We Time a Laser Echo From the Moon to a Millimeter. Nobody Knows Why the Rising Moon Looks Bigger

Notes and sources · checked 2 November 2026 ·

Two questions about one Moon. How precisely can we time a laser pulse there and back? To about a millimetre, from one telescope to one mirror. Why does the rising Moon look so much bigger? It is in fact slightly smaller, and no explanation is generally accepted.

In the video we put the echo at 95 %, the Moon's orbit at 70 %, its drift away from us at 92 % and the illusion at 35 %. Treat those numbers as our reading of the evidence, not as measured probabilities.

A laser, a mirror, two and a half seconds

About three times a week the 3.5 m telescope at Apache Point, in Sunspot, New Mexico, fires a laser at the Moon (NMSU Newsroom, June 2025). The round trip takes about 2.5 s, between 2.3 and 2.7 s (Williams & Boggs, JPL Lunar Laser Range Model 2020). The team that built it titled its 2023 summary "Fifteen Years of Millimeter Accuracy Lunar Laser Ranging with APOLLO"; the abstract concludes that "overall data accuracy and precision are both ∼ 1 mm" (Colmenares et al., PASP 135, 104503, preprint; companion paper Battat et al., PASP 135, 104504, preprint). Other stations usually reach about a centimetre (NMSU).

Echoes, then mirrors

Louis Smullin and Giorgio Fiocco at MIT caught laser light reflected from the bare Moon; their letter appeared in Nature on 30 June 1962, seven years before Apollo 11 ("Optical Echoes from the Moon"). A team in Crimea reported echoes too; a reflector on the Moon would make tracking far more accurate (Bender et al., Science 182, 1973, scan).

A corner cube is a prism shaped like the inside corner of a box: light goes back the way it came (NASA; Murphy, "Lunar laser ranging: the millimeter challenge", Rep. Prog. Phys. 76, 2013, preprint). In July 1969 Apollo 11 left a 46 cm square panel of 100 glass cubes, each 3.8 cm across; Apollo 14 left 100 more, Apollo 15 300, and the Soviet rovers Lunokhod 1 and 2 carried French-built reflectors. On 1 August 1969 Lick Observatory got echoes good to about 7 m. McDonald Observatory then reached about 20 cm for a decade, at best one photon back per five pulses; from 1984 a French station led the way toward centimetres (Bender et al.; Murphy; Battat et al.). Lunokhod 1's reflector went unranged for nearly forty years, until a NASA orbiter photographed the rover in March 2010 and Apache Point got an echo on 22 April (Murphy).

One photon at a time

Even a modern beam is about 1.9 km wide at the Moon; one photon in 25 million hits the Apollo 11 panel, and the return spreads over about 15 km of Earth. Apache Point fires 20 pulses a second of green light (532 nm, 115 mJ) through its 3.5 m telescope. Each pulse holds roughly 3 × 10¹⁷ photons; usually one comes back, or none (Murphy; Colmenares et al.). The Moon wobbles, so the panels are rarely square to us and their near and far corners return light at slightly different times: a spread of about 3 cm, which takes around 900 photons to average down to a millimetre. Over 2006–2020 the median uncertainty per night was 1.7 mm (Colmenares et al.).

A hidden calibration error

In 2016 a second laser, laying down a ruler of light pulses timed by a cesium atomic clock, caught a calibration error of about 0.4 % in one piece of timing hardware. Present for the instrument's whole history, it had shortened the ranges by about 4 mm, more than the 1–2 mm error bars. Corrected, accuracy and precision are about 1 mm each, and the median nightly uncertainty has been 1.0 mm since September 2016 (Colmenares et al.; Battat et al.).

A new reflector, and tired old ones

On 2 March 2025 Firefly Aerospace's Blue Ghost lander set down a single 10 cm cube from the University of Maryland. Grasse in France caught its first echoes the next day, Wettzell on 4 March, Apache Point on 20 March; the builders report about 0.8 mm (Grasse) and 0.79 and 1.14 mm (Wettzell), first results not yet peer-reviewed (University of Maryland; NMSU). The old panels return about ten times less light than they should, ten times less again near full Moon, probably because of a thin film of dust warmed by the Sun (Murphy; Battat et al.).

From the echo to the orbit

While a pulse is in flight the Moon moves about 2.5 km and the Earth turns about 1 km. The model must include tides on both worlds (lunar tides alone lift and drop the telescope by +27 to −14 cm), the Moon's wobble, about 2 m of delay in the air, and relativity. Fitted to 50 years of echoes, JPL's model misses the 2015–2020 data by 1.0 to 1.1 cm rms (JPL 2020; about 1.3 cm for the DE440 ephemeris, Park et al., AJ 161, 2021). Battat et al. are explicit:

To date, no ephemeris model is accurate at the millimeter level

That model is why anyone bothers: lunar ranging has given some of the best tests of Einstein's gravity (Murphy). From the same fits, James Williams and Dale Boggs found that the Moon's orbit grows by 38.30 ± 0.08 mm a year, mostly because of friction from the Earth's tides, which also slow the Earth's spin (Celest. Mech. Dyn. Astron. 126, 2016). Over an eighty-year life that is about three metres.

Bigger, smaller, and the illusion

Some size changes are real. The full Moon of 24 December 2026 (01:28 UTC) is the year's closest, 356,738 km centre to centre; the farthest, on 31 May (08:45 UTC), was 406,135 km. So December's is about 14 % wider (NASA/JPL Horizons, DE441, API; times from the U.S. Naval Observatory; timeanddate gives 12.5–14.1 %).

The rising Moon, though, is about one Earth radius farther from you than the overhead Moon: at the average distance, about 6,300 km farther and 1.6 % smaller (Earth and Moon fact sheets). Photos at the same zoom show the same width low or high; if anything the air squashes the low Moon slightly (NASA Science, 2023; NASA, 2025). Yet the horizon moon "may appear to be nearly twice the diameter" (Kaufman & Kaufman, PNAS 97, 2000).

On 15 June 1962, two weeks before the echo letter, Science printed the first of two papers by Lloyd Kaufman and Irvin Rock, "The Moon Illusion" (vol. 136, 953 and 1023): with artificial moons, they found the landscape plays a key part. The older theory: the brain places the horizon sky farther away, so the same image must mean a bigger Moon, and Kaufman's 2000 experiments did find the horizon moon farther away in depth perception. But asked which looks closer, people usually pick the horizon Moon. Defenders reply that it looks bigger first, then seems nearer. Rivals blame the eyes' focus, or trees and buildings acting like the Ponzo illusion. A 2020 paper said a model of consciousness explains it all (Rudrauf et al., J. Theor. Biol. 507); a 2021 study still found no theory generally accepted (Kovács et al., Proc. R. Soc. A 477). NASA in 2025: "there's no consensus yet."

A few details

"A millimetre" is the range from one station to one reflector; the model's 1 cm is a misfit of those ranges, not a 3-D accuracy for the Moon's centre. The 0.4 % was a timing calibration error, not a distance error.
Our 1.6 %: at a mean distance of 384,400 km, with an Earth radius of 6,371 km, the overhead Moon is 378,029 km away and the rising one 384,347 km, so 1.64 % smaller (1.77 % at the December distance). Some sources say about 1.7 %; turned around, the overhead Moon is 1.67 % wider. NASA's figure, about 1.5 % farther, fits a Moon high but not overhead; on 24 December 2026 the difference is 1.55 % at 55° N.
Also ours: 406,134.7 ÷ 356,738.3 = 1.1385; 38.30 mm × 80 = 3.06 m; 30 mm ÷ √900 = 1.0 mm; 0.115 J ÷ 3.73 × 10⁻¹⁹ J per 532 nm photon = 3.1 × 10¹⁷.
In 1969 the beam's spot on the Moon was typically 4–6 km (Bender et al.); 1.9 km is for a modern one-arcsecond beam. The MIT echoes were received by May 1962; we date them by the Nature letter.

Try it

At arm's length, cover the rising Moon with a pencil eraser; a few hours later, with the Moon high, do it again. Same night, so the real distance barely changes (at most about 0.4 % in six hours). It covers the Moon just the same: at 65 cm, our assumed arm, the full Moon is about 6 mm across (6.3 mm on 24 December). NASA suggests a fingertip, or two photos at the same zoom. The video shows a drawn example, not a filmed measurement. And 1.6 % of 6 mm is a tenth of a millimetre, too small to see: the test only shows the image doesn't grow.

Three Shorts that go with this episode

18 November 2026: Voyager 1 reaches one light-day (25,902,068,356 km) at 5:16:07 a.m. EST, 10:16:07 UTC, farther than any other human-made object (NASA Science; checked in Horizons): about 67,000 times the Moon's 1.3 light-seconds.

7 December 2026: 350 years since the Journal des Sçavans printed Ole Rømer's case that light takes time. Io leaves Jupiter's shadow about every 42½ hours; as the Earth moved away, those moments ran late, one on 9 November 1676 by ten minutes (Phil. Trans. 12, 893–894, 1677, public-domain scan). His figure gives about 22 minutes for light to cross the Earth's orbit (today: 16.63). Huygens made it a speed, about 230,000 km/s, in 1690; a note by Cassini of 22 August 1676 is the first written account of the delay (Bobis & Lequeux, 2008).

24 December 2026: full Moon at 01:28 UTC, closest point of the year at 08:38 UTC (356,648 km); about 14 % wider than on 31 May, and about 1.5–1.8 % smaller rising than high.

Image credits

Apollo 11 laser ranging retroreflector seen from inside the lunar module, NASA AS11-37-5551, 20 July 1969 (images.nasa.gov). NASA, public domain.
Apollo 14 laser ranging retroreflector, NASA AS14-67-9386, 5 February 1971 (images.nasa.gov). NASA, public domain.
All other diagrams, the map of the five reflectors (positions after Murphy 2013, Fig. 3) and the pencil drawing are ours, some redrawn after Murphy (2013).