Observations Using the Gnomon

Table of Contents

• Objective
• Introduction
• Materials
• Procedure
• Glossary
• Home

Objective

The objectives are to study the use of the gnomon to determine the length of the year, the latitude, the obliquity of the ecliptic, and the declination of the sun.

Introduction

The gnomon was one of the first astronomical instruments. The Egyptians built decorated obelisks of gnomons to keep time. These were upright shafts of stone surrounded by the hours of the day written on horizontal surfaces. The hours were read like reading a sundial, noting the position of the shadow like an hour hand of a watch across a face marked in hourly increments. Unfortunately, this system of timekeeping was complicated by the fact that the same marks could not be used to measure the same hours of the day all year long.

Materials

• A gnomon consisting of a stake, preferably metal, that is several feet in length. Ideally, it should be cemented in a upright position level to the ground, using a plumb-bob or a carpenter's square to ensure that it is perfectly vertical. In a school, a flagpole is a convenient, yet not always accurate, gnomon. However, a long, wooden dowel or stick would suffice.
• A large protractor to measure the angle between the shadow and the ground or
• A table of trigonometric functions or
• A scientific calculator to calculate the angle
• A meter stick or measuring tape to measure the height of the gnomon and the length of its shadow
• A watch

Procedure

Observe the sun to determine the standard time of the local, apparent noon. A surveyor's transit can be used to do this by measuring the altitude of the sun as it approaches and leaves the meridian. The instant of the highest altitude is apparent noon. The direction of the sun at this moment (the azimuth) should also be noted because it is due south and the opposite direction is true north, although the observer must know his longitude and the equation of time.

This north-south direction can also be found by observing the shadow when it is the shortest. Do this by measuring from the north base of a perfectly vertical gnomon to the edge of its shadow. The shadow is not perfectly sharp because the sun is not a point of light but rather has a diameter of about one-half of a degree. Be consistent with measuring, being sure to measure the same part of the shadow each time.

To find the the shadow positions in relation to standard time, first note the standard time when the shadow is centered in the north-south line, marking with chalk the north end of the shadow. The sun's altitude can be measured by stretching a string from the top of the gnomon to the chalk dot and measuring the angle that it creates. This angle can also be computed with greater precision with trigonometry by using the tangent function with the gnomon as the opposite side and the shadow as the adjacent side.

Through observation, the position of the shadows can be found for the different hours throughout the year, noted in a notebook or chart, and eventually marked on the horizontal surface surrounding the gnomon.

Adapted from Laboratory Exercises in Introductory Astronomy by Huffer and Marasso, copyright 1967.

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