# LUNAR PHASES WEB TOOL 4. Going Beyond the Basics

Introduction | Tutorials: 1) Time of Day ; 2) Time of Month ; 3) Direction | TOOL AND QUIZ | Beyond the Basics | Credits | For Teachers

The main purpose of this web site is to introduce the lunar phases diagram above as a tool for answering questions like those in the quiz. For the curious student, however, answering a few questions leads to new ones. We have added this page, therefore, to list some of these questions, to sketch out brief answers, and to give some new key words that can be used as a starting point in searching reference materials for more complete answers.

• East and west are labeled on the diagram, but not north and south. Why not? The diagram shows the view from above the North pole. (If you look close, you can see the north polar ice cap and Greenland at the center of the Earth icon.) Hence for the diagram north is the direction out of the page. South is directed into the page.
• Looking at the diagram, it seems as if there should be a lunar eclipse each Full Moon and a solar eclipse each New Moon, but there aren't. Why not?
• First, the diagram is not to scale. The actual diameter of the Moon is only one-quarter that of the Earth, while the actual separation between the Earth and Moon is thirty times the diameter of the Earth.
• Second, the plane of the Moon's orbit is tilted 5° with respect to that of the Earth. Hence there is enough tilt and separation that the shadows usually miss completely. Eclipses can only occur during the two time periods each year when the New and Full Moons occur near the line of intersection between the two orbital planes (the line of nodes).
• In the images of the Moon as viewed from Earth, the surface markings all look the same. Does this mean the Moon does not rotate on its axis (the way the Earth does)? No, it means that the Moon's rotation is synchronized to its orbit, so that it rotates exactly once each orbit. If you look closely at the diagram, you will notice the markings on the Moons surrounding the Earth (the ones viewed from above the north pole) do shift, as they must in order to keep the same face towards the Earth at all times. This synchronization is a consequence of tidally-induced friction early in the history of the Earth-Moon system.

However, since the spin of the Moon proceeds at a uniform rate while the orbit is at a slightly nonuniform rate (see below), the spin can get a little bit ahead or behind the orbit. Hence the face of the Moon presented to the Earth rocks back and forth by some 6° each month, a phenomenon known as longitudinal libration.

### Now that I have mastered the lunar phases diagram, what do I really know that I didn't know before?

• We began in the introduction with some assumptions (about the shape of the Moon and so forth). We then worked with these assumptions to understand what predictions they make (about the apparent shape and direction of the Moon). Now you can take a new look at the Moon in the sky and ask yourself whether the predictions of our simple model really hold up. And if you find they do, then you will have demonstrated for yourself that our assumptions are indeed a powerful description of the phenomenon. You no longer have to take the word of your teacher or a textbook author.
• You can actually use your own observation of the Moon's shape and direction to tell the time of day. OK, this is less exact than using a quartz wristwatch, but it is an approach that people have used for thousands of years, and there is absolutely no purchase required. Notice as you read fiction how many authors use such observations as a way for their characters to determine the time of day. (For example, this is used many times by J.R.R. Tolkien in "The Lord of the Rings.") Notice, too, how some authors who have not quite mastered the lunar phases occasionally describe impossible combinations of lunar phase, direction, and time of day!

### The nice round numbers in the web tool menus seem a little too exact. Is this really the way it works?

• The Sun doesn't really rise and set at precisely 6 am and 6 pm, does it? Well, not precisely. In fact, there are 4 reasons why it should not.
• Time zones: In principle, local time should depend on the longitude. However, in order to avoid having to adjust your watch every time you drive a short distance east or west, a system of time zones have been set up. Typically these are about 15° wide, so someone living on the eastern edge of a time zone will see the Sun rise about one hour earlier than someone on the western edge. This offset is a constant amount over time.
• The tilt of the Earth: The spin axis of the Earth is tilted with respect to the axis of its plane of orbit by 23.5°. Because of this, for example, the Sun appears 23.5° higher in the sky at noon on midsummer's day than at the vernal equinox. This results in earlier sunrises and later sunsets. This offset varies with the season.
• The latitude of the observer: The latitude of the observer, north or south and how far, will modify the amplitude of the effect caused by the tilt of the Earth. The offsets are more extreme as you move away from the equator, and they have opposite signs in the two hemispheres. Hence midsummer's day is in December in the southern hemisphere, but in June in the northern hemisphere.
• The variable speed of the Earth: The Earth's orbit around the Sun is slightly eccentric, carrying us closer to the Sun each January, and further each July. Conservation of angular momentum requires that our angular speed is therefore greater in January than in July. This leads to an annual shift in the times of sunrise and sunset. They both occur progressively later when the angular speed is high, and earlier when it is low. The tilt of the Earth also modifies this effect on a twice-annual basis. The combined effect is known as the equation of time.
• Are there a similar set of offsets for the Moon's motion as well? Yes. The observer's position within a time zone and his or her latitude affect the direction to the Moon in the same way as that to the Sun. The other two effects also have their equivalents:
• The Moon's orbital plane: The plane of the Moon's orbit is tilted by 5° with respect to that of the Earth's orbit. Hence the rotation axis of the Earth is tilted with respect to the Moon's orbital plane by an amount within 5° of 23.5°, depending on whether the two tilts are in or out of phase. The bottom line is that the length of time between moonrise and moonset for, say, a full Moon varies with the season as well. (Also, note the phasing between the two tilts varies continually with time, going full circle every 18.6 years.)
• The variable speed of the Moon: Like the Earth, the Moon moves in a slightly elliptical orbit as well. Hence, while the average time elapsed from, say, New Moon to First Quarter is 7.4 days, the actual time can be as short as 6.7 days near perigee (closest approach to Earth) or as long as 8.1 days near apogee.