1. Goal: To understand how Kepler improved the science of Astronomy 1)To learn about Kepler’s quest for a new model 2)To understand Kepler’s Laws 3)Listen to Carl Sagen talk about the subject!

2. The prelude Kepler was faced with a dilemma. How do you make the observations work with the model? Kepler retried Copernicus’s idea of the sun centered universe with circular orbits, and NO epicycles.

3. The prelude, cont. Using the very accurate observations by his mentor Tycho Brahe, low and behold, he made it work! Mostly… Mars was a problem. During most of Mars’s orbit, it fit very well. However, at a few spots, Mars’s position would differ by up to 8 arc minutes from where his model would predict.

4. Kepler’s dilemma: A) I have the right model for the solar system at long last! Those 8 arc min are just errors by Tycho. B) I am a little concerned with the deviations, but my model is very good, much better than anyone else. It should work for 1000 years before anyone else needs to tweak it further. C) No, no, this won’t do. I am going to scrap this and go another direction completely!

5. Kepler’s decision: Kepler decided his mentor had the correct observations. The error lay in his model. The planets must NOT have circular orbits around the sun. There must be another explanation.

6. Solution: Orbits have another shape. After testing many shapes, Kepler found one that worked! From that Astronomy was changed forever, and his method of using observations combined with mathematical models became the Scientific Method!

7. Law 1 Orbits are not circular. They are elliptical. Ellipses are egg shapes which have 2 foci. The separation of the foci is determined by the “eccentricity”. There is a constant distance such that for any point on the ellipse the sum of the distances to the foci is a constant.

8. For the earth – sun system, the sun is at one focus. What is at the other focus? A) the moon B) the sun C) the earth D) none of the above

9. Law 2 In an orbit, the area covered per unit time is a constant. Therefore, when an object is closer to the object it orbits, it travels faster, and similarly, slower when it is further away. Laws 1 and 2 published in 1609

10. question At is closest point to the earth (200 miles) a satellite covers an area of its orbit of 1 Unit per second. When that same satellite is at its furthest point from the earth (400 miles) then how much area of its orbit will it cover per time? Hint: Kepler’s 2 nd law A) 0.5 Units per second B) 1 Unit per second C) 2 Units per second D) It is impossible to tell from the information given.

11. Law 3 Published 1619 Period 2 = constant * a 3 a = semi-major axis = half the longest length of the ellipse.

12. Law 3 question Period 2 = constant * a 3 What is the value of the constant for any object orbiting the sun (denoted usually as k)? Hint, think about the earth sun system to try to calculate it using as easy of #s as possible.

13. Law 3 question Period 2 = constant * a 3 What is the value of the constant for any object orbiting the sun (denoted usually as k)? Hint, thing about the earth sun system to try to calculate it using as easy of #s as possible. Answer: k = 1 for the sun if P is in years and a is in AUs.

14. Another question You discover an asteroid which has a semi- major axis (a) of 4 AU. What is its orbital period in years? A) 2 years B) 4 years C) 8 years D) 16 years Hint: Kepler’s 3 rd law.

15. Conclusion Kepler started a new era of science – an era where scientific models were based off of observations, and experiments. Kepler questioned the standard models in place and thereby created a new age of Astronomy ripe with understanding the world around him. This would lead up to future scientists such as Newton.