1. Chapter 7

2. 7.1 Planetary Motion & Gravitation Nicholas Copernicus (Polish) Pulished Earth-centered model in 1543 Tycho Brahe (Danish) Vowed to be an astronomer after a solar eclips Designed and built a device for measuring stellar objects Recorded stellar positions for 20 years Johannes Kepler (German) Brahe’s assistant that inherited amassed data Studied inherited data

3. Kepler’s Laws Believed Sun exerted a force on planets Discovered laws that govern planetary (and satellite) motion First Law Paths of planets are ellipses with Sun at one focus Comets also orbit in ellipses with Sun at focus Long period – Comet Hale-Bopp (2400 yrs) Short period – Comet Halley (76 yrs)

4. Kepler’s Laws Second Law Imaginary line from Sun to planet sweeps equal distances in equal time intervals Third Law Square of the ratio of periods of any two planets revolving around the Sun is equal to the cube of the ratio of their average distances from the Sun

5. Newton’s Law of Universal Gravitation Newton recognized the relationship between the force of the Sun and the square of the distance to the planet Inverse square law

6. Universal Gravitation Falling apple and Moon obeyed the inverse square law According to Newton’s 3 rd Law, the force the earth exerts on apple is same the same as the force the apple exerts on earth Gravitational force Force of attraction between two objects must be proportional to the objects’ masses Theorized it existed between any two objects with mass

7. Universal Gravitation Objects attract each other with a force that is proportional to the product of their masses and inversely proportional to the square of the distance between them F = G Direct vs Inverse relationships Pg 175, Connecting Math to Physics m1m2m1m2 r2r2

8. Universal Gravitation & Kepler’s 3 rd Derivation

9. Measuring G Universal Constant