Seasons

 

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John Milton alluded to the obliquity of the ecliptic and its consequences for the seasons in Paradise Lost:

"Some say, he bid his angels turn askance The poles of Earth twice ten degrees or more From the sun's axle; they with labour push'd Oblique the centric globe: some say, the Sun Was bid turn reins from th' equinoctial road Like distant breadth to Taurus with the seven Atlantic Sisters, and the Spartan Twins, Up to the Tropic Crab; thence down amain By Leo, and the Virgin, and the Scales, As deep as Capricorn, to bring in change Of seasons to each clime."

Study Questions

  1. Identify which zodiac constellations are referred to in the passage from Milton quoted above.
  2. Can you identify his allusion to the Pleiades?
  3. What is the cause of changing seasons?
    • __ Distance of the Earth from the Sun
    • __ Obliquity (tilt) of the ecliptic with respect to the equator
    • __ Cooling contraction and heating expansion change the lengths of day and night

Variability of Rising/Setting Location

In contrast to fixed stars, a given planet (including the Sun and Moon) will not always rise and set at the same location on the horizon. Sometimes a planet will rise at a more southerly location; sometimes at a more northerly location (though keeping within a certain range).

How does the Sun's apparent zodiacal motion provide ways to make a calendar?

The Sun traces its rising and setting positions north and south along the horizon in an annual pattern that is exactly repeatable and that recurs seasonally. Thus it provides a reliable and convenient calendar, like a pendulum oscillating around the points due east or due west. This solar calendar was as significant for ancient cultures as the cycles of day to night and the lunar phases. For example, an ancient Chinese explanation of this pattern attributed the motion to the Earth, as if the Sun were rising each day at the same place but the Earth itself slowly sliding up and down along a north-south line. At Stonehenge (Britain), Woodhenge (Cahokia, Illinois), or other stone circles (e.g., Medicine Wheel, Wyoming), seasonal time intervals were charted by arranging sunrise markers sighted toward the eastern horizon, running north or south of due east. The average American today, though ignorant of the term "zodiacal motion" knows that the Sun appears to go through a cycle that is the basis of the "year" in our calendar (postpone considering for now whether the earth goes around the Sun or the earth).

What are the principal positions (events) in the sun's exactly repeatable zodiacal motion? How do these main events show up on a calendar?

Sunrises and sunsets reach their extreme northerly and southerly positions on the solstices; and occur due east and due west on the equinoxes.

Equinoxes

Solstices

Tropical year

Interval between two successive solstices or equinoxes of the same type; e.g., between two successive summer solstices. The modern value = 365.2422 days.

The answers to the above questions are "no," "yes," and "cannot tell without more information." However, the difference between tropical and sidereal years is subtle, and was not recognized until Hipparchos conceptualized it as the "precession of the equinoxes" in the second century B.C. See explanation in Crowe, pp. 8-10.

Difficulties of ascertaining rising phenomena

The position of the Sun on the horizon at sunset or sunrise is difficult to determine accurately and consistently. As we continue to investigate the zodiacal motion of the Sun (its annual cycle which is the basis of our solar calendar), we need to focus our attention on the problem how to determine the points on horizon at which the Sun rises on successive mornings. The exact rising position of the Sun might be crucial for an ancient culture's determination of the 4 seasons of the year (and thus religious and agricultural events as well). At first glance, one may wonder what is so complicated about such rising (or setting) phenomena so as to warrant its inclusion here. To see some of the problems, consult the appendix in Crowe, and the diagrams he offers on p. 204 and p. 214.

Other factors complicate this phenomenon as well, including local lighting and terrain and the star's magnitude--the latter contributes to starlight refraction errors, caused by the Earth's atmosphere, that affect the star's apparent rising or setting position. In Mesopotamia (where rising and setting events were of utmost significance) sand-storms could also be expected to obscure the horizon and to frustrate accurate sightings (only Babylonian eclipse records--which were not horizon phenomena--proved sufficiently reliable to later astronomers such as Ptolemy).

The Sun's Zodiacal Motion & the Lengths of seasons

It was mentioned above that the Sun, like the other planets, changes its relative position from day to day against the background of fixed stars by an unequal amount. As a consequence, the lengths of seasons (the times between a solstice and equinox or vice-versa) are unequal. For the northern hemisphere, the winter half of the year (autumnal to vernal equinox) is about eight days shorter than the summer half (vernal to autumnal). That is, the Sun changes its day-to-day position against the background of fixed stars in the greatest amounts around January 2 (the "perihelion" date, in the modern or Keplerian conceptualization). This last statement makes sense because a greater speed results in shorter a time period for traveling a given distance. Study Crowe's discussion of the equinoxes and solstices, given the Greek assumptions of a spherical Earth and a spherical heaven; pp. 3-10.

Study Questions