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| title | chunk | source | category | tags | date_saved | instance |
|---|---|---|---|---|---|---|
| Astronomia nova | 10/11 | https://en.wikipedia.org/wiki/Astronomia_nova | reference | science, encyclopedia | 2026-05-05T16:09:34.057453+00:00 | kb-cron |
I laid [the original equation] aside, and fell back on ellipses, believing that this was quite a different hypothesis, whereas the two, as I shall prove in the next chapter, are one in [sic] the same... Ah, what a foolish bird I have been!
=== Part 5 === In the final section, Kepler gives an accurate account of the ecliptic latitude of Mars. He also outlines a physical hypothesis to explain why the orbit of planets are not precisely in the same plane. In chapters 61-62, Kepler determines the values for Mars' ascending and descending nodes. Using the distance to Earth and Mars computed from the previous section, and the observed geocentric latitude of Mars, Kepler is able to determine the heliocentric latitude of Mars at any point in its orbit. From this, Kepler determines each of the parameters using the same methods from chapters 11-14. For the ascending node he finds
46
∘
32
1
2
′
{\textstyle 46^{\circ }32{\frac {1}{2}}'}
and for the descending nodes
226
∘
32
1
2
′
{\displaystyle 226^{\circ }32{\frac {1}{2}}'}
. He also determines the orbital inclination to be
1
∘
49
′
{\displaystyle 1^{\circ }49'}
. In chapter 63, Kepler gives a physical reason why the orbit of the planets are not in the same plane. He considers the idea that the rotation of the sun defines an invariable plane. All the planets are inclined at an angle to this plane, because the planets magnetic field are attracted to a fixed direction in space below this plane. In chapter 64, Kepler shows that the parallax of Mars must be small. Had there been any noticeable parallax, it would have affected the apparent location of the ascending and descending nodes. But the measured values are exactly
180
∘
{\displaystyle 180^{\circ }}
apart. In chapters 65-66, Kepler shows that the Mars does not reach closest to the Earth precisely at opposition, but the date of closest approach can be a few days before or after opposition. In chapters 67-70, Kepler examines several questions relating to the long term behavior of the orbits of Earth and Mars, by comparing his observations with those from the time of Ptolemy. The imprecise nature of some of these observations, as well as the errors, makes it difficult to arrive at conclusive results at times. Some of these questions include: do the eccentricities of orbits change over time? or do the nodes precess at a non-uniform rate?
== Kepler's laws == The Astronomia nova records the discovery of the first two of the three principles known today as Kepler's laws of planetary motion, which are:
That the planets move in elliptical orbits with the Sun at one focus. That the speed of the planet changes at each moment such that the time between two positions is always proportional to the area swept out on the orbit between these positions. Kepler discovered the "second law" before the first. He presented his second law in two different forms: In Chapter 32 he states that the speed of the planet varies inversely based upon its distance from the Sun, and therefore he could measure changes in position of the planet by adding up all the distance measures, or looking at the area along an orbital arc. This is his so-called "distance law". In Chapter 59, he states that a radius from the Sun to a planet sweeps out equal areas in equal times. This is his so-called "area law". However, Kepler's "area-time principle" did not facilitate easy calculation of planetary positions. Kepler could divide up the orbit into an arbitrary number of parts, compute the planet's position for each one of these, and then refer all questions to a table, but he could not determine the position of the planet at each and every individual moment because the speed of the planet was always changing. This paradox, referred to as the "Kepler problem," prompted the development of calculus. A decade after the publication of the Astronomia nova, Kepler discovered his "third law", published in his 1619 Harmonices Mundi (Harmonies of the world). He found that the ratio of the cube of the length of the semi-major axis of each planet's orbit, to the square of time of its orbital period, is the same for all planets.
== Kepler's knowledge of gravity ==
In his introductory discussion of a moving earth, Kepler addressed the question of how the Earth could hold its parts together if it moved away from the center of the universe which, according to Aristotelian physics, was the place toward which all heavy bodies naturally moved. Kepler proposed an attractive force similar to magnetism, which may have been known by Newton.
Gravity is a mutual corporeal disposition among kindred bodies to unite or join together; thus the earth attracts a stone much more than the stone seeks the earth. (The magnetic faculty is another example of this sort).... If two stones were set near one another in some place in the world outside the sphere of influence of a third kindred body, these stones, like two magnetic bodies, would come together in an intermediate place, each approaching the other by a space proportional to the bulk [moles] of the other.... For it follows that if the earth's power of attraction will be much more likely to extend to the moon and far beyond, and accordingly, that nothing that consists to any extent whatever of terrestrial material, carried up on high, ever escapes the grasp of this mighty power of attraction. Kepler discusses the Moon's gravitational effect upon the tides as follows: