Clock Time vs. Sun Time: The Analemma (UMAP)

In this module equations are constructed for the position of the sun in the sky at any time of day, any day of the year, as seen from any latitude. From this, an explanation of the figure-8 pattern that the sun follows annually (the analemma) is developed. The equations also predict sunrise and sunset times; these, together with the analemma insight, show why earlier sunrise times do not start just after Winter Solstice. In constructing the equations, it is assumed that the earth's orbit about the sun is a circle and that the motion along the orbit is uniform. The sunrise predictions are used to assess the error caused by these assumptions.

Table of Contents:

INTRODUCTION

TWO-DIMENSIONAL MODEL: THE YEAR

TWO-DIMENSIOANL MODEL: THE DAY

THREE-DIMENSIONAL MODEL: THE YEAR

THREE-DIMENSIONAL MODEL: THE DAY

CIRCULAR ORBIT MODEL: CONSTRUCTIONS

THE EQUATION OF TIME

MODEL SUNRISE AND SUNSET TIMES

FURTHER DIRECTIONS

SOLUTIONS TO THE EXERCISES

REFERENCES

ACKNOWLEDGMENTS

ABOUT THE AUTHOR