johannes kepler (1571-1630) discovered a set of laws that accurately described the motions of the...
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Johannes Kepler (1571-1630) discovered a set of laws that accurately described the motions of the planets.
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Kepler was a great mathematician, but he had very poor eyesight. This made it difficult to plot the locations of the planets for his studies.
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Kepler knew where to find extensive information on the locations of planets which had been kept for several decades.
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These documents had been prepared and were in the possession of Tycho Brahe.
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Tycho Brahe (1546-1601) was born in Denmark and was very well educated. He was very rude and insulting to everyone.
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He lost his nose in a duel while still a student. After that, he wore a gold and silver replacement which he glued in place.
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Tycho’s rudeness forced him to leave Denmark in 1597 after becoming the enemy of almost everyone important in the entire country.
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He moved to Prague, which is close to Graz, Austria, where Kepler just happened to be living. Kepler came to work with Tycho in 1600.
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They worked together trying to find a theory explaining Tycho’s data. Tycho died a year later, and Kepler inherited Brahe’s data (he really stole it).
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While Kepler was a Copernican, Brahe believed that the Sun orbited the Earth, but that the planets orbited the Sun.
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Kepler set to work trying to find a principle that would explain the observed motions of the planets. This work would take most of the last 29 years of his life.
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He used triangulation to plot the orbits of the planets from Tycho’s data. After many years of work he summarized the motions of the planets in three simple laws.
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Kepler’s Laws of Planetary Motion -1. The orbital paths of the planets are elliptical, with the Sun at one focus.
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2. An imaginary line connecting the Sun to any planet sweeps out equal areas of the ellipse in equal intervals of time.
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3. The square of a planet’s orbital period is proportional to the cube of its orbital semi-major axis:P(years)2 = a(a.u.)3
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1. The planet’s orbits are ellipses with the Sun at one focus.
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The eccentricity is the ratio of the distance between the foci to the length of the major axis.
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Perihelion - closest approach to the Sun.
Aphelion - greatest distance from the Sun.
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None of the planets orbits are as eccentric as these pictures. Except for Mercury and Pluto it would be difficult to tell that the orbit wasn’t a circle.
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The substitution of the ellipse for the circle was a BIG DEAL. The circle was Aristotle’s baby and even Galileo was a believer in circular motion.
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2. An imaginary Sun to planet line sweeps out equal areas in equal times.
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The planets move faster when close to the Sun and slower when farther away.
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These two laws explained all the motions without the need for epicycles.
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Kepler published the first two laws in Astronomia Nova (The New Astronomy) in 1609 proving the laws only for Mars.
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In 1619 he wrote Harmonice Mundi (The Harmony of the Worlds) where he proved the first two laws for all the known planets and added his third law.
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3. The square of a planet’s orbital period is proportional to the cube of its orbital semi-major axis. The time taken for a planet to orbit the Sun increases more rapidly than the size of its orbit (measured in astronomical units).
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One astronomical unit is a measure of distance equal to the average distance of the Earth from the Sun, or the length of the semi-major axis of Earth’s orbit.
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