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# Altitude: Vertical Coordinate (page 2)

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Author: Janice VanCleave

1. Design an experiment to determine the altitude of the Sun without looking at the Sun. (Looking directly at the Sun can damage your eyes.) One way is to measure the shadow of an object cast by the Sun (see Figure 3.3). The object can be a dowel stuck vertically in the ground. Measure the length of the dowel above the ground and the length of the dowel's shadow at different times during the day. Use these measurements to find the tangent (in a right triangle, the ratio of the length of the side opposite an acute angle to the length of the angle's adjacent side). Then use the tangent table in Appendix 4 to find the angle. For example, if the dowel is 4 inches (10 cm) high, and its shadow is 11 inches (27.5 cm) long, the tangent (tan) of the Sun's altitude is:
tan = height of dowel ÷ length of shadow
= 4 inches (10 cm) ÷ 11 inches (27.5 cm)
= 0.364
2. In the tangent table, the angle with a tangent of 0.364 is 20°. So the Sun's altitude is 20.0° . Prepare a table like Table 3.1 to represent this method.

3. Design an experiment to represent the Sun's diurnal motion (apparent daily movement of a celestial body). One way is to use the altazimuth system, plotting the two coordinates, altitude and azimuth. Use the length of the dowel's shadow to determine the Sun's altitude. The azimuth of the Sun can be determined using the method in Chapter 4. Plot these two coordinates on a circle graph (see Figure 3.4). From measurements made during the day, you can extrapolate (make a logical estimate of the next value) the coordinates on the graph line to show the azimuth and altitude of the rising and setting Sun.

### Get the Facts

In the Northern Hemisphere, the Sun is at its highest altitude on or aboutJune 21 and at its lowest altitude on or about December 21. These times are called the summer solstice and winter solstice, respectively. How does Earth move in relation to the Sun to cause this apparent change in altitude? What and when are the equinoxes? For information, see Janice VanCleave's Geography/or Every Kid (New York: Wiley, 1993), pp. 126–128.

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