The Motions of the Earth, Moon, and Sun

This is not very easy to understand, but if study what I have written here, think about it on your own, and ask me questions if you get stuck, you will succeed.  You will then be able to predict the times of sunrise and sunset anywhere in the world on any day, predict the times of moonrise and moonset (anywhere, any day), predict solar and lunar eclipses, navigate using the sun, moon, and stars, and tell time at night without a watch.  Eventually, you will be able to do all of this reasonably well, without external reference or scratch paper.

First, please become familiar with the directional names used in outer space (somewhat analogous to up, down, north, south, east, and west on the surface of the Earth).  Now (using these words) I will describe the relative motions of the Earth, moon, and sun.  (We will introduce the moon later.)  We will start with a highly simplified model and then slowly add features to better represent the actual model.

To ease you into the use of these directional words, we will first use the following substitute words.

 ecliptic north ecliptic south spring equinox fall equinox summer solstice winter solstice top bottom front back right left

Begin constructing your mental model by placing the sun in the center.  The sun is almost one million miles across.  Now place the Earth about 100 million miles to the right of the sun.  The Earth is almost eight thousand miles across.  This is our highly simplified starting model.

As you can see, the left half of the Earth is illuminated by light from the sun; the right half is in shadow.  On the left half of the Earth, it is daytime; on the right half, it is night.

To now improve the accuracy of our model, we will rotate the Earth.  Turn the earth so that the left side comes forward and the right side goes backward (i.e. counterclockwise from above).  The Earth makes approximately one revolution per day or one quarter revolution in about six hours.  Everything on the front side of the Earth is moving from the daytime side to the nighttime side, i.e. it is evening on the front side of the Earth.  On the right side of the Earth it is nighttime.  On the back side of the Earth, everything is moving from the night side to the day side; it is morning on the back side of the Earth.  On the left side of the Earth, it is daytime.  Any given point on the Earth will pass by all sides in sequence (night, morning, day, evening, night).  In fact, time of day is determined by which side of the Earth one is currently on.  On the extreme right side of the Earth, it is 12:00AM or 0h00m.  On the extreme back side of the Earth, it is 6:00AM or 6h00m.  On the extreme left side of the Earth, it is 12:00PM or 12h00m.  And on the extreme front side of the Earth, it is 6:00PM or 18h00m.  (For the way our model is set up, the north pole of the Earth is on top.)

To again improve the accuracy of our model, we must make the Earth orbit the sun.  The Earth orbits the sun in a "counterclockwise from above" fashion just as the Earth rotates (counterclockwise as viewed from above).  The Earth makes a complete orbit around the sun in about 1 year, thus it takes about 3 months to make one quarter orbit.  Our calendar (the Gregorian Calendar) is, in fact, roughly synchronized with the orbit of the Earth.  In general, the Earth is on the right side of the sun in December, on the back side of the sun in March, on the left side of the sun in June, and on the front side of the sun in September.  Putting the Earth in its December position, we see (as before) that the daytime side of the Earth is on the left.  If we place the Earth in its March position (in the back), we see that the daytime side of the Earth is on the front.  Accordingly, 12:00PM is now on the front of the Earth.  As you can see, the time of day at a particular place on the Earth depends not only on the rotational position of the Earth, but also the orbital position of the Earth.  This diagram shows the relationship between time of day, time of year, and ones position on the Earth.  (The view is from ecliptic north with fall equinox toward the top of the page.  None of these diagrams are to scale.)

At this point, we will no longer hold the sun in the center of our model, but will instead follow the Earth on its orbit around the sun, thereby holding the Earth in the center of our view.  You will imagine it something like this.  Notice that the relative positions on the Earth and sun are (at all times) the same as in our previous model.

The following exercise may help you understand this more clearly. In an open room place a chair on the floor. Stand behind the back of the chair with the chair in front of you. Now stand on the right side of the chair but continue to face in the same direction. The chair should now be on your left. Now stand in front of the chair but continue to face the same direction. Now the chair is behind you. Now stand on the left side of the chair but continue to face in the same direction. The chair should now be on your right side. Now stand behind the chair again and continue to face in the same direction. The chair should now be in front of you again. In the preceding exercise, the chair is sequentially in front of you, to your left, behind you, to your right, and in front of you again. Thus from your point of view, the chair is orbiting you.

If you will notice, one can use this model to make predictions of the times of sunrise and sunset.  Regardless of time of year and location on Earth, this model shows the time of sunrise to always be 6AM and the time of sunset to always be 6PM.
(For a particular point on the Earth, sunrise is when it passes from the nighttime side of the Earth into the daytime side.)  Experience shows that this is not exactly the case.  To make this model more accurate, we must tilt the axis around which the Earth rotates.

The counterclockwise end of the Earth's rotational axis does not point directly toward ecliptic north (as we have assumed in our model thus far).  More accurately, it points 23.4° from ecliptic north toward the summer solstice.  This diagram shows the Earth as viewed from ecliptic north.

If it were December, the left half of the Earth would be the daytime side; the right half would be night.  Notice that a hypothetical city on the equator (the green line) will spend 12 hours on the left half and then 12 hours on the right half.  A city at 30°N latitude (the third line north of the equator) will spend about 10 hours on the left and 14 on the right.  At 50° north of the equator, one spends about 8 hours on the left and 16 hours on the right.  At 60°N one spends about 6 hours on the left half and 18 on the right.  At 70°N, one is always on the right half (24 hours per day).  With this more exact model, I can now predict that on December 21, in a town 30° north of the equator, the sun will rise about 7:00AM and set about 5:00PM.

As you can see, time of day is dependent on where you are on Earth.  The time of day exactly where you are is called "local time".  The time of day at some agreed upon central point in a given region is called "standard time".  (Normally, the longitude of the central point is intentionally a multiple of 15°.  Good examples are US Eastern, Central, Mountain, and Pacific Standard Times; they are reckoned from 75, 90, 105, and 120 degrees west longitude respectively.) The time of day in Greenwich, England is called "Universal Time".  Many isolated persons set their watches to local time.  Many communities and nations (for the sake of having a common time) keep their watches set to a standard time in their region.  The World Wide Web and/or Internet generally use Universal Time (which can be thought of as standard time for the whole world).

From what we have learned, we can now try a sample problem.
Q: What time does the sun rise in Tokyo, Japan on June 21, 2000?
A: First you would use a map to find that Tokyo is at approximately 36°N latitude.  Then you can approximate that Tokyo spends about 14h40m on the right half (on June 21, the daytime half) of the Earth and about 9h20 on the left (night side).  Of this 9h20m, half is before midnight and half is after midnight.  Thus, about 4h40m after midnight, Tokyo passes from the left half of the Earth into the right half (i.e. the sun rises in Tokyo).  So sunrise is a 4:40AM local time.  Most persons in Tokyo, however, set their watches to a standard time reckoned from 135°E longitude.  Tokyo itself is at about 138°E.  Thus the standard time is about 3° (or 12 minutes) behind Tokyo (behind because the Earth is turning to the East).  Therefore the sun will rise at about 4:28AM standard time.

At this point, I think it would be useful to introduce some technical terms often used in astronomy.  These definitions are not complicated; it just makes things simpler if we can use fewer words to describe the same thing.

· north celestial pole: the direction in which the counterclockwise end of the Earth's axis of rotation points, the direction from the center of the Earth to the Earth's north pole
· celestial equator: all directions perpendicular to the north celestial pole, all of the directions from the center of the Earth to the Earth's equator
· south celestial pole: the direction opposite the north celestial pole
· north ecliptic pole: the direction in which the counterclockwise end of the Earth's orbital axis points, one of the two directions from the center of the Sun perpendicular to the orbit of the Earth
· ecliptic: all directions perpendicular to the north ecliptic pole, all of the directions from the center of the sun to the orbit of the Earth
· south ecliptic pole: the direction opposite the north ecliptic pole
· latitude: angle between a location on the Earth and the equator of the Earth as measured from the center of the Earth, often designated by a number of degrees north or south of the equator
· longitude: angle between a location on the Earth and Greenwich, England as measured from the rotational axis of the Earth, often designated by a number of degrees east or west of Greenwich
· declination: angle between a direction (normally, the direction of an object as measured from the center of the Earth) and the celestial equator, often designated by a number of degrees north or south of the celestial equator, somewhat analogous to latitude
· right ascension: angle between a direction (normally, the direction of an object as measured from the center of the Earth) and the spring equinox as measured from the celestial poles, often designated by a number of hours east of the spring equinox, somewhat analogous to longitude except that longitude rotates with the earth (right ascension does not)
· ecliptic latitude: angle between a direction (normally, the direction of an object as measured from the center of the Earth) and the ecliptic, often designated by a number of degrees north or south of the ecliptic, somewhat analogous to declination except measured from the ecliptic instead of the celestial equator
· ecliptic longitude: angle between a direction (normally, the direction of an object as measured from the center of the Earth) and the spring equinox as measured from the ecliptic poles, often designated by a number of degrees east of the spring equinox, somewhat analogous to right ascension except that right ascension is measured from the celestial poles instead of the ecliptic poles