EvC Forum: Flat Earth Theory

I'm standing here looking out my tenth story window and ...... uh uh......it looks flat from here?

There is a fairly simple experiment that can be done:

(1) set up a stick so that it is exactly 5 ft (or some other selected dimension) above a flat surface with the stick vertical (set with a plumb-bob and with the surface perpendicular to the stick.

(2) measure the length of the shadow of the sun when the sun is highest in the sky (the shadow is the shortest) and record the time of day (measured in one place).

(3) repeat this for different latitudes and longitudes for the same day of the year in all places.

Predictions:

(1) If the flat earth hypothesis is correct they will all be the same length and occur at the same time of day (measured in one place).

(2) If the round earth hypothesis is correct:

(a) the time of day (measured in one place) when the shortest shadow is measurable will be the same for the same longitudes, but the length of the shadows will be different for different latitudes,
(b) the length of the shadows will be the same for the same latitudes, but the time of day (measured in one place) when the shortest shadow is measurable will be different for different longitudes (ie why we have different time zones), and
(c) when these differences are plotted out in 3D they will match little flat planes on the surface of a sphere.

This kind of calculation was done in a couple places by the greeks (and others iirc) and they calculated an approximate diameter for the size of the earth.

Eratosthenes - Wikipedia

quote:
The exact size of the stadion he used is no longer known; the common Attic stadion was about 185 m, which implies a circumference of 46620 km, i.e. 16% too large.

Not too shabby for a first approximation, especially given the level of accuracy of available instruments..

Aristarchus of Samos - Wikipedia

quote:
Aristarchus (310 BC - c. 230 BC) was a Greek astronomer and mathematician, born on the island of Samos, in ancient Greece. He is considered the first person to propose a scientific heliocentric model of the solar system, placing the Sun, not the Earth, at the center of the known universe (hence he is sometimes known as the "Greek Copernicus").

Aristarchus argued that the Sun, Moon, and Earth form a near right triangle at the moment of first or last quarter moon. He estimated that the angle was 87. Using correct geometry, but insufficiently accurate observational data, Aristarchus concluded that the Sun was 20 times farther away than the Moon. The true value of this angle is close to 89 50', and the Sun is actually about 390 times farther away. He pointed out that the Moon and Sun have nearly equal apparent angular sizes and therefore their diameters must be in proportion to their distances from Earth. He thus concluded that the diameter of the Sun was 20 times larger than the diameter of the Moon; which, although wrong, follows logically from his data. It also leads to the conclusion that the Sun's diameter is almost seven times greater than the Earth's, which can be taken to support the heliocentric model: the volume of Aristarchus's Sun would be almost 300 times greater than the volume of the Earth, and it seems illogical that something that large would revolve around something so much smaller.

Again, not bad for a first approximation, given the level of accuracy of available instruments. You could also - for a first approximation - assume the density of the moon is relatively similar to the density of the earth (it is actually less due to no molton core), and then calculate a mass for the sun based on the effect of tides and the distances of the sun and the moon and the first approximation mass of the moon. You would again end up with a sun being many many times the mass of the earth.

One can now try an experiment where two steel balls with the proportions of mass derived from such first approximations are tied by a (thin, light but strong) cable, hold one ball-cable assembly stationary at one point and spin the whole thing so the balls rotate about the point at a set RPM (enough to get the heavy ball off the ground and relatively horizontal) and

(1) measure the force needed to hold the center point stationary for (a) the smaller ball at the center and (b) the larger ball at the center and (c) the point between the balls that they would balance at if the cable were a beam (ideally with no weight).
(2) release the center holding point and see what happens with the two balls - do they fly off in one direction? or do they stay relatively close to the starting point? do they continue to rotate about each other at a point (a) at the center of the smaller ball or (b) at the center of the larger ball or (c) at the balance point between the two balls?

How do you make a man see what he does not want to see?

Lead him to water?

Enjoy.

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