1. Very Large Telescope Finds Largest Star - Feb. 2010

2. Spring on Mars brings storms - Feb. 2, 2010

3. Spring on Mars brings storms…, and sand-slides

4. Lecture 3: In the Beginning: Physical origin of the Earth 1.The Age of the Earth 2.Radiometric dating - early chronology 3.Orbital motion - planets orbiting the Sun 4.Newton’s Law of Universal Gravitation 5.Newton’s form of Kepler’s 3rd law

5. 5 1610 January 11 January 12 January 13 January 15 Galileo’s Diary Jupiter has four moons !

6. 6

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. 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.

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

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

11. 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.

12. 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.

14. Main points to take home: 1) The Earth formed ~30 Myr after the Sun, about 4 530 Myr ago  Radioactive decay - a reliable chronometer. 2)Orbital motion - Kepler’s 3 laws describe the observed facts of planetary motion. 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 )