PHYSICS 127 - DESCRIPTIVE ASTRONOMY                                                                                                                 Observing Project #10

TELLING TIME BY THE MOON

Time keeping is essentially a process of keeping track of the position of the sun; hence any observation that serves to indicate the position of (i.e., the direction to) the sun at any instant can also serve as a way of estimating the time.  The moon offers one observational method of locating the sun, at least approximately.

The apparent phase of the moon depends upon the angle between the observer's line of sight, to the moon, and the direction of the rays of the sun.  This angle (angle θ in Figure 1) is also the angle, at the observer, between his lines of sight to the moon and the sun.  Figure 1 illustrates this relationship.  From the observed phase of the moon you can establish the angle θ.

Then, starting from your observed line of sight to the moon, directing your vision along a line that goes away from the moon exactly opposite to the direction of the cusps of the lunar crescent (see Figure 2), you estimate (or measure) this angle θ on the celestial sphere to arrive at the "line of sight" to the sun.  That is, estimating the angle θ away from the line of sight to the moon, as just described, gives you the direction in space to the sun at that time.

Now you compare this direction with the plane of your local celestial meridian (or horizon) to arrive at an estimate of the time.  The angle between the meridian plane and the solar direction (this angle being measured in a plane perpendicular to the earth's rotation axis) is a measure of the time elapsed since the sun crossed the meridian at noon--or how long it will be until the next noon crossing.  To convert angle to time we simply remember that 15° of angle corresponds to one hour of time, or one degree equals four minutes of time.  Some points of quick reference for making time estimates are:  sun on the meridian - noon; sun 90° west of the meridian (near the western horizon) - 6:00 pm; sun on the lower half of the meridian - midnight; and sun 90° east of the meridian (near the eastern horizon) - 6:00 am.  The time obtained by this method is, of course, local solar time, and it must be corrected to a standard meridian in order to convert it to the corresponding standard time or daylight saving time.  (See the instructions for using a sundial for the details of making this correction.)

To help in learning to estimate phase angles, Figure 3 shows how the thickness of the lunar crescent (or of the gibbous half of a gibbous moon) is related to the phase angle θ.