In space, what resources, are worth acquiring from one part of space, and sending to another?
3 Answers
Here's a formula for computing the cost of interstellar shipping :
$E = {1 \over 2}mv^2 \rightarrow $ (v = c %c) $\rightarrow {{(cruise speed)^2 \times c^2} \over {efficiency}}$
From the kinetic energy equation. Where cruising speed is (%c). Efficiency is between 0% and 100%. And $1 \over 2$ falls away because the load accelerates and decelerates (2 operations). This gives you a fuel cost to move the load (in Joules).
To translate from Joules to 2020 equivalent currency, refer to your local utility bill for the price of power per kilowatt hour (in my area it's between USD $0.04 per). To convert from Joules to kWh, divide 3.6 million.
$P = {{E} \over {3,600,000}} \times 0.04$
But that's not all. There's the opportunity cost of tying up these resources for the multi-decade trip.
$t = {{distance} \over {cruise speed}}$
The net present value or opportunity cost then is :
$PresentValue = {FutureValue \over {(1 + rate)^{time}}} \rightarrow FutureValue = PresentValue {(1 + rate)^{time}}$
Rate is the appreciation of some other opportunity (like stocks or bonds). 5% is an often used amount.
Try it out :
Price per kg to ship 10 light years at 30% c, using 100% efficient antimatter fuel is : (2 * 0.3^2) / 1.0 ... 2 * 0.09 ... 0.18 c^2 or 1,620 terajoules.
In USD, it'd be 4.5 billion kilowatt hours. At 4 cents a piece, that will cost $180 million per kilogram shipped.
The load will be traveling for roughly 30 years (10 light years / 30% the speed of light cruise speed). The net present value of the load is my costs, which will be locked-in for 30 years. To break-even, I hope in 30 years to sell for a future value of $(1.05)^{30} = 4.32$ times the principal.
In this case 4.32 times $180 million per kilogram.
Which is USD $777.6 million per kilogram shipped.
To be "worth it", you'd hope to get at least a reasonable profit, maybe 3% on your sunk costs. So it would need to be something you reasonably believe can be sold at it's destination for about USD $800 million per kilogram.
The price of energy is key
This is very susceptible to the price of energy. Let's say fusion technology cuts energy prices by three orders of magnitude, and antimatter technology cuts energy prices by another three orders of magnitude.
Same calculation is now $8 thousand per kilogram.
At this price many materials (like gold @ 64,000 USD per kg, or Ruthenium @ 160,000 USD per kilogram) are within reach of profitability.
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Your answer is great, I will take the formulas and make calculations that are more relevant to my setting and see what I come up with :) – speeder Aug 12 '20 at 01:59
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Added citations for kinetic energy and net present value equations. – James McLellan Aug 12 '20 at 10:21
Information. It can be sent via radio or laser beams. Most material resources can be obtained at any feasible destination. The energy cost of shipping across astronomical distances will be itself astronomical. The energy cost of sending information will be trivial by comparison.
REFERENCE:
Greg Costikyan, The 11 Billion Dollar Bottle of Wine: The Possibilities of Interstellar Trade (Originally published in ARES, January 1982).
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Any physical matter is worth transporting in space depending on two things that come to mind:
- What can be done with the matter at the destination that can’t be done at the source?
- Is the cost of transportation less than the value of the resource at the destination?
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To prevent your question from being flagged and possibly removed, avoid asking subjective questions where every answer is equally valid.Trade is very rarely dependent on the transport mechanism. It's always a function of supply-vs-demand. If a planet needs [any item] and it's cost-effective to ship it, you send [any item]. Asking for an infinite list of things is off-topic. – JBH Aug 12 '20 at 03:13