PDA

View Full Version : The Real Science of Eratosthenes

sniffy
06-23-2017, 03:02 PM
http://climatehoax.ca/erato.htm

In the 1760s Charles Mason and Jeremiah Dixon surveyed a line of the same name. They found larger than normal systematic errors, which Henry Cavendish attributed to the gravitational pull of the Allegheny Mountains. Several years later Cavendish did a series of sensitive experiments to determine the gravitational constant, which is in every physics textbook. The journey from a line in the sand to the event horizon of a black hole started more the 2,000 years ago.

The Real Science of Eratosthenes (276-194 BC)

The connection between observation, logic, and calculation couldnt be better illustrated than by Eratotheness measurement of the circumference of the Earth.

We need a reference time and place; for this document it will be:
Toronto, Canada, latitude: 48 degrees, 42 minutes.
Summer Solstice, 2017, Wednesday June 21
Warning; Solar noontime (1:19 PM) is required when shadows fall exactly north.

Only two measurements are required, a stick and the length of its shadow.

Eratostheness Method

Assume that the yellow rays of sunlight are parallel. One line strikes the equator and there is no shadow. Farther north, the black line casts a shadow. The black line crosses two parallel lines so that the shaded angles are congruent to each other.

http://climatehoax.ca/imageC/earth_sun.jpg

Example:
The Tropic of Cancer is about 23.4 degrees north. The distance to the equator is 1617 miles. Circumference of the Earth is
1617 x 360 / 23.4 = 24,877 miles

Data and Calculations

We need the distance between Toronto and the tropic of Cancer,
43 42  23 27 = 20.25 degrees. Since there are 69.1 miles per degree the distance is 1400 miles.

Stick: 115.1 cm

Tangent is 42.7 / 115.1 = 0.371
Angle is arctangent (0.3695652) = 20.354 degrees

Circumference is distance x 360 / 20.354
= 1400 x 17.687
= 24,762 miles which is about 100 miles less than the meridional circumference.

Appendix

Why do we see difference values for the Earths equatorial circumference on the internet?

This value is given by Wikipedia, <Earth> 40 075.017 kilometers, and since 1 km = 0.621371 mile we have, circumference = 24,901.45 miles.

If we use 1 km = 0.621 the value is 24,886.59 which is off by about 14 miles.

News Headline Oct 1, 1999: NASA lost its \$125 million Mars Climate Orbiter because of conversion from metric to imperial units. Whoops!