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| title | chunk | source | category | tags | date_saved | instance |
|---|---|---|---|---|---|---|
| Astronomia nova | 2/11 | https://en.wikipedia.org/wiki/Astronomia_nova | reference | science, encyclopedia | 2026-05-05T16:09:34.057453+00:00 | kb-cron |
=== Part 2 === In part 2, Kepler introduces the vicarious Hypothesis, his first hypothesis to explain the motion of Mars. In chapters 7-10, Kepler tells the story of how he was introduced to the problem of Mars' orbit. Tycho and his assistant had been working on a theory of Mars, but they had failed to accurately account for the observed position of Mars. Tycho's observational data included 12 oppositions of Mars, for which he had determined its position in ecliptic longitude and latitude. They had managed to fit a theory to the observed ecliptic longitudes accurate to within 2 minutes of arc, yet it failed completely to account for the ecliptic latitudes. Kepler was then tasked with determining a more accurate theory to match this observational data. His first step was to establish a precise definition of opposition. Since planets do not orbit in the same plane, in general they never reach precisely
180
∘
{\textstyle 180\circ }
in angular separation. Ptolemy had assumed the planet reaches opposition when its ecliptic longitude is 180 degrees from the mean position of the sun. This definition ignores the ecliptic latitude, so when constructing the table of oppositions, Tycho's assistant suggested a correction to account for this, by instead measuring when the angle between the sun and one of the nodes along the ecliptic, was equal to the angle between planet and the opposite node measured along the path of the planet. But Kepler showed this correction to be erroneous for two reasons. First, the path of the planet as seen from the Earth is not the same as seen from the sun, and second, the ecliptic longitude of Mars as seen from the sun will not be the same as the ecliptic longitude of the Earth. The whole point of using oppositions is to eliminate the effect of the Earth's orbit, so that when we observe Mars from Earth, its position will be the same as if we observed it from the sun. So this error, which Kepler shows to be as high as 9 arcminutes, defeats the purpose of the correction.