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PHY134Introductory Astronomy

The Sun and the Moon

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So Far• Stars fixed on a large celestial sphere that rotates daily East

to West about an axis through Earth’s poles• Declination is celestial longitude. Observer’s zenith is at

Declination = Latitude• Right Ascension is celestial longitude. Observer’s zenith is

at RA = Sidereal Time• Sidereal time changes by about 1h/h• Sun moves to East relative to stars once a year

Sky ChartsN

WE

S

ZenithFixed Azimuth

HorizonFixed Altitude

PoleFixed RAEquatorFixed Decl.

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Clocks• Time from noon to noon is a bit (1/365 of a day or

about 4min) longer than time it takes Earth to turn 360°

• A (mean) solar day is longer than a sidereal day• Our clocks (LT) keep solar time so run slower than

sidereal clock (ST)24 sidereal hours = 23h 56m 4s

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Finding Sidereal Time• By convention ST ≅ LT on September 21• D days later (earlier)

ST ≅ LT +/- D×4m• This is approximate. In any event ignores time zones

and Daylight Savings Time• On December/March/June 21

ST ≅ LT + 6/12/18 h

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It Tilts• Earth’s axis is tilted 23.5° from perpendicular to orbit• Celestial equator tilted 23.5° from plane of orbit – ecliptic• Sun’s orbit along Celestial sphere – ecliptic - tilted 23.5°

from Celestial equator• Sun’s Declination changes between 23.5 and -23.5• Ecliptic meets equator at Vernal/Autumnal equinox at

0h/12h RA

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Seasons• When Sun North/South of equator

– Days longer in North/South– Sun higher in the sky in North/South– Climate warming in North/South cooling in South/North– Inside Arctic circle Sun becomes circumpolar/never rises

(reverse for Antarctic circle)• At equinox day/night equal everywhere• Between tropics Sun is at Zenith once a year

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How High is Sun at Noon?• We are at Latitude 36°N • At equinox

• At summer solstice

• At winter solstice

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Why Mean?• 24h is an average Solar day• Sun’s RA increases over the year but not uniformly• Sun moves around ecliptic almost uniformly but

ecliptic is tilted near equinoxes and parallel to equator near solstices. So Eastward motion fastest near solstices.

• Almost… Earth very slightly nearer Sun in January

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It Also Wobbles• The Earth’s axis wobbles

like a spinning top – precession

• Celestial axis wobbles. • North pole moves to the

West in a circle of radius 23.5° every 26,000 years relative to stars

• So does celestial equator hence precession of the equinoxes

• Coordinates of stars change too – epoch J2000

• Age of Pisces gives way to age of Aquarius ca. 2600

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Moon Moves Too• Like Sun, Moon moves

around celestial sphere as it orbits Earth West to East

• Moon is faster: orbits in a sidereal month (27.32 days)

• RA increases by 48min per day

• Spin locked to orbit – same side always faces Earth

• Moon moves relative to Sun by 44min per day

• Full rotation relative to Sun in synodic month (29.53 days)

• Position relative to Sun controls rise/set times as well as phases

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Moon’s Declination• Moon’s orbit inclined 5° to ecliptic about line of nodes• Like Sun, Moon higher in Summer• Twice a year line of nodes aligns with Sun: Eclipse Season• Tilt precesses to the West every 18.6 years so twice an

eclipse year of 346.6 days• At New/Full Moon during eclipse season have Solar/Lunar

eclipse

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Solar Eclipse• Moon almost same angular size

as Sun• With near perfect alignment

can completely obscure Sun – from up to 250km shadow – total eclipse

• More common – partial eclipse• When Moon farthest from

Earth – annular eclipse

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Lunar Eclipse• Moon enters Earth shadow

from West• Eclipse can be total or

partial. Penumbral eclipse when Moon in partial shadow – dims slightly

• During totality Moon illuminated through atmosphere looks red

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Fun with the Moon• Moon appears larger

near horizon• This is a psychological

illusion not shared by optical instruments

• Various theories as to mechanism

• Can see dark part of crescent Moon – “old moon in new moon’s arms”

• This is physical viewing dark part by reflected Earthlight

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Signs of the Times• Astronomy and timekeeping are always closely related –

we want our time to match what happens.• Our 24-hour days are adjusted to mean solar day.• Our months are approximately lunar.• Our years match orbit – 365.2564 days is a sidereal orbit. • Tropical orbit is 365.2422 days (precession).• Julius Caesar got 365.25 so invented leap years.• Pope Gregory XIII (1582) corrected for the .0078

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Summary• Our cosmos now has moving parts

– Sun moves around Celestial Sphere to the East, completes one revolution in a year. The ecliptic tilted relative to celestial equator by 23.5° about equinoxes and precesses West every 26,000 years

– Moon moves around Celestial Sphere to the East, completes one revolution in a month. Moon’s orbit tilted relative to ecliptic by 5° about line of nodes and precesses West every 18.6 years

• The model now explains day/night, lunar phases, eclipses• What else moves?