1. Feb. 2, 2011 NEWS: Exoplanets from Kepler

6. Lecture 3: In the Beginning: Physical origin of the Earth 1.Orbital motion - planets orbiting the Sun 2.Newton’s Law of Universal Gravitation 3.Newton’s form of Kepler’s 3rd law

7. Orbital Motion - Kepler’s laws Kepler’s 3 laws: observed/empirical facts of planetary motion. (1) Generally an orbit is an ellipse; (2) Orbital speed changes along; (3) [Period] 2 = a 3

8. 8 1610 January 11 January 12 January 13 January 15 Galileo’s Diary Jupiter has four moons !

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10. Newton’s Law of Universal Gravitation Newton’s 3 principles (laws) of Classical Mechanics - the foundation. plus Kepler’s 3 facts (laws) of planetary orbital motion.

11. Newton’s Law of Universal Gravitation Newton’s understanding of Force & Acceleration on a circular trajectory helped him describe gravity.

12. Newton’s Law of Universal Gravitation Applies to any object in the Universe that has mass

13. Newton’s form of Kepler’s 3rd law P 2 = a 3 [4  2 /G(M sun +M p )] Here G is the gravitational constant, a fundamental physical constant describing the strength of gravity, e.g. as compared to electromagnetism or nuclear force. Usually with planets M star >> M p and hence M p can be omitted.

14. Newton’s form of Kepler’s 3rd law P 2 = a 3 [4  2 /GM sun ] Here G is the gravitational constant, and usually with planets M star >> M p and hence M p can be omitted.

15. Main points to take home: 1)Orbital motion - Kepler’s 3 laws describe the observed facts of planetary motion. 2) Space and motion: Newton’s 3 laws 3) Newton’s law of Universal Gravitation: F g = GM 1 M 2 / d 2 - a fundamental physics law 4)Newton’s form of Kepler’s 3rd law: P 2 = a 3 (4  2 /GM sun )

16. Newton’s Law of Universal Gravitation Why is it an inverse square law, i.e. has 1/d 2 ?

17. Newton’s Law of Universal Gravitation Explaining Kepler’s 2nd law: changing d means changing F g and hence - changing the acceleration.