The Moon's Orbit: Worksheet #2

Fall 2010 ASTR 110L, Sec. 1 Name: ________________
Date Diameter: d Distance: R/D
10-Sep 19:06 ____________ ______________
12-Sep 21:11 ____________ ______________
14-Sep _____ ____________ ______________
17-Sep 20:04 ____________ ______________
19-Sep 20:27 ____________ ______________
21-Sep _____ ____________ ______________
24-Sep 05:21 ____________ ______________
27-Sep 06:02 ____________ ______________
29-Sep 06:13 ____________ ______________
01-Oct 08:18 ____________ ______________
03-Oct 06:18 ____________ ______________
05-Oct 05:59 ____________ ______________
08-Oct 18:47 ____________ ______________
10-Oct 20:03 ____________ ______________
12-Oct _____ ____________ ______________
14-Oct 20:17 ____________ ______________
Date Diameter: d Distance: R/D
16-Oct 18:41 ____________ ______________
19-Oct _____ ____________ ______________
21-Oct 01:30 ____________ ______________
23-Oct 22:27 ____________ ______________
26-Oct 05:52 ____________ ______________
28-Oct 06:04 ____________ ______________
30-Oct 06:12 ____________ ______________
02-Nov 05:50 ____________ ______________
08-Nov 19:01 ____________ ______________
10-Nov 20:34 ____________ ______________
13-Nov 18:38 ____________ ______________
15-Nov 22:00 ____________ ______________
17-Nov 20:06 ____________ ______________
19-Nov 19:19 ____________ ______________
21-Nov 21:01 ____________ ______________
23-Nov _____ ____________ ______________

INSTRUCTIONS

First, copy the `Average diameter' values for 14-Sep, 21-Sep, 12-Oct, and 19-Oct from Worksheet #1 to the `Diameter' column for those dates here. Fill in the actual times of your observations for these dates. (See me if you missed one or more of these observations.)

Second, measure the Moon's diameter, d, on the Moon photos in class. Compared to the images we measured directly at the telescopes, these photos have been magnified 10 times; thus 1 cm in the photos is equal to 1 mm at the telescopes. You can therefore measure image diameters in centimeters on the photos, and convert your results directly to the diameters measured in millimeters at the telescopes. For example, on the 10-Sep photo the Moon's diameter is 11.6 cm; if you had measured the diameter at the telescope that night you would have found 11.6 mm, so write `11.6 mm' for the Moon's diameter on that date.

Third, once you have measured all the diameters, compute the Moon's distance, R/D, using the formula

R/D = F ÷ d  .

Here F = 1200 mm is the focal length of the telescope's main mirror. Because d and F both have units of millimeters, R/D is a pure number — the units of d and F cancel out. In fact, R/D is the Moon's distance in units of the Moon's actual diameter.

Fourth, plot R/D versus date on the chart provided with this handout. Try to plot each distance and date as accurately as you can, taking account of the time each observation was made. Once you have plotted all the data, lightly sketch a smooth curve passing close to the data points.

Once you've completed your plot, answer these questions:

1. Your plot should show the Moon reaching apogee (greatest distance from Earth) three times in total. Mark those times with a small `a'. Note the dashed lines labeled `F' on the plot; these show when the Moon was full (likewise, the lines labeled `N' show when the Moon was new). Does apogee always occur at full Moon?

2. Two images, taken 05-Oct and 02-Nov, show the Moon very close to perigee (smallest distance from Earth). Are these two perigees the same, or is one a little closer than the other? If so, which one?

3. Suppose the Moon's orbit was an ellipse with the Earth at the center, rather than at one focus. How would your plot look in this case?
Joshua E. Barnes      (barnes at ifa.hawaii.edu)
Updated: 23 November 2010
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