Moon Libration Laser — a century of near misses

The Moon Libration Laser

Lunar libration over one month (Oct 2007). Source: Wikimedia Commons.

I've always been struck by how precise the Moon's motion is: it's tidally locked, spinning exactly once per orbit, so it forever shows us the same face. What are the odds of a spin and orbit syncing that perfectly? Years ago a time-lapse GIF of a month of moon phases caught my eye, and I couldn't stop watching the wobble. What shape does that wobble trace? In 2026, with calculations established by the folks at JPL, here's an answer — in the form of an experiment.

A laser bolted to a tripod at the center of the Moon's nearside, aimed at Earth's average position: What shape does it make in space? Lunar libration swings the beam across a canvas 110,000 km wide — and Earth is a small target.
This animation was computed from JPL DE440 ephemerides and the DE421 lunar orientation kernel. {sources: see below}

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speed trail 1926

What you are looking at

The view is the target plane: a plane through Earth's center, perpendicular to the laser, seen from the Moon. The blue disk is Earth to scale. The red line is where the beam points, hour by hour, from real ephemeris data (1926–2026).

The Moon keeps the same face toward Earth only on average. Libration in longitude (orbital eccentricity, 27.55-day period) and in latitude (the 6.68° tilt of the lunar equator, 27.21-day period) make Earth's apparent position wander by up to ±8° — about ±8.5 Earth radii at lunar distance. Because the two periods differ slightly, the monthly loop precesses with a ~6-year beat, and the whole figure cycles with the 18.6-year regression of the lunar nodes. Direct hits come in seasons: a few months of roughly fortnightly crossings, then years of nothing.

Two years of monthly loops, side by side

Each tile is one calendar month of the laser's drawing, January 2024 through December 2025. All 24 share the same scale — the full ±11 Earth-radii canvas the beam ever sweeps, with Earth's disk (blue) to scale at the center — so the loops' changing size, tilt and drift are real. Hover a tile for its month.

The hidden clockwork: four kinds of month

There is only one real period here — the Moon's orbit, 27.32 days against the stars. Every other "month" is the same lap measured against a moving finish line, and the whole pattern above is the interference between them.

Month	Length	Finish line	…which moves once per
sidereal	27.322 d	the stars	— (fixed)
draconic	27.212 d	orbit's node	18.61 yr (backwards)
anomalistic	27.555 d	perigee	8.85 yr
synodic	29.531 d	the Sun's direction	1 yr

Month

Length

Finish line

…which moves once per

sidereal

27.322 d

the stars

— (fixed)

draconic

27.212 d

orbit's node

18.61 yr (backwards)

anomalistic

27.555 d

perigee

8.85 yr

synodic

29.531 d

the Sun's direction

1 yr

The beats between these nearly-equal periods generate every famous lunar cycle. Draconic × anomalistic beat in 6.0 years — that's why the rosette precesses and why Earth crossings come in seasons every ~3 years. Synodic × anomalistic beat in 411.8 days — the "full moon cycle" that schedules supermoons. And the showstopper: 223 synodic = 6585.32 d, 242 draconic = 6585.36 d, 239 anomalistic = 6585.54 d. Three different months agree to within hours over 18 years — the Saros, why eclipses repeat in series, known to the Babylonians and geared into the Antikythera mechanism. (The Saros, 18.03 yr, is not the 18.61-yr nodal cycle that frames this page — they're neighbors by coincidence.)

Fold the century yourself

This is how astronomers find pulsars: chop a long signal into pieces of a trial length and stack them. At an arbitrary period the stack is mush — but if the period is true, every cycle lines up and vertical structure snaps into focus. Below, the full 100-year laser track (876,600 hourly samples), folded by a period you control. Drag the slider slowly through 27.21 d with the north–south channel, or try the miss-distance channel at the 6-year beat to see the crossing seasons stack up.

channel 27.000 days

phase within the folding period → · each row is one cycle, 1926 (top) to 2026 (bottom)

Three more ways to see the clockwork

moire comb of draconic and anomalistic ticks — **The moiré that schedules the crossings.** The north–south libration crosses zero every 13.61 days, the east–west every 13.78 days — two tick-combs 1.2% apart. They drift through each other and re-phase every 3.0 years (gold bands), and a century of real crossings lands exactly inside the bands: the mean phase alignment at the 354 crossings is cos ψ = +0.90.

spectrum of the laser track — **The Moon's spectrum, from this site's own data.** An FFT of the century-long track resolves the monthly family: the draconic line at 27.217 d rules the north–south channel, the anomalistic at 27.545 d rules east–west — and the Sun's fingerprints, evection (31.81 d) and variation (14.77 d), show up exactly where theory puts them. The miss-distance spectrum (bottom) shows the 3-year season line the two months beat out together.

animated phase torus — **The phase torus.** Plot the east–west libration phase against the north–south phase and the track becomes a nearly-diagonal line winding around a torus (slope 27.55/27.21 = 1.0126), shifting sideways 1.3% per lap and closing only after ~6 years. The beam can hit Earth only in the small yellow patches where both librations pass through zero together — watch the line thread them during the 1955 crossing season, the century's best.