Astronomy
Moon, tides, and eclipses
Lunar phases, tides, and solar and lunar eclipses.
Basics
Lunar phases
We see sunlight on half the Moon; the Earth–Moon–Sun angle sets new, first quarter, full, and last quarter. The synodic month (new to new) is about 29.5 days, longer than the sidereal month (~27.3 days) because Earth has moved around the Sun while the Moon orbits. The same face stays toward us because spin and orbit are tidally locked.
Tides
The Moon (and more weakly the Sun) pulls Earth’s near side harder than the far side. That difference — the tidal force — raises two ocean bulges; Earth rotating under them often gives two high tides a day. At new and full Moon the Sun lines up (spring tides); at quarters they compete (neap tides). Coastline and depth change real times and heights a lot.
Eclipses
A solar eclipse is the Moon between Sun and Earth; a lunar eclipse is Earth’s shadow on the Moon. Umbra is total, penumbra partial. They do not happen every new or full Moon because the Moon’s orbit tilts about 5° to the ecliptic — only near the nodes do the shadows meet. The total-solar path is a narrow track; a lunar eclipse is visible wherever the Moon is up.
Periods and distance
The Moon’s mean distance is about 3.8×10⁵ km, on an ellipse with perigee and apogee. That its angular size nearly matches the Sun is why we get both total and annular solar eclipses. The saros (~18 years 11 days) is a cycle on which similar eclipse geometry repeats. The Moon recedes a few centimetres a year, and Earth’s day lengthens very slowly.
Formulas
Synodic month
Sidereal month and Earth’s year together set the phase period.
Symbols
-
T_sidsidereal month -
T_yearsidereal year
Tidal acceleration (sketch)
Body mass M, distance r, Earth-size d. Closer mass pulls much harder.
Symbols
-
dEarth-radius scale -
rdistance to Moon (or Sun)
Angular diameter
Total solar eclipse needs similar θ for Moon and Sun.
Symbols
-
Dbody diameter -
rdistance to observer
Shadow cone (sketch)
How far an occulting body’s umbra reaches. If the Moon’s umbra hits the ground, totality.
Symbols
-
Rocculting radius -
R_⊙solar radius
Key table
| Synodic month | about 29.53 days |
|---|---|
| Sidereal month | about 27.32 days |
| Mean Earth–Moon | about 3.84×10⁸ m |
In this field
Solar system
Planets, Kepler, gravity, escape speed.
Stars
HR diagram, fusion, lifetimes, magnitude.
Galaxies and cosmology
Galaxies, Hubble, redshift, black holes.
Observing basics
Celestial sphere, coordinates, telescopes, spectra.
Exoplanets and life
Detection, habitable zone, a SETI sketch.
The Sun and space weather
Solar structure, spots, flares and CMEs.
Magnitudes and spectra
Apparent and absolute magnitude, distance modulus, colour and spectral type, Wien’s law.
Galaxies and Hubble
Galaxy shapes, rotation curves, the Hubble–Lemaître law, and a standard-candle sketch.
Telescopes and light
Aperture, diffraction limit, collecting area, seeing versus space telescopes.
Stellar death
Red giants, supernovae, and sketches of white dwarfs, neutron stars, and black holes.