# The Sidereal Period of the Moon

Objective: To determine the sidereal period of the moon by simple means.

Theory: The amount of time it takes the moon to orbit the Earth and appear at the same place on the Celestial Sphere is called the sidereal period of the moon. This amount of time is not the same as the lunar month. The lunar month is the amount of time between successive new moons, or full moons, or any two successive, similar phases. Phases of the moon, however, depend on the relative positions of the Earth, moon, and Sun. Since the Earth is orbiting the Sun, these alignments occur at different absolute places in the moon's orbit each month.

Figure 1

The diagram in figure 1 may help explain the difference between the lunar (also called the synodic) period and the sidereal period. At new moon number one (position A) we mark the position of the Sun (or moon since they are the same) on the sky. Imagine that a bright star is in the same line of sight. Notice that because of the Earth's orbital motion, when the moon lines up with that star the next month (position B), it is not yet new moon (position C). From A around the moon's orbit to B is the sidereal period (think with respect to the stars), while from A all the way to C is the synodic period.

We intend to measure the sidereal period of the moon by noting how the moon moves with respect to a nearby star. From night to night the moon moves roughly 13° toward the east. This causes the moon to rise roughly 52 minutes later each day. These are average values, however, which are useful in judging when you have to observe. The observations are best obtained near the first quarter moon, when the moon is visible in the early evening sky. First quarter moon occurs on 19 October. Observations near the full moon are more difficult since the moonlight washes out the sky. Full moon occurs on 26 October. Prime observing time then is now until 24 October.

Imagine that on night one we find a bright star near the moon as in figure 2. On the second night the situation is like figure 3.

Figure 2

Figure 3

Let us assume that the two measurements were made 24 hours apart for simplicity. We can set up a ratio to tell us how long it takes the moon to return to the position of figure 2. Notice that in the 24 hours the moon moved 12°. Then

time for 360° = (1 day)*360°/12°= 30 days

More generally,

Sidereal period = (Elapsed Time)*360°/(Change in angle)

Procedure:

We would like to measure the angular separation between the moon and a bright star on two consecutive nights. Use your crosstaff for these angular measurements. If clouds interfere on night two, you can use a time interval of two days, but do not extend beyond that.

1. Calendar Date ______________ Time ____________

Sky conditions __________________________________

Lunar phase ______________

Find a reasonably bright star near the moon and the ecliptic and measure its separation from the moon. Try to measure from the star to the center of the moon. The star can fall on either side (east or west) of the moon. Place the moon as accurately as you can on the SC-1 constellation chart. Copy this portion of the chart as well as the position of the moon onto a blank sheet of paper. Label enough stars so that it is clear where you are. Measure the angular separation using the angular scales on the SC-1.

Angular separation using crosstaff _____________

Angular separation using SC-1 ___________

2. Calendar Date ______________ Time ____________

Sky conditions __________________________________

Lunar phase ______________

Identify the same star you used on night one, measure its angular separation from the moon, transfer its position to the SC-1, then to you sheet of paper, and measure its angular separation on the sheet of paper.

Angular separation using crosstaff _____________

Angular separation using SC-1 ___________

Change in angle ________________ (degrees)

Elapsed time __________________ (hours)

Elapsed time ___________________ (days)

Sidereal period of the moon ___________________ (days)

The End...