# The Moon's Orbit: Worksheet #2

 Fall 2008 ASTR 110L, Sec. 1 Name: ________________

 Date Diameter: d Distance: D 25-Aug 21:00 ____________ ____________ 29-Aug 09:00 ____________ ____________ 01-Sep 21:00 ____________ ____________ 05-Sep 09:00 ____________ ____________ 08-Sep _____ ____________ ____________ 12-Sep 09:00 ____________ ____________ 15-Sep _____ ____________ ____________ 19-Sep 09:00 ____________ ____________ 22-Sep 21:00 ____________ ____________ 26-Sep 09:00 ____________ ____________ 29-Sep 21:00 ____________ ____________ 03-Oct 09:00 ____________ ____________ 06-Oct _____ ____________ ____________ 10-Oct 09:00 ____________ ____________ 13-Oct 21:00 ____________ ____________ 17-Oct 09:00 ____________ ____________
 Date Diameter: d Distance: D 20-Oct 21:00 ____________ ____________ 24-Oct 09:00 ____________ ____________ 27-Oct 21:00 ____________ ____________ 31-Oct 09:00 ____________ ____________ 03-Nov _____ ____________ ____________ 07-Nov 09:00 ____________ ____________ 10-Nov _____ ____________ ____________ 14-Nov 09:00 ____________ ____________ 17-Nov 21:00 ____________ ____________ 21-Nov 09:00 ____________ ____________ 24-Nov 21:00 ____________ ____________ 28-Nov 09:00 ____________ ____________ 01-Dec 21:00 ____________ ____________ 05-Dec 09:00 ____________ ____________ 08-Dec 21:00 ____________ ____________

### INSTRUCTIONS

First, copy the `Average diameter' values for 08-Sep, 15-Sep, 06-Oct, 03-Nov, and 10-Nov 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 images in class. Note that 1 cm in the photos is equal to 1 mm on the focal plane of our telescopes. You can therefore measure image diameters in centimeters on the photos, and compare your results directly to the diameters measured in millimeters at the telescopes. For example, on the 25-Aug image the Moon's diameter is 11.2 cm; if you had measured the diameter at the telescope that night you would have found 11.2 mm, so write `11.2 mm' for the Moon's diameter on that date.

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

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, D is a pure number — the units of d and F cancel out. In fact, D is the Moon's distance in units of the Moon's actual diameter.

Fourth, plot 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.

Fifth, draw vertical lines on your plot to mark new and full Moons. The Moon was full on 14-Sep at 23:13 HST, 14-Oct at 19:02 HST, and 12-Nov at 20:17 HST; it was new on 29-Aug at 09:58 HST, 28-Sep at 22:12 HST, 28-Oct at 13:14 HST, and 27-Nov at 06:55 HST.

1. Your plot should show the Moon reaching perigee (instant of closest approach) three times in total. Mark those times with a small `p'. Does perigee always occur at full Moon?

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2. Measure (to the nearest third of a day) the number of days between the first and second perigees, and between the second and third perigees. Do you get the same result each time?

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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?

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 Joshua E. Barnes      (barnes at ifa.hawaii.edu) Updated: 24 November 2008 http://www.ifa.hawaii.edu/~barnes/ast110l_f08/moonorbit_ws2.html