Note: This was originally written just before the 2006 spring equinox.
The following are some notes on tomorrow's spring equinox that may be of use for science teachers. These notes explain how to relate the altitude of the Sun to a student's latitude.
You will need to run a detailed ephemeris for your location using the USNO Astronomical Department's Complete Sun and Moon Data for One Day or the Jet Propulsion Laboratory's Horizon's system. The easiest method of finding the time of solar transit discussed below is to go to the USNO USNO Astronomical Applications page and their "Complete Sun and Moon Data for One Day" web application. In USNO "Form A" select your state and type in your nearest large city. A typical report display looks like this:
============ SUN Begin civil twilight 6:04 a.m. Sunrise 6:31 a.m. Sun transit 12:35 p.m. Sunset 6:40 p.m. End civil twilight 7:07 p.m. ============
The time to measure the Sun, as discussed below, is the "local Sun transits".
The spring equinox is tomorrow, 3/20/2006 at 18:26 UTC (11:26 MDT).
The NASA/JPL Horizons Ephemeris shows that astrometric equinox - when the Sun crosses 0 deg ecliptic longitude - is between 18:25 and 18:26 UT:
Date/Time Az/Alt Eclip Long Lat Local solar time 2006-Mar-20 18:25 154.2263 46.2549 359.9995381 -0.0018950 10 49 00.7171 2006-Mar-20 18:26 154.5682 46.3370 000.0002209 -0.0018920 10 50 00.7313
My local transit of the Sun on the equinox - the topocentric equinox - occurs later at 19:34-19:35 UT (12:34-12:35 pm MDT):
Date/Time Az/Alt Eclip Long Lat Local solar time 2006-Mar-20 19:34 179.6279 49.2600 0.0466343 -0.0016771 11 59 01.7169 2006-Mar-20 19:35 180.0111 49.2608 0.0473167 -0.0016739 12 00 01.7312 2006-Mar-20 19:36t 180.3942 49.2604 0.0479991 -0.0016706 12 01 01.7456
When the Sun makes its local transit on the equinox, your observing point's latitude (~ 41N degs in my case) is equal to 90 degrees (zenith) minus the altitude of the Sun, e.g. -
41 degs = 90 degs - 49 degs
At the time of the local transit of the Sun on the equinox, these angles can be demonstrated using a protractor with a string and hanging weight (like a bolt or nut) run through the center hole. The protractor is held so that the string hangs through the 90 degree mark. Then stick a pencil perpendicular to the protractor into the center hole. A fuzzy shadow will be cast by the Sun. To reduce the chance of eye injury, advise students to not sight along the protractor at the Sun. Measure angles indirectly using the pencil's shadow.
An accurately aligned north-south building edge (check with a compass) can also be used. Use the protractor to make a large graduated quarter circle on a piece of paper. Using the protractor with plumb bob, tape the graduated circle to the north-south side of the building. Hold a pencil perpendicular to the building and take a shadow measurement.
Degree of accuracy for such methods is ~ 1.0 - 3.0 degrees.
Thus, you can demonstrate the relationship between latitude and the equinox transit of the Sun. ( geo latitude = 90 - equinox transit altitude ).
At the equinoxes, the Sun rises and sets at azimuth 90 degrees (due East) and 270 degrees (due West). That the sun sets at due west can be illustrated using an accurately aligned east-west edge of a building, or two stakes driven in the ground aligned with a magnetic compass. Your magnetic declination (the degrees that you subtract or add to a compass heading to find the geographic direction, can be estimated from magnetic declination maps at this web site: http://disitron.com/freeresources/.
Another demonstration that can be done on the equinox uses a gnomon, a single stick driven in the ground. Or you can use any existing feature, like a basketball backboard, a street lamp or a flag pole.
The equinoxes are the only day of the year that the shadow cast by a gnomon moves in a straight east-west line. Go out at one or two hour intervals and mark the location of the shadow of the top of the gnomon on the ground with chalk. The line traced by the shadow will be a straight east-west line. If repeated in few weeks, the line traced by the gnomon's shadow will be curved.
At the spring equinox, the axis of the Earth is tangent to the Earth's orbit. The North Pole points away from the direction of the Earth's travel around the Sun. At the time of the local transit of the Sun on the equinox, the Earth's direction of travel is along the observer's local horizon east-west line - toward due West. At midnight on the day of the equinox, the Earth's direction of travel is along the observer's local east-west line - toward due East. At the autumnal equinox, the axis of the Earth is tangent to the Earth's orbit, but the North Pole points towards from the direction of the Earth's travel around the Sun.
Prepared by K. Fisher fisherka@csolutions.net 7/2006