EARTH-SUN RELATIONS

Vocabulary: revolution, orbit, aphelion, perihelio, equator, rotation, parallelism, equinox, Tropic of Cancer, Tropic of Capricorn, solstice, subsolar point, 90° rays, perpendicular rays, vertical rays, direct rays, tangent rays, Arctic Circle, Antarctic Circle, Circle of Illumination, darkness

Behavioral Objectives
• The student will be able to identify the equinoxes and solstices, the locations of the direct and tangent rays of the noon sun, and the approximate locations for the other dates of the year.
• The student will be able to determine how many times a year a location receives the sun's direct rays.
Introduction
At one time, it was believed that the earth was the center of the solar system; however, with the advent of new tools and research, the heliocentric theory, that the earth and other planets move around the sun, became adopted and proven. This motion of the earth around the sun is called revolution, and the path the path the earth follows is it's orbit. The earth makes one complete revolution in approximately 365 1/4 days which gives us the time period we call the year. The time period called the day comes from the length of time that it takes the earth to complete one turn on its axis, the motion called rotation.

The earth's revolution plays a very important role in our life here on earth, for it is this motion which affects the weather and climate. The earth's orbit is elliptical, which means that it is like an elongated circle, with the sun being located at one of the two foci or center points. Therefore, at one time of the year, about July 4, they are farthest apart, termed aphelion. At perihelion, the distance between the two is about 91 1/2 million miles; and, at aphelion, it is about 94 1/2 million miles. The average distance is considered to be 93 million miles, so the shape of our elliptical orbit is not really far from that of a circle. (To calculate the percentage that the change in distance of the earth from the sun is of the average distance from the sun, divide 3 million by 93 million and multiply by 100.) This relatively small amount of change could not cause the seasons which we experience here on earth because, first of all, we, in the northern hemisphere experience winter when the earth is closest to the sun, and secondly, the seasons in the northern hemisphere rather than being the same are opposite those of the southern hemisphere. Therefore, we must look to something besides the distance between the earth and the sun to explain the seasonal variations.

If we imagine ourselves in space looking toward the earth so that we see the north pole, the earth would be traveling in its orbit counterclockwise around the sun. If we were in a direct line with the earth's axis, we would find that we would not be looking directly at the earth's orbit, but rather looking at it from an angle. The reason for this is that the earth's axis is tipped 23 1/2° from the position perpendicular to the plane of the earth's orbit. In other words, if we would extend the direction north out into space, it would point toward a star named Polaris, not in a direction exactly "above" our orbital plane or what is more commonly called the plane of the ecliptic. Furthermore, the earth's axis is always pointed toward this same direction throughout its revolution. This is called the parallelism of the earth's axis and can be illustrated by the following experiment.

The distance between the earth and the sun is so far and because of the relative sizes of the two bodies, the rays of light coming from the sun which are intercepted by the earth can be viewed as being parallel rays. If the earth's axis were not tipped, these rays would always strike the earth directly at the equator, and due to the curvature of the spherical earth, extend 90° around the globe from this point. However, the tilt of the earth's axis causes this point of the direct rays to migrate from 23 1/2°N of the equator to 23 1/2°S of the equator.

Let's return to the above experiment. In "POSITION ONE," we see the earth's axis (pencil) pointed toward the sun (left fist) in the northern hemisphere (top or thumb). On this date, the earth will be receiving the direct rays of the sun at 23 1/2°N. This position represents the summer solstice which occurs on June 21. If we move to "POSITION TWO," we are illustrating September 23, the autumnal equinox of the northern hemisphere. In this position, the earth's axis is not inclined toward the sun, so the sun's direct rays fall on the equator. In "POSITION THREE," the axis in the souther hemisphere is pointed toward the sun, so the direct rays are striking 23 1/2°S. This represents the winter solstice which occurs on December 22. In "POSITION FOUR," we have the same positioning as we did "POSITION TWO." The sun's rays strike the earth directly at the equator. This position in the earth's orbit represents the vernal equinox of the northern hemisphere which occurs on March 21. Revolve your earth around your sun several more times and observe how the inclination of the earth's axis changes in relationship to the sun. Between "POSITIONS ONE and TWO," the northern axis is decreasing its inclination toward the sun, and so the direct rays will be located farther and farther south until they reach their southernmost position of 23 1/2°S on the winter solstice of the northern hemisphere. During the next 1/2 revolution, they will be moving northward as the inclination of the axis reverses itself until it returns to that of "POSITION ONE."

Since the sun is only one light source and the earth is a sphere, only half of the earth can be illuminated by the sun at any one time. The light, therefore, reaches 90° around the globe from that point at which it is striking directly. These rays which strike the earth directly are called the direct rays, 90° rays (the angle at which they hit the earth's surface), vertical rays, and also perpendicular rays. As the earth rotates under these rays, or as noon moves around the earth, these rays trace out a line of latitude (a parallel) as illustrated below. 90° away from this one noon point, the subsolar point, which is receiving the direct rays, we find what are called the tangent rays. These are the rays which strike the earth and then continue on out into space or, in other words, the point on the earth that is between daylight and darkness. All of these points on the earth's surface connect up to form the circle of illumination. The most important points of the circle of illumination are the northern- and southernmost points. (Remember, directions refer to the point of the earth's axis and not to top and bottom or up and down.) These can be found by moving 90° north or south from where the direct rays are striking the earth. When the direct rays are at the equator, March 21 and September 23, that is 90° north or south from the equator or 0° latitude. 90° in either a northerly or southerly direction would by definition designate the poles, so these would be the locations of the important tangent rays. The solstices, however, are not quite as easy to compute. On June 21, the summer solstice of the northern hemisphere, the direct rays are striking 23 1/2°N which is given the special name Tropic of Cancer. The point is 23 1/2° north of the equator, so if we measure 90° around the globe starting north, we will go past the north pole by 23 1/2°. This will put the tangent point on the far side of a parallel we have already passed. 23 1/2° on past the pole which has a latitude of 90° will put us at a latitude of (90° - 23 1/2° =) 66 1/2°N. This parallel is called the Arctic Circle. For the southernmost tangent ray on this date, measuring 90° toward the south from the direct ray, we must first measure 23 1/2° to get to the equator, our base line for latitude. Once we reach the equator, we only need 66 1/2° more to total 90°, so that the latitude of this tangent ray will be 66 1/2°S. This line is called the Antarctic Circle. Remember, we did not pass the south pole. A rubber band stretched around the globe between these two points will illustrate the circle of illumination. On the winter solstice in the northern hemisphere, December 23, when the direct rays are at 23 1/2°S, called the Tropic of Capricorn, the northernmost tangent ray will be received 90° to the north or at the Arctic Circle on the same side of the pole, and the southernmost tangent ray will be received 23 1/2° past the south pole or at the far side of the Antarctic Circle. (See the diagram below.)

The location of the circle of illumination becomes very important when we consider the length of daylight versus darkness. One the summer solstice in the northern hemisphere, we experience the longest period of daylight and on the winter solstice in the northern hemisphere, it is the shortest. This is due to the proportion of a parallel on the daylight side of the circle of illumination. The equator always receives 12 hours of daylight. But other points on the globe have variations in the length. If the entire parallel is on the light side of the circle of illumination, that point will experience 24 hours of daylight, but if the entire parallel stays on the dark side, a point on it will experience 24 hours of darkness.

Experiment 2: Have your neighbor do experiment one for you while you identify the dates and names of those positions. Have him check your identifications. You may get further practice by also identifying the location of the direct and tangent rays, though you may wish to use a globe for this practice.
Write a statement to thoroughly explain the difference you observed between experiment 1 and experiment. 2. YOU MUST ACTUALLY DO experiment 2 in order to answer this question. ***If you have any doubt about what the purpose is of this question (and you have actually done the experiment), ASK!! I will be glad to work with you. It is the KEY to this ENTIRE lesson!***

See a diagram of the solar rays to earth.
Earth-Sun Relations Practice
Illustration of the Migration of the Direct Rays
Earth-Sun Relations Review Exercise
For more practice with earth-sun relations, see this exercise on revolution.
An analemma