Expert: Philip Stahl - 10/29/2006

Question
I am working on a moon project for my Geoscience class in college.  I am really stuck with this question and can't seem to pinpoint an answer anywhere.  Here is the question as it is written on my sheet.

The sun always rises in the morning and sets in the evening.  The moon, other the other hand, rises and sets at any and all times of the day or night.  Why?  Is there any pattern to the changes in the times of moon rise and set?  What is that pattern?  Why does that pattern exist?

I am mosting having problems with why it can set at any time of the day.  I know the pattern is along the lines that it rises about 90 minutes later each day and that the new moon rises with the sun.  Any help would be most helpful.  

Thank you,
Becky

Answer
Hello.

Bear in mind the Moon's orbit around the Earth. Specifically, both revolve about a common center of mass. In fact, however, this center of mass is located inside the Earth - about 2960 mi. from its center. This can be deduced by using the fact that the ratio of the lunar mass to the Earth's is only 1/81. Hence, the center of mass of the system is 1/81 of the distance (from the Earth's center) of the Earth to the Moon.

This motion about the common mass center is such that the Moon makes one complete revolution in 27 1/3 days.

From this it is possible to obtain its approximate *mean motion*:

n =   360 deg/ (27 1/3 days)  ~  0.5 deg/ h

Which also amounts to just over 13 degrees in a 24 hour period (or one day on Earth).

Thus, as the Earth has rotated through 360 degrees on its axis, the Moon will have moved an additional 13 degrees, or in terms of time:

13/15  (60 mins.) = 52 mins.

Bearing in mind that every 15 degrees of Earth rotation is equivalent to 1 hour of time elapsed.

Thus, "90 mins. later each day" is flat wrong  - it is rather approximately 52 minutes later each day. Which we worked out using the Moon's mean period.

A general pattern to times of Moon rise and Moon set can be acquired from a simple consideration of the geometry, in terms of Moon phases.

For example, the 'New Moon' will always be interposed between the Sun and the Earth. The Earth revolves from W. to E. so that this means the 'New Moon' will tend to *rise* at dawn.

By contrast, the 'Full Moon' occurs 180 degrees in opposition to this (Earth now between the Sun and Moon) so will rise at sunset. (Or, roughly, 12 hrs (= 180 deg) from the New Moon position.

Based on these inferences, the rise and set times can also be deduced: e.g. the New Moon will set at sunset, the Full Moon will set at sunrise.

From this information, you should also be able to roughly deduce the rise and set times of the itnermediary phases (first and last quarter).

Now, from this it is obvious that neither Full Moons, nor New Moons can rise or set at "any time of day" but rather at least close to specific times as I noted. And this is because of specific geometry considerations.

Hopefully, this will prove useful - but I fear you may need a real astronomy course to really clarify the issues - as opposed to "geoscience."

Where they may not be as particular about these sort of issues, and evidently the care taken with the language to describe them either!