ARC_CALC_3   —   Spherical Trigonometry Calculator by James Q. Jacobs

Finding the shortest distance between two points on the earth given latitude and longitude

Download ARC_CALC_3 
This small program will do spherical trigonometry calculations (shown below) in an Excel spreadsheet. You only need to input the coordinates. 

The program supports input of three sites and calculates the three arc distances, the area of the spherical triangle and the bearings between sites.

Arc Distance Formula (below)

Most spreadsheet programs should be able to import this file format.  The graphic below illustrates the spreadsheet, before corrections in 2002.  Previous downloads have "A to C" and "B to C" labels swapped for arcs and bearings. Please let me know if there are other bugs in the applet.

Epoch_Calc Temporal Epoch Calculator is a similar Excel spreadsheet.  It calculates
the temporal changes in astronomic constants,  just enter a date.



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The oldest exact astronomic constant?
Archaeogeodesy Pages
Archaeogeodesy can be defined as that area of study encompassing prehistoric and ancient
place determination, point positioning, astronomy, geodynamic phenomena, measure
and representation of the earth, and navigation (on land or water).

NEW: Google Earth™ Ancient Monuments Placemarks

" 11 Ahau was the katun when they carried on their backs. Then the land-surveyor first came; this was Ah Ppizte who measured the leagues. Then there came the chacté shrub for marking the leagues with their walking sticks. Then he came Uac-hab-nal to pull the weeds along the leagues, when Mizcit Ahau came to sweep clean the leagues, when the land-surveyor came. These were long leagues that he measured. ..."

"... the great mounds came to be built by the lineages and all the things which the rulers did. They were the ones who built the mounds. It took thirteen katuns and six years for them to construct them. The following was the beginning of the mounds they built. Fifteen four-hundreds were the scores of their mounds, and fifty more made the total count of the mounds they constructed all over the land. "

THE BOOK OF CHILAM BALAM OF CHUMAYEL, Ralph L. Roys, 1933, Carnegie Institution Washington D.C.

Newark Archaeogeodesy
Assessing Evidence of Geospatial Intelligence in the Americas

Spherical triangle with parts labeled.Spherical Trigonometry
Arc Distance Formulas

Note: a and b are distinct from a (alpha) and b (beta).

1. Find distances a and b in degrees from the pole.

2. Find angle P by arithmetic comparison of longitudes. (If angle P is greater than 180 degrees subtract angle P from 360 degrees.)

Subtract result from 180 degrees to find angle y.

3. Solve for 1/2 ( a - b ) and 1/2 ( a + b ) as follows:
tan 1/2 ( a - b ) = - { [ sin 1/2 ( a - b ) ] / [ sin 1/2 ( a + b ) ] } tan 1/2 y
tan 1/2 ( a + b ) = - { [ cos 1/2 ( a - b ) ] / [ cos 1/2 ( a + b ) ] } tan 1/2 y
4. Find c as follows:
tan 1/2 c = { [ sin 1/2 ( a + b ) ] x [ tan 1/2 ( a - b ) ] } / sin 1/2 ( a - b )
5. Find angles A and B as follows:
A = 180 - [ ( 1/2 a + b ) + ( 1/2 a - b ) ]
B = 180 - [ ( 1/2 a + b ) - ( 1/2 a - b ) ]

Download ARC_CALC_3 

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©2000 by James Q. Jacobs. All rights reserved.
Your comments, etc. are appreciated: Contact.
Published June 30, 2000.  Cite as