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# Angular Separation: Angular Distance between Celestial Bodies (page 3)

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Author: Janice VanCleave

1. Design an experiment to test the accuracy of the cross-staff in measuring angular separation between celestial bodies. For example, you might measure the angular separation of some of the stars in the Big Dipper, such as separation A shown in Figure 2.4 from Alkaid to Dubhe, separation B from Megrez to Dubhe, and separation C from Dubhe to Polaris. Record your measurements in a table like Table 2.2. If it is too dark to read your cross-staff, stand with the light from a building behind you. Make five measurements for each separation and average them. Compare your average with known angular separations given and record the difference. If the difference is more than the known value, record a positive (+) error. If the difference is less, record a negative (–) error. For more information about the angles between the stars of the Big Dipper, see Terence Dickinson, Night Watch (Willowdale, Ontario: Firefly Books, 1998), p. 30.
2. Design an experiment to determine if the angular separation of celestial bodies changes. Perhaps you can repeat the measurements between the stars of the Big Dipper at different times in one night or at the same time on different nights.
3. Use your cross-staff to measure the angular diameter of a celestial body such as the Moon. Since the Moon's diameter appears to be relatively small, use the smaller notch, S2, on the left side of the crosspiece. If it is not a full moon, measure the Moon's height rather than its width. Compare this method with the method you used in Chapter 1, "Apparent Diameter."

### Get the Facts

The cross-staff was the first practical instrument for measuring the altitude of the Sun from the deck of a ship. The cross-staff measured the distance between the horizon and the Sun quite well, but it had problems. The user had to look directly at the Sun, risking eye damage or blindness. Another problem was aligning the crosspiece so that one end appeared to touch the Sun while the other touched the horizon. In 1594, John Davis (1550–1605), a British navigator, published his book The Seaman's Secrets, in which he described an improved instrument called the backstaff. What advantages did the backstaff have over the crossstaff? How were these two instruments different? For information about these and other navigational instruments, see Richard Moeschl, Exploring the Sky (Chicago: Chicago Review Press, 1993), pp. 115–123. Another resource is Dennis Fisher, Latitude Hooks and Azmuth Rings: How to Build and Use 18 Traditional Navigational Instruments (New York: TAB/McGraw-Hill, 1994).

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