Geometry and the Cause of the Seasons: The Changing Hours of Daylight and Elevation Angle of the Sun at Noon

Autor/in	Greenwood, Margaret Stautberg
Titel	Geometry and the Cause of the Seasons: The Changing Hours of Daylight and Elevation Angle of the Sun at Noon
Quelle	In: Physics Teacher, 60 (2022) 8, S.694-698 (5 Seiten)Infoseite zur Zeitschrift PDF als Volltext Verfügbarkeit
Sprache	englisch
Dokumenttyp	gedruckt; online; Zeitschriftenaufsatz
ISSN	0031-921X
Schlagwörter	Geometry; Light; Physics; Astronomy; Washington + Suchen Sie Ihr Suchwort? Geometrie; Licht; Physik; Astronomie
Abstract	From my home on the west bank of the Columbia River in Richland, Washington (46.3°N latitude), I have an unobstructed view of the sunrise along the east bank during an entire year. As a retirement project after a career of teaching and research in physics, I decided to take photographs of the sunrise for a year and, and at the same time, carry out calculations to determine 1) the hours of daylight on a given day and 2) the elevation angle of the Sun at noon. My goal is to use geometrical diagrams along with a simplified model so that results are very easy to understand. In this model, the spherical Earth revolves around the Sun in a circular orbit, and the parallel sunbeam striking Earth is directed along a line connecting their centers. However, Earth's axis of rotation maintains the same direction throughout its motion around the Sun, which causes the seasons and the variations that we observe. My article entitled "95 Sunrises along the Columbia Riverbank" has recently been published on "Sky and Telescope's" website Stargazers Corner, where collages of the sunrise photos show the path of the sunrise along the east bank. The distance of a sunrise on a given date from that on December 21 shows a sine wave behavior that is expected for such a periodic occurrence. My calculations have been completed using the simplified model. While the direction of the Sun's rays on Earth does change gradually by 0.986° (360°/365 d) during 24 h, the model further assumes that the direction of the Sun's rays on Earth remains constant during a single day, but changes by 0.986° each day. This paper will show how information from two geometrical diagrams can be used to determine the number of daylight hours (defined as the time between sunrise and sunset) and the elevation angle of the Sun at noon. These calculations show a small difference of about 0.2% to 2%, when compared with precisely calculated values available on the internet that include many small corrections to the basic theory. Trigonometry is the highest mathematical level in this paper. A literature search was carried out to find related articles and texts. Many websites on the internet provide a great deal of information about the times of sunrise and sunset for a given location and about the solar elevation angle at noon at any time and location. The algorithms used to determine these values are explained by Meeus. Refs. 2-4 also describe algorithms for very precise calculations should the reader wish a comparison. (As Provided).
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Erfasst von	ERIC (Education Resources Information Center), Washington, DC
Update	2024/1/01