Search All of the Math Forum:
Views expressed in these public forums are not endorsed by
NCTM or The Math Forum.



project for high school student
Posted:
Nov 21, 2004 8:40 PM


Here is a possible project for a high school junior or senior who likes math and physics. It would need to be started in early December, and it would last until early January. It includes a chance to do some study and measurements in astronomy, and to make a presentation to the class or to a school extracurricular club. Course credit seems appropriate.
The times of sun rise and sun set exhibit some apparently strange behavior around the shortest and longest days of the year. According to standard time,
The sun sets earliest a few weeks before the shortest day of the year, and rises latest a few weeks after the shortest day of the year. The sun sets latest a few weeks after the longest day of the year, and rises earliest a few weeks before the longest day of the year. These effects are quite noticeable to a person who is outside at the same time every day. The exact amount of "a few weeks" depends mainly on the observer's latitude, and changes very slightly from year to year. In the continental United States, it is about 2 weeks.
These effects are caused mainly by the inclination of Earth's axis of rotation, with respect to the perpendicular to the plane of Earth's orbit around the sun. There also is some minor effect from the eccentricity of Earth's orbit around the sun. The times also are affected slightly by atmospheric refraction, and by the observer's elevation.
An interested student can note the time and azimuth of sunset every day, beginning in late November, and continuing through early January. Then the student can compute the expected times and azimuths from solar data, compare the expected values with the observed values, explain the effects, and make a presentation to his class, or to his school science or math or astronomy club, or to a high school science fair. The solar data can come from an ephemeris, or from US Naval Observatory Web pages of varying complexity according to how far the student wants to go into analysis.
Requirements are that the student be at home every late afternoon during that whole period, have an unobstructed view reasonably close to the horizon, and have clear weather most of the time. A Christmas vacation trip more than a few days long, would disqualify the student. The student will need to have studied (and liked) trigonometry, and must have access to good calculating power (a highend scientific calculator, or spreadsheet software with scientific calculating power). The student will need to know his latitude and longitude, which generally are readily available. If the student and her faculty advisor are not familiar with this phenomenon, then probably considerable contact, preferably by telephone conferencecalling and fax, will be necessary.
There also are some apparently strange effects with the moon, like "harvest moon" during the summer and fall seasons; but those effects generally take much longer to observe, and are not as spectacular as the times of sun rise and sun set.
WARNING! Never, absolutely NEVER, look at the sun without proper eye protection. To do so, can cause severe and permanent eye damage.
Dick Alvarez alvarez at alumni dot caltech dot edu
 submissions: post to k12.ed.math or email to k12math@k12groups.org private email to the k12.ed.math moderator: kemmoderator@k12groups.org newsgroup website: <a href="http://www.thinkspot.net/k12math/">http://www.thinkspot.net/k12math/</a> newsgroup charter: <a href="http://www.thinkspot.net/k12math/charter.html">http://www.thinkspot.net/k12math/charter.html</a>



