Finding location and direction using the sun

• Our objectives include learing to utilize the sun
• learning the suns movement

ABOUT: global coordinates

These days, one finds one's location on a map or using global
positioning satellites.  It is possible to use simpler means to
find one's global position.



FINDING ONE'S GLOBAL POSITION WITH THE SUN

This approach to find one's longitude and latitude requires minimal
equipment.  It does require two days.

Setup:

Find a very flat surface.  A large room with a South facing
window (North in the Southern Hemisphere) is perfect. Tape a
black piece of paper with a hole in it on a chair near the
window. The hole in the paper should be about 1/4" or (6mm). The
hole should be about 3 to 4 feet (one meter) above the floor.
Make sure the sun will be able to hit the hole throughout the
day, and the chair's position won't move for 2 days.  Draw a X on
the floor directly below the hole.  A string with a weight can be
used to find the spot for the X.

Day 1

Mark X's on the floor, where the center of the light-spot hits
the floor, throughout the day. (use a pencil or a marker that can
be cleaned up later).  The X's will make an rough EAST-WEST arc.  At
the end of the day draw a perpendicular line through the East-
West arc which intersects the X below the hole.  This line will
be the NORTH-SOUTH line. Look here for an even more
accurate method.

Day 2

Be ready  for this measurement close to noon local time. (Usually
between 11:30 and 12:30).  When the light-spot crosses the NORTH-
SOUTH line, record the time, and make an X on the floor.  The
time should be converted to UT (Universal Time at the prime
meridian.  This used to be called Greenwich Mean Time or Zulu
Time). Add five hours for EST, six hours for CST, seven hours for MST,
and eight hours for PST.  Measure the distance from the X (at 
NORTH-SOUTH crossing) to the X under the hole.  Measure the height
of the center of the hole above the floor.

CALCULATIONS

LONGITUDE

Your WEST longitude in degrees should be equal to 15 times the UT
in hours - 12.
     eg. if the measured UT was 18hrs and 48 minutes (18.8 hours)
         then your longitude is 15 x (18.8-12) = 102 degrees WEST

If the longitude is greater than 180, the convention is to
convert it to EAST longitude by subtracting your result from 360.
     eg. if the WEST longitude is 200 degrees, the EAST longitude 
         = 360 - 200 = 160 degrees
If the longitude is less than zero, multiply times - 1 to get the
EAST longitude

NOTE:
This method will have a small error introduced because Universal 
Time relates to the mean solar day.  There is a way to correct
for this error.


LATITUDE
This is a little more complex.

The angle the sun made to horizontal is equal to the arctangent
of the height of the hole divided by the distance between the two
X's.  You can find this angle from a trigonometry table or using
a scientific calculator.
eg:  X to X = 45"
     hole height = 36"  
     angle = arctan ( 36/45) = 38.66 degrees

Since the sun's ecliptic coordinate changes through the year, ie.
the sun is higher is the sky in the summer,  one must know the
sun's position to calculate one's latitude.

Here is a table of the sun's equitorial coordinates:

The dates are local in New Mexico, at noon
 
TABLE



To find the latitude at your observing position use the
following:

Northern Hemisphere:

     90 + sun's declination - measured angle from horizontal = NORTH
     latitude of your site.

     eg. if the angle = 38.66 degrees on January 25th 

     latitude = 90 + (-19.14) - 38.66 = 32.2 degrees

Southern Hemisphere:

     90 - sun's latitude - measured angle from horizontal = SOUTH
     latitude of your site