2. Chapter 9 & 10 Gravity

3. Pythagoras (550 BC) n Claimed that natural phenomena could be described by mathematics

4. Aristotle (350 BC) n Asserted that the universe is governed by physical laws

5. n The ancient Greeks believed that the earth was at the center of a revolving sphere with stars on it.

6. n The Geocentric Model implies Earth-Centered Universe.

8. Copernicus(1500's) n Developed a mathematical model for a Sun-centered solar system

10. Tycho Brahe (1500's) n Made precise measurements of the positions of the planets

11. Kepler(1600's) n Described the shape of planetary orbits as well as their orbital speeds

13. Kepler’s First Law n The orbit of a planet about the Sun is an ellipse with the Sun at one focus.

14. Kepler’s Second Law n A line joining a planet and the Sun sweeps out equal areas in equal intervals of time.

15. Kepler’s Third Law n The square of a planet's orbital period is proportional to the cube of the length of its orbit's semimajor axis. n Or simply… T 2 = R 3 if T is measured in years and R is measured in astronomical units.

16. An Astronomical Unit... n …is the average distance of the Earth from the Sun. n 1 AU = 93,000,000 miles = 8.3 lightminutes

17. Kepler’s Laws n These are three laws of physics that relate to planetary orbits. n These were empirical laws. n Kepler could not explain them.

18. Kepler’s Laws...Simply (See page 192.) n Law 1: Elliptical orbits… n Law 2: Equal areas in equal times… n Law 3: T 2 = R 3

19. Newton’s Law of Universal Gravitation n From Kepler's 3rd Law, Newton deduced inverse square law of attraction. G=6.67  10-11 N m 2 /kg 2 G=6.67  10-11 N m 2 /kg 2

20. Gravity Questions n Did the Moon exert a gravitational force on the Apollo astronauts? n What kind of objects can exert a gravitational force on other objects? n The constant G is a rather small number. What kind of objects can exert strong gravitational forces?

21. Gravity Questions n If the distance between two objects in space is doubled, then what happens to the gravitational force between them? n What is the distance is tripled? n …is quadrupled? n What if the mass of one of the object is doubled? n …tripled? n …quadrupled?

22. Weight and Weightlessness n Weight »the force due to gravity on an object »Weight = Mass  Acceleration of Gravity »W = m g n Weightlessness - a conditions wherein gravitational pull appears to be lacking –Examples: »Astronauts »Falling in an Elevator »Skydiving »Underwater

23. Ocean Tides n The Moon is primarily responsible for ocean tides on Earth. n The Sun contributes to tides also. n What are spring tides and neap tides?

24. Sun Earth New MoonFull Moon Spring Tides

25. Sun Earth First Quarter Last Quarter Neap Tides

26. End of Section…

27. Einstein’s Theory of Gravitation n Einstein perceived a gravitational field as a geometrical warping of 4-D space and time.

28. BLACK HOLES 4Let’s observe a star that is shrinking but whose mass is remaining the same. 4What happens to the force acting on an indestructible mass at the surface of the star? SFA

29. R2R2 F R2R2 F R2R2 F R2R2 F R R R R Remember that the force between the two masses is given by

30. 4If a massive star shrinks enough so that the escape velocity is equal to or greater than the speed of light, then it has become a black hole. 4Light cannot escape from a black hole. BLACK HOLES

31. Near a Black Hole