What If the Moon Vanished Tonight? What the Wobble Story Gets Wrong

What if the Moon vanished tonight? A thought experiment (it breaks the laws of physics): the Moon's mass disappears at once and everything else stays. We follow the clock from the first night to the very long run and check the claim that Earth would "wobble out of control" against the studies. NIGHT. A typical full-Moon night is about 60 to 125 times brighter than a moonless night. Measure: typical full-Moon illuminance of 0.05 to 0.1 lux at temperate latitudes in summer (Kyba, Mohar and Posch 2017) against about 0.0008 lux for the natural moonless sky (US National Park Service). TIDES. In equilibrium theory, the Sun's tide is about 0.46 of the Moon's. "Biggest tides" means the largest high-to-low range of the month (spring tides); without the Moon they would shrink to roughly a third in theory. At three NOAA tide stations (Eastport ME, The Battery NY, Honolulu HI), our own prediction from NOAA's harmonic constants gives 13 to 25 percent of today's biggest tide, below today's neap tides. "Weakest tides" means the smallest range of the month (neap tides). The first tide curves are equilibrium theory, not a real harbour; the harbour curves are NOAA data. EARTH AND MOON. The two circle a shared point about 4,671 km from Earth's centre, inside the Earth. OUR OWN CALCULATION (not a published result). If the Earth keeps the position and velocity it had when the Moon vanished, a full-Moon vanishing shrinks its orbit by about 135,000 km on average (0.09 percent) and shortens the year by about 12 hours (11 to 12.5, depending on the Moon's distance that night); a new-Moon vanishing lengthens it by about the same amount; at the quarter phases it barely changes (under an hour). The seasons would then slip against the calendar by about half a day a year. We checked it against two independent numerical integrations; the premise is the thing to challenge. DAY LENGTH. Tides lengthen the day by about 2.3 thousandths of a second per century (1.8 observed in eclipse records since 720 BC, Stephenson, Morrison and Hohenkerk 2016). Without the Moon, our estimate from the Sun's share of tidal friction is about a sixth of that. TILT. With the Moon the tilt varies by about 1.3 degrees either way (Laskar, Joutel and Robutel 1993). Without it, their chaotic zone extends from nearly 0 to about 85 degrees: a zone of possible tilts, not a swing. Lissauer, Barnes and Chambers simulated moonless Earths for up to 4 billion years and found the tilt stays within a range typically 20 to 25 degrees in extent. Li and Batygin estimate roughly 10 million years to cross one chaotic zone, slow enough not to preclude long-term habitability. The studies disagree about how far; they agree it is slow. ECLIPSES. The Sun is about 0.53 degrees wide and the Moon about 0.52 on average (0.49 to 0.56 over its orbit; NASA fact sheets), so a total eclipse needs the Moon in the nearer part of its orbit. CHAPTERS 0:00 The Moon vanishes 0:25 The rules of the thought experiment 0:56 The first night 1:32 Earth and Moon circle a point inside Earth 2:34 Tides: the Sun still raises them 3:55 A month in: phases and eclipses 4:32 Corals and the Moon's calendar 5:16 A year in: our own calculation 6:35 A century on: the length of the day 7:18 The tilt: what the studies say 9:06 What the wobble story gets wrong 9:45 The real answer 10:09 One last question SOURCES Laskar, Joutel and Robutel, Nature 361, 615-617 (1993), doi 10.1038/361615a0 Lissauer, Barnes and Chambers, Icarus 217, 77-87 (2012), doi 10.1016/j.icarus.2011.10.013 Li and Batygin, ApJ 790, 69 (2014), arXiv 1404.7505 Stephenson, Morrison and Hohenkerk, Proc. R. Soc. A 472, 20160404 (2016), doi 10.1098/rspa.2016.0404 Kyba, Mohar and Posch, Astronomy and Geophysics 58(1) (2017), doi 10.1093/astrogeo/atx025 Duriscoe, US National Park Service, natural night sky (2016) Bosboom and Stive, Coastal Dynamics, 3.7.6 NOAA CO-OPS harmonic constants, Eastport ME, The Battery NY, Honolulu HI; NOAA Tides and Currents, What are Harmonic Constituents Murray et al., Nature 565, 222-225 (2019), doi 10.1038/s41586-018-0805-8 (tidal flats) Harrison et al., Science 223, 1186-1189 (1984); Lin et al., PNAS 118, e2101985118 (2021) (coral spawning and moonlight shading) Wunsch and Ferrari, Annual Review of Fluid Mechanics 36, 281-314 (2004) (deep-ocean mixing) NASA NSSDC Moon and Sun fact sheets The narration is a synthetic voice. The animation, the sound effects and the ambient music bed were generated by us; there is no third-party music. No photographs or footage are used. Tide data: NOAA CO-OPS. Map data: NOAA NCEI, ETOPO 2022 (public domain, CC0-1.0).