With the recognition of diurnal phenomena, one can tell the time from the changing height of the Sun or, at night, of certain stars above eastern or western horizons.

Example: Aboriginies and European peasants (before the development of church clocks) were able to determine the time from the Sun (except on cloudy days!). Sailors, too, might learn to tell time at night by the height of the stars.

A stick in the ground that is vertical and placed so that the Sun can cast its shadow on the ground is called a gnomon. The shadow will fall on the ground in the opposite direction to the Sun, so that if the Sun rises to the southeast of the gnomon, then the gnomon's shadow will fall to the northwest. Its length will be greatest when the Sun is closest to the horizon; i.e., at sunrise or sunset it would reach infinity. Its length will be shortest when the Sun reaches its highest altitude in the sky; i.e., when the Sun crosses the meridian, which is "local noon." At that moment the Sun will be due south of the gnomon, and the gnomon's shadow will point due north.

Each hour a given celestial body such as the Sun (or a star) should shift its position by about 15 degrees (360 degrees ÷ 24 hours = 15 degrees/hr) due to the daily motion alone. This angle can be determined (and found to be roughly constant) for the Sun with a sundial. Note that since the angular diameter of the Sun is about 1/2 degrees, the Sun shifts its position by an angular distance equal to its own diameter every two minutes (1/2 degrees x 60 min/15 degrees = 2 min).

- 1. How can one tell when a stick or pole is exactly vertical?
- 2. At what time is a shadow cast by the Sun the shortest?
- 3. Where is the Sun when it is highest in the sky each day?
- 4. At what time is a shadow cast westward by the Sun the longest?
- 5. At what time is a shadow cast eastward by the Sun the longest?
- 6. Let the top of a pyramid serve as a gnomon. Explain how one could thereby orient the pyramid to the four cardinal directions (north, south, east, and west).
- 7. (a) In view of the daily motions discussed above, is there anything wrong with the narrative in Charles Dickens' Hard Times where Dickens places a dying man in the bottom of a deep vertical shaft, where the man finds solace in the light of a single star that shines down to him throughout the night?
- (b) If the field of view in a telescope is about one degree, then how long will it take for a given star to drift out of the field of view due to the Earth's daily motion, if the telescope is held stationary?
- 8. Solve Crowe's Problem #1, p. 3. 1 For an introduction to sundials see Albert E. Waugh, Sundials: Their Theory and Construction (Dover, 1973), and Frank W. Cousins, Sundials (London: John Baker, 1969).