moon can throw a manned mission anywhere from sun-grazer to solar escape. – Loren Pechtel Jun 23 '17 at 22:39
  • @sethrin Note that my rejection of catapult approaches was based on your single launch requirement. An interplanetary catapult is quite a bit of equipment and some skilled people to install it. – Loren Pechtel Jun 23 '17 at 22:41
  • @sethrin In the long term, mining Kuiper belt and even Oort cloud bodies for ice and catapulting the ice to the inner solar system is economical. It takes over a decade for the ice to arrive at the inner solar system, but once it does, it arrives at a steady rate. This is a plot point in "Blue Remembered Earth". – user19742 Jun 24 '17 at 01:54
  • @KaiaLeahy - I suspect there be any break even point; if a big lump of gold were in high orbit it would still be more expensive to bring gold back than sourced on Earth – Ken Fabian Jul 17 '22 at 00:49
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I just realized that your question does not specify to where the gold must be retrieved (sure, "retrieve" could mean to physically bring back to Earth, but it could also simply mean "carry away and into [the people of] Earth's possession"). One of the biggest advantages of space mining is for use of the resources in situ or elsewhere in space. Therefore, I am going to argue that from that perspective the only way that the distance of the gold matters is in whether or not we need to be that far out in the first place. If we have a reason to be out that far, then it is economical to mine it.

called2voyage
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  • "If we have a reason to be out that far, then it is economical to mine it."

    That seems circular. Also, arguing from a different definition is equivocation.

     – Kaia Leahy Jun 23 '17 at 20:40
  • Think of it this way. If we were already going to the Moon and we had reason to use gold on the Moon then what does it hurt to mine it while we're there. – called2voyage Jun 23 '17 at 20:44
  • In fact, every kilo we mine is a kilo we don't have to bring with us. – called2voyage Jun 23 '17 at 20:48
  • You never stated a definition. – called2voyage Jun 23 '17 at 20:49
  • Avoid semantic arguments. In-situ mining has been studied by NASA, and I'm sure that someone will pull it off eventually. The focus of this question should be on the round-trip cost per kilogram to and from a given orbital height. – Kaia Leahy Jun 24 '17 at 01:51
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    This is spot on. The true value of mining in space is to not have to bring it with you. – Erik Jun 24 '17 at 02:45
  • @Erik While that is true, this question does not seek to explore that, because that topic has already been better covered in this question. – Kaia Leahy Jun 24 '17 at 12:43
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Question irrelevant (as currently stated). “Far” is somewhat meaningless in celestial mechanics, as spacecraft coast. Not “they can coast,” they coast by definition. The metric is delta V- the acceleration needed to start and stop. A started vehicle then coasts however long as required.

In the case of the Moon (overwhelmingly silicates), the gravity is large (that’s why it’s a round body- “hydrostatic equilibrium”) and the fuel required is also large. Should the Moon turn to gold, the gravity would also turn enormous. The cost to lift gold out of a gravity well- a now brutal gravity well- would turn to something brutally costly. I don’t have any numbers, but I don’t need them; a silicate Moon is already uneconomical.

caInstrument
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    This does not seem to answer the question, that was expicit that the moon was a smaller body with the same mass of gold, so the conclusion only referring to silicates and a moon sized body is wrong twice. Also in general any answer where you need to type 'I don't have any numbers' is on shaky ground, especially in this case where reading an existing answer helpfully tells us 1.2 million per kg. – GremlinWranger Jul 17 '22 at 01:42