Problem

Sailors have used celestial navigation for centuries to find their way across the oceans....

Sailors have used celestial navigation for centuries to find their way across the oceans. For an observer on earth, the position of an object clockwise from true north and above the horizon can be measured by its azimuth and its altitude (see problems 1 and 2). Research celestial navigation and write a summary explaining how fixed stars are used. Why is Polaris important and what is its azimuth? Locate Polaris in the night sky and estimate its altitude. Locate a star pattern such as the Big Dipper and estimate the altitude and azimuth of each star in the pattern. Use the fact that the width of your thumbnail held at arm’s length is approximately 1°, and the width of your palm is approximately 10°. Create a diagram using your altitude and azimuth estimates that shows the horizon, Polaris, and each star in the pattern.

Problem 1

The azimuth of a line segment is the angle that the line segment makes with a north-south line. It is measured from 0° to 360° in a clockwise direction from the north. In the following example, the azimuth of is 250°.

Sketch with the following azimuths.

a. 115°
b. 225°
c. 72°
d. 329°25′

problem 2

For any location on the earth, the apparent position of the sun at any time can be given by its azimuth (see problem 3) and its altitude. The altitude is the angle of the sun measured up from the horizon. Because the sun is at the horizon at sunrise or sunset, we can ignore altitude at these times of day and use just azimuth to locate the sun. Use a circle as shown to represent the horizon and locate the apparent positions of the sun at sunrise and sunset for the following cities on July 1, 2006.

a. Oslo, Norway: sunrise at 3:03 AM, azimuth 36.7°; sunset at 9:38 PM, azimuth 323.1°
b. Cuiaba, Brazil: sunrise at 6:07 AM, azimuth 66.8°; sunset at 5:48 PM, azimuth 293.2°
c. Ushuaia, Tierra del Fuego: sunrise at 9:00 AM, azimuth 48.1°; sunset at 4:14 PM, azimuth 311.7°

Problem 3

The azimuth of a line segment is the angle that the line segment makes with a north-south line. It is measured from 0° to 360° in a clockwise direction from the north. In the following example, the azimuth of is 250°.