astlmoon - Laboratory 6 The Orbit of the Moon Materials...

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41 Figure 2. Vernier Calipers. Laboratory 6 - The Orbit of the Moon Materials Used: Vernier caliper, moon photographs, Excel spreadsheet with Polar Plotter add-in. Objective: To measure the eccentricity of the Moon's orbit. Discussion: The Moon has a very low orbital eccentricity. Knowledge of the Moon’s slight variance from a circular orbit extends all the way back to the Classical age of astronomy. The Greeks were aware of small periodic changes in the Moon's size. We can compute the eccentricity for the Moon’s orbit by making the same observation as the Greeks, i.e., by noting the apparent change in the Moon’s diameter throughout a lunar cycle. Consider Figure 1 below. D is the apparent diameter of the Moon as viewed from Earth, θ the angle subtended by the Moon as viewed from Earth, and d the distance to the Moon. In this procedure we will measure D in a series of photographs and use this value to compute θ and d for each image and ultimately the eccentricity of the Moon’s orbit. The relationship: θ D d = will be used to compute the radius ( d ) of the Moon's orbit about the Earth for each image. We will use the small variances in d to compute the eccentricity of the Moon’s orbit about the Earth. Vernier Calipers Vernier scales are used to make precise measurements. Vernier devices employ dual scales to allow measurements with one digit greater accuracy than that afforded by ruled scales. A vernier caliper is a caliper with a vernier scale that measures the distance between the caliper arms. Figure 1 . The geometry of the arc length relationship.
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42 Figure 3.
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43 To use a set of vernier calipers the arms are spread to accommodate the item being measured and then closed until they just grasp the item along the desired dimension (the thumb dial in the center of Fig. 2 works well for this). The first digits of the measurement are read from
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