The earliest known measurement from the earth to sun was in 200 B. C. Aristarchus of Samos, a man of astronomy and Mathematics, made this discovery. He believed the Earth revolved around the Sun. Aristarchus of Samos used what is known today as right-angle trigonometry. By connecting Earth to Moon, Moon to Sun, and Sun to Earth, one forms a right triangle as shown below.
The measure of angle “a” is 90^0; an observer on Earth can then measure the angle measure of “b.” Then for one to find the distance between Earth and Sun simply find the sine of angle “c.” Aristarchus of Samos would have expressed this a little differently for the sole fact of modern Trigonometry had not yet been discovered. Although this is strong in theory, it had its downfalls. This method in was proven to be very inaccurate. The Earth to Moon ratio is very small compared to the Earth to Sun ratio, which leads one to infer that angle “a” would measure close to 90^0.
With the measure of angle “b” is close to 90^0; which would leave angle “c” very small. If a small human error occurs in measuring angle “b,” one is left with an emasculate error in the ratio of Earth to Moon over Earth to Sun. In modern trigonometry, it is describe as 1/ (sin c) 2, which is very large when “c” is small. Aristarchus measured angle “b” as 87^0, but in fact was 89^0 50 minutes. Although this error seems small, it leads to a 95% error. Aristarchus believes the Earth to Moon over Earth to Sun measured 19, but in all reality is measured as 397.
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But all in all Aristarchus of Samos was the first to mathematically set the spatial scale of cosmos. During the time of Kepler, most people still believed the Earth was the center of the Universe. Copernicus, in 1543, published his book, De Revolutionibus, states the Sun is the center of the Universe, and the planets orbit around, yet he didn’t know how the planets did so. In 1601, Kepler became the proud owner of Tycho Brache’s, an astronomer whom Kepler was an assistant for, meticulous measurements of planets, stars and sun that Brache had gathered in his last 38 years. With these measurement, Kepler came up with a formula T 2 = kr 3. In every day terms, T is the time of the orbital period of the planet, K is a constant, and r is the ratio of the Sun to the planet.
If more than on planet is involved, the ratio becomes (Ta 2 / Tb 2) = (Ra 3 / Rb 3).
This is still used today to find distances of objects found inside the Milky Way.