ANNUAL VARIATIONS

The annual variations (seasons and changing constellations) are due to the orbital motion (revolution) of the Earth around the Sun. The Earth moves from the west-to-east around the Sun (i.e., in the CCW-sense as viewed from the NCP). The Earth rotates and revolves in the same sense (west-to-east). Due to the orbital motion of the Earth, the Sun moves slowly through the stars on the Celestial Sphere from west-to-east. The path it traces out is referred to as the; Ecliptic and the constellations through which it passes are referred to as the Zodiac Constellations.

The Sun takes one sidereal year (roughly 365.2564 days) to make one complete trip around the Celestial Sphere with respect to the stars.

Sidebar: Coordinate Systems

CONSEQUENCES OF THE ORBITAL MOTION OF THE EARTH

The primary effect is the changing of the seaons. The seasons change on a period of 365.24199 days (the Tropical year); a period slightly shorter than the sidereal year. The cause of the seasons is the tilt of the rotation axis of the Earth with respect to the orbital axis of the Earth. But, How does this lead to seasonal variations?

There are two major effects:

• Angle at which the sunlight strikes the Earth and how the angle varies over the course of a year

• The length of time which the Sun is above the horizon.

Annual Variations in the Diurnal Motions of the Sun

On December 21 (or so), the Sun reaches its farthest point south of the Celestial Equator, the Winter Solstice. The Sun then moves toward the Celestial Equator in the CCW-sense. It passes throught the Celestial Equator on around March 21, the Vernal Equinox. The Sun reaches its maximum distance north of the Celestial Equator on around June 21, the Summer Solstice. The passes through the Celestial Equator, heading South, on around September 21, the Autumnal Equinox.

To see how this affects the weather, consider how the diurnal circles for the Sun vary over the course of a year in Eugene, OR (roughly latitude ~ 45 degrees N, longitude ~ 123 degrees W).

In Eugene, the altitude of the NCP above the north point on the horizon is equal to the latitude of Eugene, ~ 45 degrees. [ How far is the Celestial Equator above the south point on the horizon? Answer: ~ 45 degrees.] So, now, what is the altitude of the Sun above the (South/North?) point on the horizon at roughly noon on the equinoxes and solstices?

Altitude at noon:
Equinoxes -- 45 degrees above the south point.

Winter Solstice -- 21.5 degrees above the horizon.

Summer Solstice -- 66.5 degrees above the horizon.

We see that around the time of the Summer Solstice: (1) the fraction of the Sun's diurnal circle which is above the horizon is greater than 1/2 and so the hours of daylight will exceed the number of hours of darkness. (2) The Sun is higher in the sky and so a given bundle of sunlight heats a smaller amount of the surface of the ground. These two effects cause the seasons.

How did I figure out the above numbers?

What is the definition of noon?

The Arctic circle is the region on the Earth where the Sun can be above the Horizon for longer than 24 hours, i.e., the Sun can be circumpolar. Above and below what latitudes is the Sun circumpolar during the summer?

SOLAR VERSUS SIDEREAL DAY

The sidereal day is 23 h 56 m 4.091 s and is defined as the time it takes a star to make two successive crossings of the Celestial Meridian. The solar day is defined as the time it takes the Sun to make two successive crossings of the Celestial Meridian:

If the Earth were stationary, then the Solar Day and the Sidereal Day would be precisely the same. However, we know that the Earth also revolves about the Sun. How does this affect the Solar Day?

Well, since the Earth moves roughly at a rate of (360 degrees)/(365/25 days) ~ 1 degree per day, the Earth will have moved 1 degree after 1 day. This means that in order for Sun to return to the Celestial Meridian, the Earth must turn roughly 1 more degree. That is, the Earth must turn 1/360-th of the way around again to have the Sun reappear on the Meridian. This means that the Solar Day will be roughly 1/360-th times longer than the Sidereal Day.

If the Earth's orbital motion were steady, then this would be the entire story. Unfortunately, the Earth's orbital speed is not constant; it varies throughout the course of the year. This means that the length of the solar day also varies throughout the course of the year. From a clock standpoint, this is clearly unacceptable and so the Mean Solar Day was defined to be the average length of the true solar day. The mean solar day defines our clock day.

This is the reason that the Sun sometimes appears to be late and sometimes appears to be early. By early and late, I mean that the Sun does not cross the Celestial Meridian at the same time every day! This information is carried in the analemma.