Kepler’s Third Law: The movement of solar system planets

[Admin]

Kepler's Third Law not only calculated the planetary movements in the solar system, but also helped to determine the average distance of the planet from its stars.

Kepler’s Third Law: The movement of solar system planets : Read more

 

[rod]

I note this in the article about Mars and Tycho Brahe. "Not only did the orbit of Mars not fit well with the geocentric model, but it was also a problem for early Copernican models that suggested the orbits of the planets were perfect circles. Thus, Kepler came to the realization that the orbits of the planets were not circular, but were flattened circles or ellipses. By handing Kepler the study of the orbit of Mars — that most elliptical planetary orbit — Brahe had unwittingly unraveled his own geocentric model before its completion and had facilitated the creation of laws that would help cement heliocentrism as the accepted model of the solar system."

Tycho Brahe was desperate to show Copernicus was wrong using his Mars observations.

Tycho Brahe's Copernican campaign, https://ui.adsabs.harvard.edu/abs/1998JHA....29....1G/abstract, January 1998. "In 1584 Tycho Brahe wrote to Heinrich Brucaeus, his former teacher in Rostock, that his attempt to find whether Mars approaches closer to the Earth than the Sun (as predicted by Copernicus) had yielded a negative result, and that the Copernican hypothesis must therefore be rejected. Five years later he reversed himself, writing to Thaddeus Hagecius that in 1582 by most subtle measurements he had in fact found a sufficiently large diurnal parallax to convince himself that that Copernican model, or (more important) his own geo-heliocentric system, could be justified. In hindsight we know that the Martian parallax was in fact too small to be detected even by Tycho's remarkable instruments. What was going on in the letter to Hagecius? Was Tycho deliberately prevaricating or merely deluding himself in his eagerness to find support for his new cosmology?"

TYCHO Brahe's Copernican Campaign, https://ui.adsabs.harvard.edu/abs/1997AAS...191.0103G/abstract, December 1997. "Historians of astronomy have generally assumed that the Ptolemaic and Copernican systems give equivalent predictions of planetary positions, but Tycho Brahe knew that in the Ptolemaic arrangement Mars' distance was always greater than the sun's, whereas in the Copernican system Mars at opposition approached to half the sun's distance. Because Tycho accepted the traditional solar distance scale, 20 times too small, he expected to measure a Martian diurnal parallax of 4.5' at opposition if the Copernican system was true. (In reality the horizontal parallax was too small to measure by naked-eye observations.)..."

 

[Helio]

Tycho Brahe was desperate to show Copernicus was wrong using his Mars observations.

Indeed. He wanted his Tychonic model to reign supreme. He could argue the lack of stellar parallax would favor his model over Copernicus.

In his model, Mars would come very close to Earth during opposition, much closer than Ptolemy's model. His remarkable observations, sometimes with less than 1 arcminute resolution, allowed Kepler using his data to not quit trying to figure out Mars odd , but subtle, orbital changes.

The article's equation seems odd...R = (T^2*Ms)/3. Can someone explain this to me?

I use this one for semi-major axis...

a^3 = (G(M+m)*T2)/(4 pi^2)