Hello Axel,
I think you have made a mistake with the number 40231.264 (miles?).
If you take the formula for size of a latitude degree, as you stated:
dx/d theta = 111.133+0.559*cos(2*theta) km per degree latitude
if we integrate this formula with respect to theta from 0 to 360
X = 111.133 * ( 360 - 0) + 2*0.559 * (sin(2 * 360) - sin (2 * 0))
the two terms with sin equate to 0, so
X = 360 * 111.133
= 40007.88 km
Cheers
Hank
________________________________
From: sundial-boun...@uni-koeln.de [mailto:sundial-boun...@uni-koeln.de] On
Behalf Of axel törnvall gonzalez
Sent: Monday, 19 March 2012 11:42
To: Sundials
Subject: Eratosthenes
I am studying a subject related to the Greek Eratosthenes, as measured by the
circumference of the earth, but I have a problem with measuring the distance
between 2 points (coordinates) formulas I used were taken from writings of Carl
Sabanski, who says that books are ancient astronomy. No further information;
1 ° latitude = 111,133 to 0,559 cos (2 x latitude) [km]
1 ° longitude = 111,413 cosine (latitude) - 0.094 cos (3 x latitude) [km]
By calculation using the formula 1 ° latitude, for each grade, from 0 ° to 90 °
for the southern hemisphere and 1 ° to 90 ° for the northern hemisphere the
result is 40,231.264 miles, and as I read the value is 40,009.15 km
I have not found more formulas or ways of doing the calculation to get a better
result.
I will thank answers
Best Regards
Axel
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