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,
- 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
- The student will be able to determine how many times a year a location receives the sun's
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
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
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.
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.
Experiment 1: Hold your left fist in front of you to represent the sun.
Grasp a pencil in your right fist, and tip the
top a little (23 1/2°) to your left to illustrate the earth's axis. Put
this hand directly off to the right of your left first.
This will be the "STARTING POSITION." Now for "POSITION TWO," move your
right fist so that your left fist
is between your body and your right fist. Do not change the position of (rotate) your right wrist.
circle with your right hand around your left. One complete circle around your left fist illustrates
one year or one
complete revolution of the earth.
Let's look closer at this illustration or experiment. Return to the "STARTING POSITION OR
The top of the pencil is tipped toward your left fist. When you move your right hand around to
though, the pencil top is no longer tipped toward your left first. Continuing 1/4 of the way
around the circle, so that
your right hand is to the left of your left fist. Call this "POSITION THREE." And continuing 1/4
more of the circle,
so that your right fist is between your left and your body, "POSITION FOUR," we again have the
toward your left and not toward your left fist.
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
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
most important points of the circle of illumination are the northern- and southernmost points.
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
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
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
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
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.
Illustration of the Migration of
the Direct Rays
Earth-Sun Relations Review
For more practice with earth-sun
relations, see this exercise on revolution.