1. Chapter 7 Gravitation

2. Newton’s Law of Universal Gravitation If two particles with masses m 1 and m 2 are separated by a distance r, then a gravitational force acts along a line joining them, with magnitude given by:

3. Universal Gravitation G is the constant of universal gravitational. G = 6.673 x 10 -11 N m² /kg² This is an example of an ________ ___________. The gravitational force is always ____________.

4. Universal Gravitation The force that mass 1 exerts on mass 2 is equal and opposite to the force mass 2 exerts on mass 1. The forces form a Newton’s third law action-reaction.

5. Gravitation Constant, G Determined experimentally. Henry Cavendish 1798 The light beam and mirror serve to amplify the motion.

6. Applications of Universal Gravitation Acceleration due to gravity. g will vary with ___________.

7. Sample Problem Three 0.300 kg billiard balls are placed on a table at the corners of a right triangle. Find the net gravitational force on the cue ball (designated as m 1 ) resulting from the other two balls if the cue ball is between the other two. The distance between one ball and the cue ball is 0.400 m and the distance between the cue ball and the other ball is 0.300m.

8. Kepler’s Laws: A Brief History Claudius Ptolemy: In ~2AD developed a geocentric model of the solar system.

9. Kepler’s Laws: A Brief History Nicolas Copernicus: In 1543 developed a heliocentric model of the solar system. Believed planets traveled in a circular orbit.

10. Kepler’s Laws: A Brief History Tycho Brahe: Made accurate measurements which were used to developed the currently accepted model of the solar system. Kepler was Brahe’s assistant.

11. Kepler’s Laws: A Brief History Johannes Kepler: Showed that the circular model had to be abandoned and an elliptical model better represented the movement of the planets.

12. Kepler’s First Law: “The Law of Orbits” All planets move in __________ orbits with the Sun at one focus. Any object bound to another by an inverse square law will move in an elliptical path. Second focus is empty.

13. Kepler’s Second Law “The Law of Areas” A line drawn from the Sun to any planet will sweep out __________ in ___________. Area from A to B and C to D are the same.

14. Kepler’s Third Law “The Law of Periods The square of the orbital period of any planet is proportional to cube of the average distance from the Sun to the planet. For orbit around the Sun, K = K S = 2.97x10 -19 s 2 /m 3. K s is ______________ of the mass of the planet.

15. Deriving Kepler’s 3 rd Law

17. Chapter 7 Gravitation THE END