Why the Moon Has No Atmosphere: The Two-Speed Rule

The Moon does have an atmosphere

Stand on the Sea of Tranquillity and the sky above you is black at noon. The textbook line is that the Moon has no atmosphere, and the textbook line is wrong.

NASA’s Moon Fact Sheet puts the abundance at the lunar surface near 2 × 10⁵ particles per cubic centimetre at night. Air at sea level holds about 2.5 × 10¹⁹ per cubic centimetre, so lunar air is a hundred trillion times thinner — but not zero. All of it weighs about 25,000 kilograms, less than a loaded lorry, at a night-time pressure near 3 × 10⁻¹⁵ bar.

An atom’s mean free path there exceeds the size of the Moon, so a particle leaving the surface will almost never hit another. There is no pressure gradient, no convection, no fluid — only ballistic arcs under lunar gravity. This is a surface-bounded exosphere, the same regime as the outermost fringe of Earth’s own atmosphere.

So the real question is why the Moon cannot hold a substantial atmosphere, and the answer is a contest between two speeds.

Two speeds that decide everything

The first is escape velocity, from one line of energy accounting:

v_esc = √(2GM/R)

with G = 6.674 × 10⁻¹¹ N m² kg⁻². The Moon’s mass of 7.346 × 10²² kg and radius of 1,737 km give 2.38 km/s; Earth’s 5.972 × 10²⁴ kg and 6,371 km give 11.19 km/s. That well is nearly five times deeper in speed, which is why you would weigh a sixth as much on the Moon; in the full derivation the escaping mass cancels out.

The second comes from kinetic theory. Equate the average kinetic energy per molecule to (3/2)kT:

v_rms = √(3kT/m)

with k = 1.381 × 10⁻²³ J K⁻¹ and m the mass of one molecule. Warmer gas moves faster, as √T; lighter molecules move faster too, also as a square root, so hydrogen at mass 2 outruns nitrogen at mass 28 by √14, about 3.7 times. That is the picture behind the ideal gas law, in which temperature just measures molecular motion.

At the Moon’s mean 270 K a nitrogen molecule has v_rms ≈ 490 m/s against an escape speed of 2,376 m/s — a fifth of what it needs. Naively it should stay forever. It does not.

The six-times rule, and why it is not exactly six

Maxwell and Boltzmann showed that molecular speeds follow a distribution with a long high-speed tail. At any instant a small fraction move two, three or four times faster than average, and that fraction is never zero. Those are the ones that leave; collisions repopulate the tail, for billions of years.

Work out how fast the tail drains and a criterion emerges. A body keeps a gas over the age of the solar system only if its escape velocity is roughly six times the molecule’s mean thermal speed. Below about four it is gone on geological timescales; between four and six it leaks measurably.

Why “roughly”, and why do texts quote five to ten? “Mean thermal speed” is ambiguous — most probable, arithmetic mean and root-mean-square differ by up to 22 per cent. The temperature that matters is the exobase, where collisions stop, and on Earth that runs at 600 to 1,500 K rather than 288 K. And the criterion is necessary, not sufficient: Earth’s helium ratio is a comfortable 8.4 at surface temperature, yet Earth loses helium anyway.

Running the numbers world by world

On the Moon at 270 K, water vapour gives a ratio of 3.9, nitrogen 4.85 and oxygen 5.2. Only carbon dioxide reaches the threshold, at 6.1, and only at the mean temperature — at the 390 K the lunar equator hits at noon it falls to about 5.1. There is no common molecule the Moon can keep.

Earth’s column tells its own story. Nitrogen and oxygen sit above twenty, utterly secure. Hydrogen sits at 5.9, right on the line — and Earth duly loses some 95,000 tonnes of it a year, 3 kilograms a second. Helium goes too, roughly 1,600 tonnes a year, because the exobase is far hotter than the surface and charged helium is flung out along open field lines over the poles.

Titan is the clincher. Its escape velocity is 2.64 km/s, barely 11 per cent above the Moon’s, so on gravity alone it should be as bald. But its surface sits at 94 K, and because v_rms scales as √T that cold drops nitrogen to 289 m/s and lifts the ratio to 9.1. The result is a nitrogen atmosphere at about 1.5 bar, half again Earth’s, on a world with a seventh of Earth’s gravity. Temperature is half the equation.

How the gas actually leaves

Lump every loss process together as “it escaped” and you miss the point: four mechanisms run at once.

Jeans escape is the thermal one: molecules in the Maxwellian tail at the exobase head outward faster than escape speed and leave without colliding again, at a rate James Jeans worked out in 1904.

Photodissociation is sneakier. A molecule too heavy to escape can be broken by solar ultraviolet into fragments that are not. H₂O splits into H and OH, and the hydrogen, now at mass 1, leaves easily — which is how a world loses its water without losing a water molecule. Mars cautions against the simple criterion: its thermal ratios say it should keep CO₂, N₂ and H₂O comfortably, yet only 6 millibars remain.

What stripped Mars, and strips the Moon, is the solar wind: protons and electrons leaving the Sun at 400 to 800 km/s. A strong global magnetic field deflects it — Earth’s magnetosphere turns the flow aside thousands of kilometres out — and the air beneath never feels it. The Moon has neither, so the wind hits the regolith directly, knocking atoms loose from mineral grains — sputtering — and ionising exospheric neutrals, which its electric field then picks up and carries downstream. Once an atom is charged, its thermal speed stops mattering.

Impact vaporisation is the fourth, and works both ways: micrometeoroids flash-heat rock, delivering fresh vapour as well as removing it.

What is actually up there

That is why the exosphere persists at all: it is resupplied as fast as it is lost. Today’s population is a steady state, not a remnant of an ancient thick atmosphere.

Measurement began with Apollo 17, whose Lunar Atmospheric Composition Experiment, deployed in December 1972, made the first in-situ detection, finding helium and argon-40. Argon-40 is fine forensic evidence: it is radiogenic, from potassium-40 decay in lunar rock, proving the Moon outgasses from its own interior. NASA’s LADEE orbiter, flying 2013 to 2014, confirmed helium, argon and neon as the dominant species, found each peaking at a different local time, and detected neon credibly for the first time; the Lunar Reconnaissance Orbiter has mapped hydrogen and helium from orbit since 2009.

The strangest constituent is sodium. In November 1998 a Boston University team, aiming a camera away from the Moon to catch the Leonids, found sodium glowing in an apparently empty sky. It was the Moon’s tail: atoms knocked off the surface by micrometeorite impacts, pushed out by sunlight pressure and focused by Earth’s gravity into a stream traceable to at least 800,000 kilometres.

No wind, no sound, no weather

The engineering consequences are real; the aerodynamic ones are nil. The dust and plasma environment can charge spacecraft, abrade seals and coat optics. But there is no atmosphere in the fluid sense, so nothing carries a pressure wave, nothing blows and nothing forms a cloud — the flags were stiffened with wire because there is no breeze. And none of the scattering physics that makes Earth’s sky blue has anything to work with, which is why the lunar sky is black with the Sun overhead.

Air is a relationship, not a property

Whether a world has air is not a fact about the world. It is a relationship between four things: how deep its gravity well runs, how hot its gas is, whether a magnetic field deflects the solar wind, and how long it has stood there leaking.

Cool the Moon to Titan’s 94 K and it would hold nitrogen; warm Titan to lunar temperatures and it would be bare rock and ice. The Moon is not airless because it is small. It is airless because it is small and warm and unshielded and four and a half billion years old, and the Maxwell-Boltzmann tail has had every one of those years to do its work.

Sources and Further Reading

• NASA NSSDCA Moon Fact Sheet — surface abundance of 2 × 10⁵ particles/cm³, total atmospheric mass ~25,000 kg, escape velocity 2.38 km/s, diurnal range 95–390 K, night-time composition.
• NASA NSSDCA Planetary Fact Sheets — masses, radii and mean temperatures for Earth, Mars, Mercury, Titan and Europa as used in the calculator.
• D. C. Catling and K. J. Zahnle, “The Planetary Air Leak”, Scientific American / review on atmospheric escape — Jeans escape, the exobase, and the one-sixth thermal-speed criterion.
• NASA: LADEE Spacecraft Finds Neon in Lunar Atmosphere — helium, argon-40 and neon as dominant species and their diurnal variation.
• R. M. Killen et al., LADEE Neutral Mass Spectrometer results (NASA Technical Reports Server) — in-situ exospheric composition and variability.
• Boston University / NASA: Lunar Sodium Tail Discovered — the November 1998 detection during the Leonid shower.
• A. E. Hofmann et al., Journal of Geophysical Research: Planets, on the source of the lunar sodium tail — micrometeorite impacts as the dominant sodium source.
• NASA Apollo 17 Lunar Atmospheric Composition Experiment (LACE) — the first in-situ measurement of the lunar exosphere, December 1972.
• Royal Society of Chemistry / Science Focus on Earth’s atmospheric mass loss — ~95,000 tonnes of hydrogen and ~1,600 tonnes of helium lost per year.