The Moon, tides and eclipses
On 8 April 2024 the Moon's shadow swept from Mexico across the United States and into Canada, and for a few minutes millions of people watched the afternoon go dark. That is the Moon at its most dramatic. Every other day it does quieter work: it lights the night, drags the oceans around, and is very slowly leaving us. In A tour of the solar system it was one speck among many. Here it gets the whole post.
A big moon, far away
The Moon is 3,475 km across, more than a quarter of Earth's diameter, which makes it the largest moon relative to its planet among the eight planets. It orbits 384,400 km away, about 30 Earth diameters. Most diagrams squeeze that gap. Drawn to scale it looks like this:
() o
|<--------------------- 384,400 km = 60 columns ----------->|
Earth Moon
1 column = 6,400 km. Earth is 2 columns wide; the Moon is only about
half a column wide, drawn here as one.That gap is wide enough to hold all seven other planets side by side: laid edge to edge (with mean diameters) they span about 380,000 km. Light needs 1.28 seconds to cross it.
Where it came from
The best current explanation is the giant-impact hypothesis, proposed in the mid-1970s by William Hartmann and Donald Davis, and independently by Alastair Cameron and William Ward. About 4.5 billion years ago a Mars-sized body, nicknamed Theia, struck the young Earth. The debris formed a ring that gathered into the Moon.
The evidence is circumstantial but strong. The Moon is less dense than Earth (3.3 against 5.5 g/cm3) because it has only a tiny iron core, as if the heavy iron stayed with Earth. Its oldest rocks show it was once covered by a global ocean of magma, which a violent birth explains. The 382 kg of rock brought back by six Apollo landings (1969 to 1972) fit this picture.
There is one real puzzle. Moon rocks have nearly the same oxygen isotopes as Earth rocks, but a simple impact should leave a Moon made mostly of Theia, which should differ. Variants answer this with a faster-spinning Earth or a thoroughly mixed vapour cloud. The big idea is accepted, the details are still being argued.
Phases
The Moon always has one half lit by the Sun. What changes is how much of that half faces us:
.#### ...## ....#
..####### .....#### .......##
.######## .....#### ........# <- sunlight
..####### .....#### .......##
.#### ...## ....#
waxing gibbous first quarter waxing crescent
##### OOO@@ .....
######### OOOOO@@@@ .........
######### OOOOO@@@@ ......... <- sunlight
######### OOOOO@@@@ .........
##### OOO@@ .....
full moon Earth new moon
####. ##... #....
#######.. ####..... ##.......
########. ####..... #........ <- sunlight
#######.. ####..... ##.......
####. ##... #....
waning gibbous last quarter waning crescent
View from above Earth's north pole. The Moon circles counterclockwise;
faces show what a northern observer sees (mirror image in the south).The common mistake is to think phases are Earth's shadow on the Moon. That would be an eclipse, and it is rare. A full Moon rises around sunset because it sits opposite the Sun; a first quarter Moon is high in the sky at sunset.
A subtle detail: the Moon circles Earth in 27.32 days (against the stars), but the cycle of phases takes 29.53 days. Meanwhile Earth has moved about 27 degrees along its own orbit, and the Moon needs two more days to catch up with the Sun's direction.
# synodic month from the sidereal month and Earth's year
sidereal = 27.3217 # days, Moon against the stars
year = 365.2564 # days, Earth against the stars
synodic = 1 / (1/sidereal - 1/year)
print(f"synodic month = {synodic:.2f} days")
# the Moon rises later each day by the fraction of a lap it has moved
lunar_day_h = 24 * synodic / (synodic - 1)
print(f"lunar day = {int(lunar_day_h)} h {round((lunar_day_h % 1) * 60)} min")
print(f"high tide every {lunar_day_h/2:.2f} h")synodic month = 29.53 days
lunar day = 24 h 50 min
high tide every 12.42 hThe same face, always
We see only one side because the Moon is tidally locked: it rotates once per orbit. The far side is not dark. It gets as much sunlight as the near side, and at new Moon it is fully lit. The Soviet probe Luna 3 photographed it for the first time in 1959, and in January 2019 China's Chang'e 4 made the first soft landing there. Slight wobbles called libration let us see about 59 percent of the surface from Earth over time.
Locking is a tidal effect. Earth's pull raised a bulge on the young, rotating Moon, friction in the rock dragged the bulge, and that brake stopped the spin relative to Earth. Pluto and Charon are locked to each other, and so are most large moons of the giant planets.
Why two tides a day
Gravity weakens with distance. The Moon pulls the near side of Earth harder than the centre, and the centre harder than the far side. Only the differences matter for tides: they stretch Earth along the line to the Moon.
low tide
~~~~~~~~~~~~~~~~
far side: ~~~~~##############~~~~~ near side:
pulled least ~~~~~####################~~~~~ pulled hardest
~~~~~######################~~~~~
~~~~~##########################~~~~~
~~~~~##########################~~~~~
~~~~~############################~~~~~ _
HIGH ~~~~~############################~~~~~ HIGH (o)
~~~~~############################~~~~~ '
~~~~~##########################~~~~~ Moon
~~~~~##########################~~~~~
~~~~~######################~~~~~
~~~~~####################~~~~~
~~~~~##############~~~~~
~~~~~~~~~~~~~~~~
low tide
Not to scale: the real bulge is under 1 m on a planet 12,742 km wide.
The Earth turns under the two bulges: two high tides per day.The ocean is drawn into two bulges, one on each side. As Earth turns, most coastlines meet a bulge roughly every 12 hours and 25 minutes, half a lunar day (24 h 50 min, from the code above). That is why high tide arrives about 50 minutes later each day. (You often hear about a "centrifugal force" on the far side. The simple picture of unequal pulls is cleaner.)
The Sun raises tides too. It pulls Earth about 180 times harder than the Moon does, but tide strength falls with the cube of distance, so the Sun's tides are only about 46 percent as big as the Moon's. When they line up, you get spring tides. When they work at right angles, neap tides:
phase idealised tide range (moon 2.2 units + sun 1.0 unit)
new moon ################### 3.2 spring
first quarter ####### 1.2 neap
full moon ################### 3.2 spring
last quarter ####### 1.2 neap"Spring" means "leap up" and has nothing to do with the season. Real ranges depend on the shape of the coast: in the open ocean they are roughly a metre, in the Mediterranean only tens of centimetres, and in the Bay of Fundy, where the water sloshes in resonance, up to about 16 m.
Tides have a price. Friction in the sea slows Earth's rotation, adding about 2 milliseconds to the day each century, and pushes the Moon outward by 3.8 cm per year. We know this from laser ranging to mirrors left on the Moon by Apollo astronauts. Fossil corals hint that 400 million years ago a year had about 400 days (an approximate figure).
Eclipses
By coincidence the Sun is about 400 times wider than the Moon and about 390 times farther away, so both span about half a degree of sky (0.53 and 0.52 degrees). That is why the Moon can just cover the Sun. The match is not exact: the Moon's distance varies between about 363,000 and 405,000 km, and when it is far its disc is a little too small, leaving a bright ring. That is an annular eclipse.
::::::
::::::
OOOOOOOOOO :::::
OOOOOOOOOOOOO :..++++++
OOOOOOOOOOOOOO :::++++++++++++++
OOOOOOOOOOOOOOO :::::: ++++++++++++++++
OOOOOOOOOOOOOOOO @@: ++++++++++++++++++
OOOOOOOOOOOOOOOO @@@@######+++++++++++++++++
OOOOOOOOOOOOOOOO @@: ++++++++++++++++++
OOOOOOOOOOOOOOO :::::: ++++++++++++++++
OOOOOOOOOOOOOO :::++++++++++++++
OOOOOOOOOOOOO :..++++++
OOOOOOOOOO :::::
::::::
::::::
SUN Moon (new) EARTH
# umbra: total eclipse + penumbra: partial eclipse
Not to scale: the real Sun is 400 times wider than the Moon.Inside the umbra, the core shadow, the Sun is fully covered. Where the umbra touches Earth, the path of totality is at most about 270 km wide, and totality lasts no more than 7 minutes 32 seconds; on 8 April 2024 the longest was about four and a half minutes. In the surrounding penumbra, thousands of kilometres wide, people see only a partial eclipse.
A lunar eclipse is the same alignment seen from the other side: at full Moon, the Moon passes through Earth's shadow. At the Moon's distance Earth's umbra is still about 2.6 Moon diameters wide, so the crossing takes hours, with totality up to roughly 1 hour 40 minutes. Everyone on the night side can watch. The Moon does not go black but copper-red, lit by sunlight that has been bent and reddened by Earth's atmosphere: all the sunrises and sunsets on Earth at once.
:::::::::::::::::::
=:::::::::::::::::::::::::::::::::::::::
@@@@@@@@====================================
@@@@@@@@@@@@@@#################################===================#
@@@@@@@@@@@@@@@@####################################################
@@@@@@@@@@@@@@@@@@######################################oo###########
@@@@@@@@@@@@@@@@@@#####################################oooo##########
@@@@@@@@@@@@@@@@@@######################################oo###########
@@@@@@@@@@@@@@@@####################################################
@@@@@@@@@@@@@@#################################===================#
@@@@@@@@====================================
=:::::::::::::::::::::::::::::::::::::::
:::::::::::::::::::
sunlight --> EARTH Moon (full)
# umbra (Earth's core shadow) : edge of the penumbra
Distances compressed. At the Moon the umbra is still ~2.6 Moons wide.Why not every month?
If the Moon passes between us and the Sun at every new Moon, why isn't there an eclipse every month? Because its orbit is tilted by 5.1 degrees against the plane of Earth's orbit, the ecliptic. It crosses that plane only at two points, the nodes.
OOOOOOOOOOOOOOOOOOOOOOO
OOOOO OOOOOOO
OOOO OOOOO
OO OOOO
OO ................................. OOOO
OO ....... .....OOO
O ..... .Ooo. <- node
O.. oo..
.O oo..
.OO (E) oo.
..OO o.
..OO ..o
node ->Ooo. ..... o
ooo..... ....... oo
oooo ................................. oo
oooo oo
ooooo oooo
ooooooo ooooo
ooooooooooooooooooooooo
. Earth's path round the Sun (the ecliptic), seen at a slant
O Moon above that plane o Moon below it node = where it crosses
Tilt drawn 4 times too large: the real angle is only 5.1 degrees.Five degrees sounds small, but at its farthest the Moon is about 34,000 km above or below the plane, 2.7 Earth diameters, so its shadow passes over our heads. An eclipse needs the new or full Moon to fall near a node. The line of nodes keeps pointing at the same stars while Earth circles the Sun, so it lines up with the Sun twice a year.
no eclipse: Moon's shadow misses Earth
.............E............
..... .....
.... ....
... ...
. .
- - - - - - -.E - - - - - - - - - * - - - - - - - - - - E.- - - - - -
eclipse . . eclipse
season ... ... season
.... ....
..... .....
.............E............
no eclipse: Moon's shadow misses Earth
Top view. * Sun, E Earth at four dates, one year round the ellipse.
- - - the Moon's line of nodes: it keeps pointing at the same stars,
so it lines up with the Sun twice a year, about 173 days apart.These eclipse seasons come about 173 days apart (half of a 346.6-day "eclipse year", shortened because the nodes drift slowly backwards). Each lasts roughly a month, and a solar and a lunar eclipse often fall about two weeks apart. Counting partial and penumbral ones, every year has at least four eclipses and at most seven. After 6,585.3 days, 18 years 11 days and 8 hours, the geometry almost repeats: the Saros cycle, already used by Babylonian astronomers to predict eclipses. Coming up are total lunar eclipses on 14 March and 7 September 2025, and a total solar eclipse on 12 August 2026 over Greenland, Iceland and northern Spain.
Try it
For a month, note when the Moon rises each evening and sketch its shape. You will see the 50-minute daily delay and the phases in order. Then check the tide table of the nearest sea: the highest tides should come a day or two after new and full Moon.
The Moon also makes Earth wobble. The two orbit a common centre of mass 4,670 km from Earth's centre, inside the planet, so Earth swings round it at about 12 m/s, almost exactly what Jupiter does to the Sun (12.5 m/s). That wobble is how astronomers first found planets around other stars; see Exoplanets: how we find other worlds.