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Topic: project for high school student
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Richard Alvarez

Posts: 4
Registered: 12/6/04
project for high school student
Posted: Nov 21, 2004 8:40 PM
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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 sun-set
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

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 high-end scientific calculator, or
spread-sheet 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 conference-calling
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

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