Johannes Kepler was a German astronomer who discovered the three laws of planetary motion. The first law states that planets orbit the sun in ellipses, with the sun located at one focus. The second law describes how a line connecting a planet to the sun sweeps out equal areas in equal times. Kepler's third law relates the orbital period of a planet to its average distance from the sun. These laws helped usher in the modern era of astronomy and supported the Copernican model of a sun-centered solar system.

1. The birth of modern astronomy Johannes Kepler

2. Johannes Kepler Johannes Kepler German astronomer Birth December 27, 1571 Death November 15, 1630 Place of Birth Weil der Stadt, Württemberg Known for: Discovering the three laws of planetary motion, now known as Kepler's laws.

3. Johannes Kepler Career: 1594: Became professor of mathematics at Graz 1600: Assisted Danish astronomer Tycho Brahe with his astronomical research in Prague 1601: Took over as imperial mathematician and court astronomer to Emperor Rudolf II in Prague upon Brahe's death 1609: Published Astronomia Nova (New Astronomy), which included the first and second laws of planetary motion 1612: Accepted a position as mathematician to the states of Upper Austria at Linz 1619: Published Harmonice Mundi (Harmony of the World) which contained the third law of planetary motion

4. Johannes Kepler Did You Know? In addition to astronomy, Kepler studied astrology, which proposes that astronomical bodies influence the course of earthly events. A Lutheran, Kepler was forced to move and change jobs several times during his life to escape religious persecution.

5. Johannes Kepler Johannes Kepler (1571 to 1630) A German astronomer born in Wurttemberg in southwestern Germany. Ushered in the new age of astronomy. A very good mathematician. Strongly believed in the accuracy of Tycho’s works. He derived the three basic laws of planetary motion.

6. Johannes Kepler’s Portrait in 1610 by an unknown artist

7. Kepler’s Law The first two laws resulted from his inability to fit Tycho’s observation of Mars to a circular orbit. This led him to discover that orbit of Mars is not a perfect circle but is elliptical. He also realized at about the same time that Mars orbital speed varies in a predictable way. In 1609, after almost a decade of work, Kepler proposed his first two laws of planetary motion.

8. PARTS OF AN ELLIPSE Ellipse – is the simplest kind of closed curve. It belongs to a family of curves known as conic sections. Conic section – the curve of intersection between a hollow cone and a plane that cuts through it. Foci – from any point on the curve the sum of the distances to two points inside the ellipse, called the foci is the same.

9. PARTS OF AN ELLIPSE Major axis – the maximum diameter of the ellipse. Semimajor axis – the distance from the center of the ellipse to one point. Eccentricity – ratio of the distance between the foci to the major axis.

10. DRAWING AN ELLIPSE WITH TWO PINS, A PEN AND A STRING.

11. AN ELLIPSE OBTAINED WITH THE INTERSECTION OF PLANE ON THE CONE

12. Conic Sections

13. A group of ellipses with the same major axis but various eccentricities

14. Ellipses with the same eccentricity but various major axes

15. Diagram of the geocentric trajectory of Mars through several periods of apparentretrograde motion.

16. Johannes Kepler The Three Laws of Planetary Motion as proposed by Kepler: 1. The path of each planet around the Sun is an ellipse. > The Sun is located at one focus. > The other focus is symmetrically located at the opposite end of the ellipse.

17. Johannes Kepler The Three Laws of Planetary Motion 2. The planet revolves so that an imaginary line connecting it to the Sun sweeps over equal areas in equal intervals of time. > Expresses geometrically the variation in orbital speeds of the planet.

18. KEPLER’S LAW OF EQUAL AREAS

19. Johannes Kepler The Three Laws of Planetary Motion Kepler was a very religious person. He believed that the creator made an orderly universe. In 1619, Kepler published his third law in “The Harmony of the Worlds”.

20. Johannes Kepler The Three Laws of Planetary Motion 3. The orbital speeds of the planets and their distances to the Sun are proportional. > The third law states that the planet’s orbital period squared (p2) is equal to its mean solar distance cubed (d3). (p2=d3)

21. Johannes Kepler The solar distances of the planets can be calculated when their periods of revolution are known. E.g. Mars has a period of revolution equal to 1.88 years. How far away is it from the Sun. 1.88 years (squared) = 3.54. 3.54 (get the cube root of it) = 1.52 The answer is 1.52 AU. 1.882 = 1.523 (p2=d3)(Both has the value of 3.54)

22. OBSERVATIONAL TEST OF KEPLER’S LAW

23. Johannes Kepler Kepler attempted to associate numerical relations to the Solar System with music. The Earth plays the note mi, fa, mi. Kepler’s laws assert that the planets revolve around the Sun and therefore support the Copernican theory. Kepler fell short on determining the forces that act to produce the planetary motion he had described.

24. Detail from Kepler’s “Harmony of the World’s”

25. CARL SAGAN Video

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