Transcript Powers of ten notation - Case Western Reserve University

Near edge-on view
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.
Discussion
What is the latitude of the arctic circle?
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?
Discussion
How far above the southern horizon is the
Sun on the summer solstice as viewed from
a latitude of 42 degrees north?
Earth’s rotation
Discussion
Why is Kennedy Space Center in Florida and
not in Maine?
Centrifugal force
This extra velocity at the equator pushes the
matter out at the equator.
The Earth is not a perfect sphere
The Earth is oblate, it bulges out at its
equator.
The diameter measured along its equator is
43 km larger than its diameter from the
north to the south pole.
Sun and Moon apply a torque
Precession
This off axis force, or torque, on the Earth
causes Earth’s 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.
Precession
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?
Discussion
If the position of the north and south celestial
poles changes in the sky, what else changes
position on the celestial sphere?
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.
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.
Discussion
Why is the changing of the equinox position
important?
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.
Sidereal year
However, because the equinox positions
slowly change, this is not the Earth’s 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.
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.
Leap Years
There are 365.242 days per tropical year, or
about a quarter of day more than 365. To
make everything come out even we therefore
add an extra day to our year every four years.
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.
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.
TRADITIONAL
ASTROLOGICAL DATES
Constellation Date Span
ACTUAL ASTRONOMICAL DATES
TODAY (c. 2000 C.E.)
Days
Constellation
Date Span
Days
Aries
21 Mar - 19 Apr 30
Aries
19 Apr - 13 May
25
Taurus
20 Apr - 20 May 31
Taurus
14 May - 19 Jun
37
Gemini
21 May - 20 Jun 31
Gemini
20 Jun - 20 Jul
31
Cancer
21 Jun - 22 Jul
32
Cancer
21 Jul - 9 Aug
20
Leo
23 Jul - 22 Aug
31
Leo
10 Aug - 15 Sep
37
Virgo
23 Aug - 22 Sep 31
Virgo
16 Sep - 30 Oct
45
Libra
23 Sep - 22 Oct
Libra
31 Oct - 22 Nov
23
Scorpio
23 Oct - 21 Nov 30
Scorpius
23 Nov - 29 Nov
7
Ophiuchus
30 Nov - 17 Dec
18
30
Sagittarius
22 Nov - 21 Dec 30
Sagittarius
18 Dec - 18 Jan
32
Capricorn
22 Dec - 19 Jan
29
Capricornus
19 Jan - 15 Feb
28
Aquarius
20 Jan - 18 Feb
30
Aquarius
16 Feb - 3/11
24-25
Pisces
19 Feb - 20 Mar 30-31
Pisces
12 Mar - 18 Apr
38
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.
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?
First quarter Moon
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.
The real reason
The Moon’s 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 Moon’s surface facing us illuminated.
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.
Waxing crescent
When less than ½ of the Moon’s face is
illuminated. It is the western side of the
Moon’s face that is illuminated and the Moon
is visible in the sky before Sunset. Waxing
means increasing.
First Quarter
When exactly ½ of the Moon’s face is
illuminated. It is the western side of the
Moon’s face that is illuminated and the Moon
is up before sunset. Although ½ of the Moon’s
face is illuminated it is called a quarter
because the Moon is ¼ of the way through it’s
cycle and occurs about one week after the
new phase. The Moon is 90 degrees away
from the Sun in the sky.
Waxing Gibbous
When more than ½ of the Moon’s western
face is illuminated.
Full Moon
when the Moon’s face is fully illuminated. At
this time the Moon is directly opposite the Sun.
Occurs about 2 weeks after the new phase.
Waning Gibbous
when more than ½ of the Moon’s face is
illuminated. But now it is the eastern face that
is illuminated and waning means decreasing.
Last Quarter
when ½ of the Moon’s 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.
Waning Crescent
When less than ½ of the eastern half of the
Moon’s face is illuminated.
Discussion
If the Moon is in its full phase on March 21st
and the Sun sets at 6:00 P.M. what time does
the Moon rise? What time does the Moon
reach the meridian? What time does the
Moon set?
The full Moon is exactly opposite the Sun or
180 degrees away in the sky. Astronomers
would measure this angle in hours and say it is
12 hours from the Sun. If sunset is at 6:00 P.M.
the full Moon rises at 6:00 P.M., crosses the
meridian at midnight and sets at sunrise at
6:00 A.M., 12 hours different from the Sun.
Discussion
If the Moon is in its last quarter phase on
March 21st and the Sun sets at 6:00 P.M.
what time does the Moon rise? What time
does the Moon reach the meridian? What
time does the Moon set?
The last quarter Moon is 90 degrees to the
west of the Sun in the sky, or 6 hours before
the Sun. If sunset is at 6:00 P.M. and rises at
6:00 A.M. (we are at the equinox) the last
quarter Moon rises at midnight, crosses the
meridian at 6:00 A.M and sets at noon.
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?
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?
If the Moon is at the position of the vernal
equinox it must be 180 degrees from the Sun
and therefore full.
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 winter solstice?
Explain.
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.
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.
The Moon is 90 degrees behind the Sun.
Because the Sun is moving eastward relative
to the stars, the Moon is 90 degrees to the
west of the Sun and therefore in last quart
phase.
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?
In the 27.32 days that the Moon has taken to
orbit the Earth the Earth has moved in its
orbit relative to the Sun. The Earth moves
about 1 degree per day so that after 27 days
the Moon needs to move through an extra 27
degrees in the sky to get back to the same
position relative to the Sun.
Discussion
The Moon always keeps the same side facing
the Earth. Does this mean the Moon does not
spin on its axis? Explain?
Synchronous Rotation
If the Moon did not spin on its axis we would
see the Moon’s 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 Moon’s rotation
period is synchronous with its orbital period.