Daily Spin

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Daily Spin

• Round Earth spins once a day to the East, so
• At poles, universe seems to spin daily about a
  vertical axis to the West
• At equator, universe seems to spin about a
  horizontal N-S axis
• At intermediate latitudes, universe seems to spin
  about a tilted axis, parallel to axis of Earth
• The view at longitude XW now is the same as view
  at longitude 0 was X/15 hrs ago (or 24-(X/15)
  hours hence
• Can imagine stars fixed on Celestial Sphere which
  rotates daily about a N-S axis to the West

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Annual Motion

• In addition to spinning, Earth orbits Sun
  annually, in same sense (roughly).
• The stars visible at night change with the
  orbital position.
• Thus Sun appears to move along Celestial Sphere
  from West to East.

• How long does Earth take to complete a rotation?
• 23h 56m 4.091s 1 sidereal day is time between
  rising times of any star
• 24h 1 (mean) solar day is average time between
  sunrises
• Sidereal time is right ascension of the meridian

1 Sidereal Day 24 Sidereal hrs 23h 56m 4s
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Tilt of Axis and Seasons

• Seasons are caused by tilt of Earths rotation
  axis relative to orbit, and timed by orbital
  motion.
• Hemisphere facing sun gets more heat summer
  warmer, days longer.

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If we locate sun in the sky at same time each
day, how does it move over the course of a year?
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Where is the Sun?
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Sidereal Time

• Sidereal Time is the right ascension of our local
  meridian
• There are no sidereal time zones
• Sidereal midnight is when vernal equinox is on
  our meridian
• Around March 21 (spring equinox) this happens
  about local midnight
• Sidereal clock gains 4m on solar clock every day

• At the vernal equinox, at noon local time the Sun
  and with it the equinox at R.A. 0h are overhead,
  so Local Sidereal Time is midnight so
• S.T. L.T. 12h
• D days after March 21 sidereal clock which is
  faster is now ahead by
• S.T. L.T. 12h D3.9318m
• Include a correction for time zone location.
  Above is precisely true in Greenwich. Our local
  time is
• E.S.T. G.L.T. 5h
• While our sidereal time is
• G.S.T. (79/15)h G.S.T. 5.27h
• So our sidereal time is
• E.S.T. 11.73h D3.9318m

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Finding a Star

• Declination tells us what angle from Polaris.
• The star will cross our meridian when our
  sidereal time is equal to its Right Ascension.
• For each hour after this time it will be 15o
  west of the meridian
• Beware of DST

• Bellatrix is at RA 5h 25m
• When will it be highest in our sky tonight?
• When our sidereal time is 525am
• Our sidereal clock is behind our solar clock by
• 12h 4m 65 12h 260m
• 16h 20m
• because we know they will agree on March 21
• So our local time will be 945pm

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Precession of the equinoxes

• Earths axis wobbles, or precesses, every 26,000
  years.
• This moves celestial poles and equator, hence
  equinoxes.
• So star charts need to list date epoch. Our
  charts are epoch 2000.

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Why Solar Days Differ
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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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The moon moves too

• Like the sun, the moon moves from west to east on
  celestial sphere because it orbits Earth.
• Moon is faster. Completes its path in four weeks
  (29.5 days). Can notice its motion!
• For all we know so far, consistent with Sun and
  Moon both orbiting Earth!
• As the moon moves it changes shape going through
  phases.
• To understand why, recall moonlight is just
  reflected sunlight.

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As the moon orbits it also spins. In fact the
two motions are locked together so we always see
the same side of the moon.
Sidereal month (stars) is 27.32 days
long. Synodic month (sun, hence phases) is 29.53
days long.
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Eclipses

• Lunar - Shadow of Earth on Moon. Happens at
  Full Moon.
• Solar Shadow of Moon on Earth. Happens at New
  Moon.
• Why not every orbit?

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• Moons orbit is tilted relative to Earths orbit
  by 5o (but nearly in the ecliptic plane!).
• Most passes (full/new) moon is above or below
  ecliptic.
• Eclipses occur when moon is new or full AND on
  line of nodes.
• Line of nodes rotates to the west once per 346.6
  days.
• Eclipses can happen when it is directed at the
  Sun.

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Lunar Eclipse

• When alignment occurs at full moon, shadow of
  Earth can cover moon.
• Umbra complete dark. Part of moon in umbra is
  dark.
• Penumbra partial shadow. Part of moon in
  penumbra is dim.

During totality, moon illuminated through
atmosphere looks red
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Solar Eclipse

• Moon and Sun same size at 0.5o. Moons umbra
  just reaches Earth (lt270 km.).
• In umbra, total solar eclipse darkens sun.
• In penumbra, partial solar eclipse.
• More often annular eclipse.

During totality, Solar corona visible
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Some History

• Mayans, Greeks (Thales 585 BC), others predicted
  eclipses.
• Erastothenes (200 BC) computed circumference of
  Earth by measuring angle of sun in two places at
  same time. Got 42000 km (?)

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The Saros

• Today, accurate predictions possible.
• 223 29.53 19 346.6 6585 days
• In fact, 6585.3 11yr, 11.3 days is the saros
  interval.
• Eclipses repeat roughly every third saros.

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More History

• Aristarchus (280 BC) computed sizes and distances
  of Moon, Sun.
• Sun-Moon angle at quarter moon gives relative
  distance (got 20 for 290).
• Length of lunar eclipse gives size of moon 1/3
  Earth.
• Angular size gives size of sun 20 (390) moons.