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| title | chunk | source | category | tags | date_saved | instance |
|---|---|---|---|---|---|---|
| Astronomia nova | 7/11 | https://en.wikipedia.org/wiki/Astronomia_nova | reference | science, encyclopedia | 2026-05-05T16:09:34.057453+00:00 | kb-cron |
In chapter 40, Kepler gives a method for computing the orbit of the Earth based on these physical hypotheses. Kepler notes the extreme difficulty that arises when trying to compute the speed of the planet as the distance is constantly changing. For this reason, he introduces a shortcut, inspired by Archimedes' method of computing pi. If we break the orbit up into little triangles drawn from the sun, then the distance the planet travels is given by the base of the triangle, and the distance from the sun is given by the height of the triangle. If we choose triangles that divide the planet's motion into equal units of time, then the triangles are shown to have equal area, because as the height decreases, the base must increase by the same amount, as the planet moves faster, and vice versa. Kepler therefore introduces his law of areas, equal areas correspond to equal times. To calculate the orbit from this, we define the mean anomaly as the time since planet has last reached aphelion divided by the orbital period times 360 degrees. The true anomaly is defined as the angle between the planet and aphelion as viewed from the sun, and eccentric anomaly is the same angle viewed from the center of the orbit.