The Moon's Orbit: Worksheet #2

 Fall 2005 ASTR 110L, Sec. 2 Name: ________________

 Date Diameter: d Distance: D 09/06 19:43 ____________ ____________ 09/07 21:00 ____________ ____________ 09/09 18:53 ____________ ____________ 09/12 21:18 ____________ ____________ 09/16 20:17 ____________ ____________ 09/19 23:40 ____________ ____________ 09/22 05:11 ____________ ____________ 09/25 04:13 ____________ ____________ 09/27 05:40 ____________ ____________ 09/27 05:53 ____________ ____________ 09/28 05:10 ____________ ____________ 09/28 05:12 ____________ ____________ 10/04 18:53 ____________ ____________ 10/07 19:10 ____________ ____________ 10/07 19:11 ____________ ____________ 10/10 20:07 ____________ ____________
 Date Diameter: d Distance: D 10/12 21:00 ____________ ____________ 10/13 21:29 ____________ ____________ 10/16 21:01 ____________ ____________ 10/20 06:39 ____________ ____________ 10/24 06:17 ____________ ____________ 10/26 06:22 ____________ ____________ 10/28 05:56 ____________ ____________ 10/28 05:59 ____________ ____________ 10/29 10:31 ____________ ____________ 11/06 20:56 ____________ ____________ 11/06 20:58 ____________ ____________ 11/08 20:24 ____________ ____________ 11/12 00:20 ____________ ____________ 11/16 21:00 ____________ ____________ 11/17 23:20 ____________ ____________ 11/20 06:20 ____________ ____________

INSTRUCTIONS

First, copy the `Average diameter' values for 09/07, 10/12, and 11/16 from Worksheet #1 to the `Diameter' column for those dates here.

Second, measure the Moon's diameter, d, on the Moon photographs 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 09/06 photograph the Moon's diameter is 10.6 cm; if you had measured the diameter at the telescope that night you would have found 10.6 mm, so write `10.6 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. Note that the observation from 10/04 is very unreliable, so discount the data for that date in sketching your curve; you may also want to discount other data points if they seem incorrect. Lightly cross out any points you discount.

Fifth, draw vertical lines on your plot to mark new and full Moons. The Moon was full on 9/17 at 16:01 HT, 10/17 at 2:14 HT, and 11/15 at 14:57 HT; it was new on 10/03 at 0:28 HT and 11/01 at 15:25 HT.

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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