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?

This extra velocity at the equator pushes the matter out at the equator.

Centrifugal force

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.

TRADITIONALASTROLOGICAL DATES

ACTUAL ASTRONOMICAL DATESTODAY (c. 2000 C.E.)

Constellation Date Span 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 30 Libra 31 Oct - 22 Nov 23

Scorpio 23 Oct - 21 Nov 30 Scorpius 23 Nov - 29 Nov 7

Ophiuchus 30 Nov - 17 Dec 18

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.

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?

Discussion

First quarter Moon

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 Earth is round

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.

The real reason

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?

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.

Synchronous Rotation