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Commerce · VII.09 · MMXXVI · daylight

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WORKBOOK — THE STUDENT

Chapter VII.09 · Space, Materials, and Real Abundance

For the person studying this alone, or in a seminar, with no launch vehicle and no balance sheet. You are not too early. What you build here is a habit of costing the most exciting claim in the room, and that habit is worth more over a career than any single subject you will study.

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WHY THIS WORKBOOK IS DIFFERENT

Space is the subject where enthusiasm is cheapest and arithmetic is rarest. That combination is exactly why it is the best possible training ground.

Every chapter in this edition asks you to check a number. This one asks you to check a number you want to be true, which is a different and much harder skill. The chapter's finding is not that space is a disappointment. It is that the real asymmetry — three billion to one between escaping Earth and escaping Bennu — points in a direction almost nobody is pointing, and that you can only see the direction once you have done the division.

So the transferable skill here is not orbital mechanics. It is this: when somebody hands you a magnificent claim, find the one ratio that decides it, and compute that ratio before you form an opinion. Everything in this workbook is practice at that.

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PART ONE — DISCOVERY

Weeks 1–4: reproduce, then find the ratio that decides

Exercise 1.1 — Reproduce the chapter's figures (3 hours)

Do not take the numbers on trust. Open lib/verify/VII_09.py, read the docstring first, and then compute these independently — by hand, in a spreadsheet, in whatever language you use.

1. The three specific escape energies. ½v², with escape velocities of 11.186 km/s, 2.38 km/s and 0.20 m/s. Confirm 62.6 MJ/kg, 2.83 MJ/kg and 0.02 J/kg, and the ratios 22.1 and three billion.
2. The two mass ratios, exp(Δv/v_e) with v_e = 2.942 km/s. Confirm 5.661 and 1.1852.
3. The chain that gives 1.049 kg in low orbit per kilogram returned, and then $3,208 per kilogram.
4. The launch-cost trend: from $18,500 to $2,720 over thirty-seven years. Confirm 6.8 times, −5.05 percent a year, and a halving time of 13.4 years.

Then the thing that matters most: find one figure in this chapter you can check against an outside source, and check it. Metal prices move; launch prices are published; the catalogued object count is updated annually. If you find a discrepancy, write it down and bring it to your seminar. This edition wants to be checked, and a student who arrives with a corrected figure has done the most valuable possible thing with the text.

Exercise 1.2 — The claim audit (2 hours)

Collect five public claims about space resources — from a company's investor page, a newspaper, a documentary, a conference talk, a social post. For each, write three lines:

You will find, almost certainly, that four of the five are statements about total mass and none is a statement about grade, delta-v or the demand curve. That is not dishonesty. It is what happens when a subject is loved more than it is costed.

Exercise 1.3 — The appreciative interview (45 minutes, with another person)

Find somebody who works on something physical — a mechanic, a brewer, a nurse, a farmer, a logistics planner — and ask exactly this:

"Tell me about a time when the cost of moving something turned out to matter more than the thing itself. What did you do about it? What did you change?"

Take notes on the remedy, not the anecdote. You are collecting the human version of a delta-v map: people who already know that position is the price.

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PART TWO — THE ARITHMETIC

Weeks 5–8: learn to compute before you argue

Exercise 2.1 — Your own break-even (1 hour)

Pick any body from the JPL NHATS list, or invent one with a rendezvous delta-v between 3.80 and 6.00 km/s. Choose a launch price. Then compute:

  v_e     = Isp × 9.80665 / 1000
  m_out   = exp(Δv_out / v_e)
  m_ret   = exp(Δv_ret / v_e)
  LEO/kg  = (m_ret − 1) × m_out
  P*      = LEO/kg × launch price per kg

Write P down. Then take a price list — any commodity exchange publishes one — and mark which materials clear it and which do not. Do this once and you will never again be able to hear the phrase asteroid mining* without a number appearing in your head. That is the whole exercise.

Exercise 2.2 — The elasticity trap (90 minutes)

Marginal revenue is P × (1 + 1/ε). Take four goods you can find elasticity estimates for — a staple food, a medicine, a fuel, a luxury — and for each, compute the multiplier and say in one sentence what happens to total revenue when supply rises.

Then answer the chapter's question in your own words: why is it that the only materials worth returning from space are the ones a successful mission would devalue? Write it in five sentences. If you can write it in five sentences you have understood the chapter's central cut.

Exercise 2.3 — The bracket, not the number (90 minutes)

Recompute the carrying capacity n* = 2/(k F τ) at three cross-sections of your own choosing, and at residence times of one, twenty-five, two hundred and a thousand years. Produce a table.

Then write, in one paragraph, the answer to this: a regulator asks you for a single number. What do you give them, and what do you insist appears beside it? There is no correct answer. There is a defensible one and an indefensible one, and the difference is whether the assumptions travel with the figure.

Exercise 2.4 — The two spellings (45 minutes)

Take any three figures from the chapter and write each one in the two forms a reader might see: the form the prose uses and the form a computation prints. Then check whether a person holding one could find the other. This is a small exercise and it is the origin of more errors in published work than any other single cause.

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PART THREE — DESIGN

Weeks 9–12: build something small and real

Exercise 3.1 — The one-page term sheet (3 hours)

Write a one-page delivered-in-orbit offtake for a commodity of your choosing, to an orbit of your choosing. It must contain: the commodity, the altitude, the benchmark price and its source, the strike as a discount to benchmark, the minimum volume, the disposal bond, and the single inequality on the front page.

Length is the discipline. One page. If it does not fit, you have not decided something.

Exercise 3.2 — The shell brief (2 hours)

Choose an altitude band. Find, from the ESA Space Environment Report or an equivalent public source, how many catalogued objects are in it. Compute its capacity bracket. Write a two-page brief for a non-technical reader that contains the bracket, the three assumptions, and one sentence saying what you would need to know to narrow it.

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Exercise 3.3 — The closure audit of your own life (2 hours)

The multiplier 1/(1 − p) is not an aerospace idea. It is arithmetic, and it applies to anything that can come round again.

Pick four consumables you personally run through: water, clothing, food packaging, books, tools, cabling, notes. For each, estimate p honestly — the fraction that returns to service rather than leaving — and compute the multiplier. Then pick the one nearest 0.9 and work out what five more points would cost you, in money and in effort, and what it would return.

You will find the same convexity the station found. The item you are already good at is the one where improvement pays, and the item you are worst at is the one where improvement barely registers. That is counter-intuitive and it is the whole reason the exercise is here: effort goes where the curve is steep, not where the shame is loudest.

Exercise 3.4 — Rewrite a claim without shrinking it (1 hour)

Take the single most extravagant space claim you found in Exercise 1.2 and rewrite it so that every quantity in it is true, every ratio is computed, and the sentence is more interesting than the original, not less.

This is harder than it sounds and it is the core editorial skill of this whole edition. The chapter you have just read does exactly this to the sentence a single asteroid holds more platinum than has ever been mined. It does not deny it. It agrees with it, adds grade, adds the demand curve, and arrives somewhere stranger and better. Do that once, deliberately, and you will have the move.

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PART FOUR — DESTINY AND DELIGHT

Weeks 13–14: what you keep

Exercise 4.1 — The hundred-year question (90 minutes)

Write one page answering this: what would you want to still be true about low Earth orbit in a hundred years, and what is the smallest decision this decade that would make it so?

The constraint: your page may not contain the words should, must or urgent. It may contain a fee, a bond, a published bracket, a monitoring arrangement, or a released deposit. A commons is not held by conviction. It is held by a rule with a number in it, and the exercise is to find the smallest such rule you actually believe in.

Exercise 4.2 — The dull question (30 minutes, repeated)

For two weeks, whenever somebody brings you an exciting technical proposition — in a seminar, at work, online — ask one dull question: what does that cost per kilogram, and to whom, and where? Keep a tally of what happens.

Record, for each: did the conversation get smaller, or better? You will find, more often than you expect, that it gets better, and that the person is grateful. That is the pleasure the chapter's Delight movement is describing, and you cannot be told it. You have to run it.

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THE TERM PROJECT

The costed proposal

The brief. Take one space-resource proposition — any real company, agency programme or published concept — and produce the document its investors should have been handed.

What it contains, in this order.

1. What is working. Two pages, appreciative and sourced, on what this proposition genuinely has: the demonstrated hardware, the real physics, the named customer if there is one. Begin here. A costing that opens on the problem has already stopped being read.
2. The delta-v map. One page. Where the material is, in the only geography that costs money.
3. The break-even. One page, computed, with the inputs printed. Say which materials clear and which do not.
4. The demand curve. One page. What happens to the price if the proposition succeeds at the volume it proposes?
5. The honest negative. One page. The threshold below which this fails, and how far from it we are.
6. Three ways it is better than proposed. One page. Not three ways round the obstacle — three things the proposition should do whether or not the obstacle exists, that it is not currently doing. This is the hardest page and it is the one that will get you hired.
7. The instrument. One page. The contract that would make it fundable, with the number that decides it on the front.

Length. Eight pages. Nothing in it may be uncomputed, and every figure carries its source and its date.

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SELF-ASSESSMENT

Mark yourself honestly against these

The last two are the ones that transfer. Everything else in this chapter is a worked example of them.

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A READING ORDER, IF YOU WANT TO GO FURTHER

Read in this sequence, because each one makes the next one legible.

1. Kessler and Cour-Palais (1978). Six pages of arithmetic that named a failure mode two decades before anyone could observe it. Read it for the method, not the conclusion.
2. Ostrom (1990). The eight design principles, and in particular the ones about monitoring and graduated sanctions. Orbit fails several of them; work out which.
3. Rao, Burgess and Kaffine (2020). Four pages that turn the whole debate from an ethical one into a pricing one.
4. Jones (2018). Short, and the source of the trend everybody quotes without reading.
5. Lewis (1996). The most enthusiastic case ever made for space resources, written by a genuine planetary scientist. Read it last, and read it generously — then check three of its numbers. That exercise, done kindly, is the whole education.

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WHAT TO CARRY OUT OF THIS CHAPTER

Three sentences, and they are not about space.

Position is the price. The same kilogram of water is worth a tenth of a penny at a tap and $3,059 in low orbit. Nothing about the water changed. Before you ask how much of something there is, ask where it is — and you will be right more often, faster, from data that already exists.

Circulation beats extraction, and the last few points are worth the most. The multiplier 1/(1 − p) goes from 14.3 to 50.0 between 93 and 98 percent closure. Wherever you find yourself later — a factory, a hospital, a household — that convexity will be waiting, and almost nobody will have noticed it.

The claim you most want to be true is the one to compute first. Not because enthusiasm is a vice. Because the arithmetic, done properly, usually finds something better than the claim — and in this chapter it found that the real prize was never the metal.