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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.

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    $\begingroup$ 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? $\endgroup$
    – Nathan Tuggy
    Jun 23, 2017 at 0:22
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    $\begingroup$ Have you tried to answer this question for yourself? The answer is not likely to be of broad interest. $\endgroup$
    – Russell Borogove
    Jun 23, 2017 at 0:26
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    $\begingroup$ 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? :-) $\endgroup$
    – J. Doe
    Jun 23, 2017 at 0:29
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    $\begingroup$ @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. $\endgroup$
    – Kaia Leahy
    Jun 23, 2017 at 3:47
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    $\begingroup$ Gold has very little intrinsic value -- in space or on earth. $\endgroup$
    – Erik
    Jun 24, 2017 at 2:46

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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.

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  • $\begingroup$ 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? $\endgroup$
    – Kaia Leahy
    Jun 23, 2017 at 5:15
  • $\begingroup$ For mining Moon-sized bodies, yes. Bodies with negligible gravity are easier to exploit. $\endgroup$
    – Russell Borogove
    Jun 23, 2017 at 7:11
  • $\begingroup$ 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. $\endgroup$
    – Rory Alsop ♦
    Jun 23, 2017 at 8:15
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    $\begingroup$ 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. $\endgroup$
    – LocalFluff
    Jun 23, 2017 at 12:49
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    $\begingroup$ +1 for pointing out that the setup in the question is not necessarily a good guideline for the viability of space mining. $\endgroup$
    – called2voyage ♦
    Jun 23, 2017 at 13:28
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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.

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  • $\begingroup$ > "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. $\endgroup$
    – Kaia Leahy
    Jun 23, 2017 at 20:40
  • $\begingroup$ 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. $\endgroup$
    – called2voyage ♦
    Jun 23, 2017 at 20:44
  • $\begingroup$ In fact, every kilo we mine is a kilo we don't have to bring with us. $\endgroup$
    – called2voyage ♦
    Jun 23, 2017 at 20:48
  • $\begingroup$ You never stated a definition. $\endgroup$
    – called2voyage ♦
    Jun 23, 2017 at 20:49
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    $\begingroup$ This is spot on. The true value of mining in space is to not have to bring it with you. $\endgroup$
    – Erik
    Jun 24, 2017 at 2:45
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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.

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    $\begingroup$ 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. $\endgroup$
    – GremlinWranger
    Jul 17, 2022 at 1:42

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