Kepler used trigonometry to discover the relative distances between Earth and Mars, basing his study in the old theory that the Earth movement has a uniform speed over its path and exhibit a circular orbit. This allowed him to discover a difference in the lengths between Earth and Mars and found the planet´s orbit was not a circle, instead the Earth was traveling on other path.

According to "www.keplersdiscovery.com":

---Quote---
Kepler examined the motion of the Earth using Brahe's observations of Mars. He postulated that the Earth does not move around the center of its orbit at a uniform speed. “This is in a way surprising,” writes Donahue, “because ever since the time of Hipparchus” (second century BCE) a theory of this kind, either of an Earth or Sun moving at uniform speed depending on which was at the center, “had been used with no problems.”

Kepler knew that the time of Mars' orbit was 687 days. Therefore, Mars will be in the same place every 687 days. If he could find multiple observations of Mars separated by this interval of time, he could observe how the angle between Earth and Mars changed and thus learn something about the parameters of Earth's orbit.

Using trigonometry Kepler discovered the relative distances between Earth, Mars, and the center of Earth’s orbit, taking the Earth-Mars distance as a constant.

http://www.keplersdiscovery.com/Images/Keplers.Ch24%20Diagram.jpg

Kepler reasoned as follows: Assuming that the Earth moves uniformly, all the angles around the orbit's center, "A," (see below) would be equal (FAH, HAE, EAC), since they are equally spaced in time (687 days). The distances from the Earth to the center of its supposedly circular orbit should also all be the same.

He determined that the relative distance AD from the Earth to the assumed center its orbit would be 67,794 units.

He computed the other distance ratios to be:
AB = 66,774
AC = 67,467
AE = 67,478

His calculations demonstrated a difference among the lengths. This indicated either that A is not the center of Earth’s circular orbit, or that the orbit is not a circle. Kepler knew the radii of a circle should all be equal.

As a result of his geometrical investigation Kepler concluded: “Therefore, the circle D, which Copernicus described about the point A of uniformity of the Earth’s motion, is not the Earth’s path. There is instead some other circle ... on which the Earth is found.”
---Quote---
Source(s):
http://www.keplersdiscovery.com/Earth.html

Asker's Rating:

Permalink | Report