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Earths axial tilt the seasons
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Solstices
The Sun therefore spends six months above the
celestial equator and six months below. The
furthest is gets from the celestial equator is
23.5 degrees. When the Sun is 23.5 degrees above
the celestial equator (June 21) we have the
summer solstice (summer in the north), and when
it is 23.5 degrees below the celestial equator
(Dec 21) This corresponds to the winter solstice.

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Equinoxes
When the Sun crosses the celestial equator we
have an equinox, where the length of the day and
night are exactly equal. The autumnal equinox
(Sept. 21) is when the Sun is moving below the
celestial equator and the vernal equinox (March
21) is when the Sun is moving above the celestial
equator.
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Why is summer warmer?

• The Sun, being above the celestial equator
  remains in the sky longer during the summer, the
  longest daylight time occurs on the summer
  solstice.
• The Suns rays hit the earth more directly during
  the summer months, i.e. the summer hemisphere
  receives more energy per square meter.

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The arctic circle
The arctic circle is the northern latitude at
which on the summer solstice the Sun never sets
and on the winter solstice the Sun never rises
above the horizon.
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Discussion
What is the latitude of the arctic circle?
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Discussion
The tropics mark the furthest points north and
south where the Sun can appear at the zenith.
What is the latitude of the tropics?
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The Earth is not a perfect sphere
The Earth bulges out at its equator. Its
diameter measured along its equator is 43 km
larger than its diameter from the north to the
south pole.
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The Earths rotation
The speed at which points on the Earths equator
are moving is larger than points on the Earth at
higher latitudes. At the equator you would be
moving at 1,650 km/hr, while at the north pole
your speed would be 0. You are just rotating
around a point.
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This extra velocity at the equator pushes the
matter out at the equator. The same thing
happens on a merry-go-round. The closer you are
to the edge, the faster you will be moving, and
the greater the force pushing you off.
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Discussion
Why is Kennedy Space Center in Florida and not in
Maine?
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Conservation of angular momentum

Anything that spins on an axis or revolves around
another object has angular momentum.
Conservation of angular momentum requires that
the axis of rotation of any spinning object
remains in a fixed direction in space as well as
spin at the same rate.
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The Earths rotation axis remains in a fixed
direction as Earth orbits the Sun.
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The Sun and Moon apply a torque to the Earth
Because the Earth is not a perfect sphere and its
rotation axis is tilted 23.5 degrees from its
orbital plane, the Sun and the Moon pull on the
extra mass in Earths equatorial bulge and try to
straighten out the tilt.
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Precession
This off axis force, or torque, on the Earth
causes Earths rotation axis to vary slightly, or
precess, over long periods of time. Thus, the
celestial poles trace out a circle against the
stars over a period 26,000 years.
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Discussion
The Great Pyramid at Giza has a tunnel which
points toward the north celestial pole. At the
time the pyramid was built, around 2600 BCE,
toward which star did it point?
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Precession of the Equinoxes
If the celestial poles change with time, so too
must the celestial equator, which is 90 degrees
away from the poles. If the celestial equator
changes with time, than the intersection of
ecliptic and the celestial equator will also
change with time.
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Age of Aquarius?
The age is defined by which constellation the
Sun is in on the vernal equinox. Currently, it
is the age of Pisces.
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Discussion
Why is the changing of the equinox position
important?
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Tropical year
The length of our calendar year is defined by the
time it takes between two vernal equinoxes. This
is called the tropical year and is 365 days 5
hours 48 minutes and 46 seconds long.
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Sidereal year
However, because the equinox positions slowly
changes, this is not the Earths actual orbital
period around the Sun. The actual orbital period
is called the sidereal year and is 365 days, 6
hours, 9 minutes and 10 seconds, or 20 minutes 24
seconds longer.
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What is the difference?
If we used the sidereal year for our calendar
year the seasons would slowly migrate through the
different months over time. Spring would come
one day earlier every 70 years.
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Astrology
Your astrological sign is the constellation the
Sun was in on the day you were born. But, the
constellation the Sun is in at any given time of
the year changes due to precession. Astrology
ignores this change.
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Discussion
Do you think the ancient Egyptians, unlike modern
astrologers, were aware of precession?
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Astronomical coordinates
Because of precession and the changing position
of the celestial poles and the vernal equinox,
celestial coordinates of astronomical objects
change from year to year.
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The Moon
As we pass through the month, the appearance of
the Moon changes each night. We say the Moon
goes through a series of phases.
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Discussion
Many people believe incorrectly that the phases
of the Moon are caused by the shadow of the Earth
on the Moon. What simple observation of the Moon
could you make to prove that they are wrong?
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First quarter Moon
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The Earth is round
The shadow on a first or last quarter Moon is a
straight line dividing the face of the Moon in
half. The Earth is round and will always cause a
curved shadow on the Moon. When the shadow of
the Earth does fall on the Moon we call this a
lunar eclipse.
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The real reason
The Moons phases are actually cause by the
changing position of the Moon with respect to the
Sun. The side of the Moon facing the Sun is
always fully illuminated (except during a lunar
eclipse). But because the angle we view the Moon
differs from that of the Sun, we see varying
degrees of the Moons surface facing us
illuminated.
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New Moon
Occurs when the Moon is in the same part of the
sky as the Sun. Thus the Moon is up during the
day, and the illuminated side of the Moon faces
away from the Earth. The Moon is not visible
when it is new.
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Waxing crescent
When less than ½ of the Moons face is
illuminated. It is the western side of the
Moons face that is illuminated and the Moon is
visible in the sky before Sunset. Waxing means
increasing.
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First Quarter
When exactly ½ of the Moons face is illuminated.
It is the western side of the Moons face that
is illuminated and the Moon is up before sunset.
Although ½ of the Moons face is illuminated it
is called a quarter because the Moon is ¼ of the
way through its cycle and occurs about one week
after the new phase. The Moon is 90 degrees away
from the Sun in the sky.
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Waxing Gibbous
When more than ½ of the Moons western face is
illuminated.
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Full Moon
when the Moons face is fully illuminated. At
this time the Moon is directly opposite the Sun.
Occurs about 2 weeks after the new phase.
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Waning Gibbous
when more than ½ of the Moons face is
illuminated. But now it is the eastern face that
is illuminated and waning means decreasing.
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Last Quarter
when ½ of the Moons face is illuminated. Again
it is the eastern half that is illuminated and
the Moon is visible after sunrise. Occurs about
3 weeks after the new phase.
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Waning Crescent
When less than ½ of the eastern half of the
Moons face is illuminated.
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Discussion
If the Moon is in its full phase on March 21st
and the Sun sets at 600 P.M. what time does the
Moon rise? What time does the Moon reach the
meridian? What time does the Moon set?
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Discussion
If the Moon is in its last quarter phase on March
21st and the Sun sets at 600 P.M. what time does
the Moon rise? What time does the Moon reach the
meridian? What time does the Moon set?
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Discussion
Suppose it is the first day of autumn in the
northern hemisphere. What phase is the Moon if
the Moon is located at the position of the vernal
equinox?
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Discussion
Suppose it is the first day of autumn in the
northern hemisphere. What phase is the Moon if
the Moon is located at the position of the summer
solstice? Explain.
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Discussion
The Moon goes through its phases in 29.53 days.
This is called the synodic month, i.e. the month
relative to the Sun. The actual orbital period
of the Moon is 27.32 days, the sidereal month.
Why is there a difference in the synodic and
sidereal months?
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Discussion
The Moon always keeps the same side facing the
Earth. Does this mean the Moon does not spin on
its axis? Explain?
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Synchronous Rotation
If the Moon did not spin on its axis we would see
the Moons entire surface over the month. The
Moon therefore does rotate but the rotation
period is exactly equal to its orbital period and
rotates such that we always see the same face.
Thus, the Moons rotation period is synchronous
with its orbital period.
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