La Bourse / Volume VII / Nº VII.09 / Quiz, reflection, essays

A watercolour of a young woman with an open book, flowers and leaves around her. — Plate VII.09 · Quiz, reflection, essaysThe Weight of the Bottle.The bottle holds one kilogram. On this bench it is worth a tenth of a penny. Four hundred kilometres above her head, the same kilogram is worth three thousand and fifty-nine dollars — and nothing about the water has changed.

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

Three instruments: a ten-point quiz, eight reflection questions, five essay prompts. The quiz checks comprehension rather than recall. The reflections are private and first-person. The essays are arguable from more than one side.

THE QUIZ — ten points

Four on recall.

1. Write the break-even expression for returned material and define each term.

P = (LEO mass required per kg returned) × (launch cost per kg to LEO). With 1.049 kg and $3,059/kg it gives $3,208 per kilogram. One mark for the expression, one for naming what is excluded — hardware, development, refining and capital. The floor is propellant only, which is why it is a floor.*

2. Give the specific escape energy of Earth, the Moon and Bennu, and the two ratios.

62.6 MJ/kg, 2.83 MJ/kg, 0.02 J/kg. Earth is 22.1 times the Moon and three billion times Bennu. The second ratio is the case for using space material in space, and, read the other way, the case against bringing it home.

3. What are the only two prices ever actually paid for asteroid material delivered to Earth?

OSIRIS-REx: $1.16 billion for 121.6 grams of Bennu — $9.54 million per gram, or $9.54 billion per kilogram. Hayabusa2: about $150 million for 5.4 grams of Ryugu — $27.78 million per gram. Credit any answer noting these are the honest baseline against which projections are measured.

4. State Kessler's carrying-capacity condition and name its three uncertain terms.

Generation equals removal: 0.5 · k · n² · F = n/τ, so n* = 2/(k·F·τ) with k = σ v̄ T / V. The uncertain terms are σ (mean collision cross-section), F (fragments per break-up) and τ (mean residence time).

Four on application.

5. A founder tells you a single metallic asteroid holds more platinum than has ever been mined on Earth, and concludes that platinum scarcity is over. Which half is true, and what is missing?

The first half is true and is a statement about total mass. What is missing is grade and the demand curve. Best-case asteroid grade is about 10 ppm against the Merensky Reef's 6 g/t — a factor of 1.67 — so you must process 100,000 kg for every kilogram returned. And platinum's price is its scarcity: supplying it destroys the revenue that justified the mission. Full marks require both; naming only one is half the answer.

6. Your board is shown a return mission whose break-even assumes $100 per kilogram to orbit. Diagnose it.

It is a bet on a price somebody else controls. The best price ever charged is $3,059, so the plan requires a 30.6-fold cut by a third party. At $100/kg, P is $105/kg and nickel still misses by 7.0 times — so even if the bet wins, base metals do not clear. The stronger answer distinguishes the two failures: the financing risk and the fact that the physics does not reward the bet even when it lands.*

7. A depot operator asks you what to put on the front page of the term sheet. What is the one number, and why that one?

delivered price at the depot ÷ launch price to that orbit < 1. Because the buyer is comparing two prices for the same kilogram in the same place, and geology is not one of the terms. Credit any answer noting the benchmark is falling at 5.05 percent a year and the strike should therefore float.

8. An engineer proposes spending a research budget on raising water closure from 93 to 98 percent. A colleague says the money should go to launch-cost reduction. Who is right, and on what grounds?

The engineer, on the convexity of 1/(1−p): closure rises from 14.3 times to 50.0 times, a factor of 3.5, which beats a threefold cut in launch price and is inside the programme's own control. The stronger answer notes launch price is exogenous and closure is endogenous, which matters more than the ratio.

Two that require the arithmetic to be done.

9. A body has a rendezvous delta-v of 4.20 km/s from low Earth orbit and a return leg of 0.60 km/s. Specific impulse is 300 seconds. Launch to low orbit costs $2,000 per kilogram. Compute the propellant-only break-even price per kilogram of returned material, and say whether silver at $1,286/kg clears it.

v_e = 300 × 9.80665 / 1000 = 2.942 km/s. Outbound exp(4.20/2.942) = 4.169. Return exp(0.60/2.942) = 1.2262. Propellant at the body per kg returned = 0.2262. LEO mass per kg returned = 0.2262 × 4.169 = 0.943 kg. P = 0.943 × $2,000 = $1,886 per kilogram. Silver at $1,286 does not clear — it misses by about 1.47 times. Credit any method landing between $1,800 and $1,950. The point of the question is that a cheaper launch and an easier body together still fail to bring silver home, which is the chapter's negative arriving under the student's own hand.*

10. A 100 km shell has a residence time of 200 years. Using n* = 2/(k F τ) with F = 2,900 and the chapter's geometric-mean cross-section, the chapter computes a capacity of 375 objects. An operator proposes a constellation of 1,200 satellites in that shell. State the ratio, and state the one thing you would need to know before calling it a violation.

1,200 / 375 = 3.2 times the shell's computed capacity. Before calling it a violation you need the cross-section assumption, because the chapter's own capacity estimate for the whole of low orbit spans a bracket 44.4 times wide — 4,412 to 196,111 — and the same width applies here. Full marks require both halves: the ratio, and the refusal to treat one end of a bracket as a number. A student who gives only the ratio has done the arithmetic and missed the lesson.

REFLECTION — eight questions, for one person and a pen

These are not for a room. Write the answers by hand if you can; the slowness is the point.

What have you believed about space and abundance that you had never costed? Write the sentence as you used to say it, then write what you would now put beside it.

Where in your own life are you paying for position rather than for a thing — rent, a commute, a membership, a seat — and would you pay the same for the thing somewhere else?

Think of something you own that you keep in circulation rather than replace. Estimate your own p. What would it take to add five points to it?

When did you last argue for something on the grounds of how much of it there was, when the honest constraint was where it was or whose it was?

What is the largest number you have quoted in the last year that you have never checked? Go and check one of them now, and write down what you find, whichever way it goes.

Where are you holding a bracket in your head as though it were a number — a budget, a date, a capacity, a risk? Write the two ends of it.

Recall a time somebody brought you an exciting proposition and you asked a dull question that improved it. What was the question? Could you ask it more often?

What would you want to still be true about the orbital shells in a hundred years, and what is the smallest thing that would have to be decided this decade for that to hold?

ESSAY PROMPTS — five

Each is arguable from more than one side. Each requires at least one source the chapter cites and at least one it does not.

1. The self-liquidating asset. The chapter argues that the only materials clearing the transport floor are ones whose price is a function of their scarcity, so a successful return mission destroys its own revenue. Argue either that this is a permanent structural feature of precious-metal return, or that it can be engineered around — by staged release, by long-dated offtake, by moving into industrially elastic demand, or by state purchase at a supported price. Use the chapter's elasticity arithmetic, and one source on commodity market power or supply management that the chapter does not cite.

2. Is the launch-cost trend a trend? The chapter computes a compound decline of 5.05 percent a year and a halving time of 13.4 years from two points, 1981 and 2018, in Jones's survey. Argue whether a two-point fit across a technology discontinuity is evidence of a trend at all, and what would have to be shown for it to be. Engage Jones directly, and at least one published launch-cost dataset the chapter does not cite.

3. Space-based solar power, honestly. The chapter's arithmetic makes space solar 7.06 times the cost of bare utility-scale PV per unit of annual energy, counting launch alone, and finds a break-even launch price of $434 to $867 per kilogram depending on whether the ground comparator is firmed. Take a position on whether that is a reason to fund it now or to wait, and be explicit about which comparator you think is honest and why. Use the NASA Office of Technology, Policy, and Strategy report and Brown on transmission efficiency, and one source on grid firming costs that the chapter does not cite.

4. Is orbit a commons at all? Ostrom's design principles assume a bounded resource with identifiable appropriators and a plausible monitoring regime. Argue whether low Earth orbit satisfies those conditions or whether it is better modelled as an open-access resource with sovereign actors who cannot be charged, and say what follows practically in each case. Use Ostrom and Rao et al., and one source on space law or sovereign compliance that the chapter does not cite.

5. The measurement that decides the budget. The chapter publishes carrying capacity as a bracket 44.4 times wide and insists the width is part of the finding. Argue the counter-case: that policymakers cannot act on brackets, that a regulator asked for a number will produce one regardless, and that publishing the uncertainty hands the argument to whoever benefits from delay. Then argue the chapter's side. Conclude with which you find more persuasive. Use Kessler and Cour-Palais, and one source on decision-making under scientific uncertainty that the chapter does not cite.