The MOON

Earth’s rotation ≈ 1 mean solar day (Looking down on Earth’s N pole)

The MOON Earth’s rotation ≈ 1 mean solar day moon’s orbital period ≈ 29 ½ days (synodic month) A complete cycle of lunar phases i.e. orbit w.r.t. the sun. Note right-hand rule again

The MOON ≈ 1 week moon’s orbital period ≈ month ≈ 1 week “Quarters”

The moon’s phases

Moon as seen from earth E W New ESun W Can’t see anything of the moon! (Unless there’s an eclipse!)

Moon as seen from earth E W New(ish) ESun→ W Sun rises first, then the crescent moon. Moon is near the sun, and to the east.

Moon as seen from earth E W Waxing Crescent ESun→ Sun rises first, then the moon. Moon is farther from the sun, but still to the east. W

Moon as seen from earth E W 1 st Quarter ESun→ Sun rises first, then the moon W moon is ≈ 90 ̊ East of sun now! moon due south ≈ 6PM

Moon as seen from earth E WESun→ Sun rises first, then the moon. At some point this week, the moon starts to rise after the sun sets W Waxing Gibbous

Moon as seen from earth E WE Moon would be due south ≈ midnight W Full

Moon as seen from earth E WE Moon would be to the south after midnight. W Waning Gibbous ←Sun

Moon as seen from earth E WE W 3 rd Quarter moon rises first, then the sun moon is ≈90 ̊ west of sun now! Moon due south ≈ 6AM ←Sun

Moon as seen from earth E WE W Waning Crescent moon rises first, then the sun shortly thereafter ←Sun

The terminology: Waxing = getting bigger OR Waning = getting smaller Crescent = less than ¼ OR Gibbous = bigger than ¼ “Wayne-ing” “Wain-ing”

new 1 st ¼ full 3 rd ¼

Waxing or waning ? (Northern hemisphere) horizon

Waxing or waning ? (Northern hemisphere) premier? dernier? bloating? diminishing? horizon (fr: “last”)

Waxing or waning ? (Northern hemisphere) premier? dernier? bloating? diminishing? horizon (fr: “first”)

start 12 synodic months later +10 days

Easter? VBA Function For Easter The date of Easter can be computed in VBA. The algorithm below is from the United States Naval Observatory, at Computing The Date Of Easter.Computing The Date Of Easter Public Function EasterUSNO(YYYY As Long) As Long Dim C As Long Dim N As Long Dim K As Long Dim I As Long Dim J As Long Dim L As Long Dim M As Long Dim D As Long C = YYYY \ 100 N = YYYY - 19 * (YYYY \ 19) K = (C - 17) \ 25 I = C - C \ 4 - (C - K) \ * N + 15 I = I - 30 * (I \ 30) I = I - (I \ 28) * (1 - (I \ 28) * (29 \ (I + 1)) * ((21 - N) \ 11)) J = YYYY + YYYY \ 4 + I C + C \ 4 J = J - 7 * (J \ 7) L = I - J M = 3 + (L + 40) \ 44 D = L * (M \ 4) EasterUSNO = DateSerial(YYYY, M, D) End Function You can call this from a worksheet cell with a formula like =EasterUSNO(YYYY) 325 A.D. The first Sunday after the full moon (the Paschal Full Moon*) following the northern hemisphere's vernal equinox. *14th day of a lunar month

The moon’s Synchronous orbit

The MOON: an odd fact Earth’s rotation ≈ 1 mean solar day moon’s orbital period ≈ 29 ½ days (synodic) moon’s rotational period ≈ 29 ½ days too!

Q: Coincidence? A: No!

The Lunar day: Moon’s rotational period ≈ 29 ½ earth days! Length of Day/night on moon ≈ 14 3/4 days

Eclipses The moon’s orbital plane is inclined relative to the ecliptic! (by about 5°) Solar eclipse: Moon in front of Sun Lunar eclipse: Earth shades the Moon Sun and moon appear to have the same size ( ½ °) These are Rare events because:

Missing a lunar eclipse: max relative tilt: 5° earth’s shadow (1 st guess)

Missing a solar eclipse: max relative tilt: 5° apparent solar disk

Lunar eclipses, the earth’s shadow sun earth PENUMBRA UMBRA

An observer within the penumbra would see … sun earth

sun earth An observer within the umbra would see …

sun earth An observer beyond the umbra would see …

to scale …. ←sun earth moon PENUMBRA UMBRA

5° 1° ←sun earthmoon to scale ….

Solar eclipses, the moon’s shadow ←sun earth moon PENUMBRA UMBRA

The PLANETS

E W

E W

E W

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Using a telescope!!