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6. 5 Phys 181-701 Astronomy Galileo’s Apparatus – Deutches Museum, Munchen, Germany

7. 6 “Numero pondere et mensura Deus omnia condidit.” Sir Isaac Newton – Principia Mathematica “If I have been able to see further, it was only because I stood on the shoulders of giants.” Newton, in a letter to Robert Hooke “To command the professors of astronomy to confute their own observations is to enjoin an impossibility, for it is to command them to not see what they do see, and not to understand what they do understand, and to find what they do not discover.” Galileo Galilei – In Science

8. 7 Programming NotesProgramming Notes Programming Notes…..

9. 8 Martin Reese Martin Reese

10. 9 Exam ResultsExam Results The Results Are In… Exam Average = 74.2% = 44.52/60

11. 10 Review REVIEW: Kepler Develops Three Laws: Law of Ellipses Law of Areas Harmonic Law We now understand HOW the planets move… but not WHY they move.

12. 11 Galileo: The Death of the Earth Centered Universe 1564-1642 Contemporary of Kepler Demonstrated that all objects are accelerated by gravity by the same amount Moving objects remain in motion Built a telescope in 1609 * and observed the Sun, Moon, Milky Way, Moons of Jupiter and the phases of Venus. * Hans Lippershey invented the telescope in 1608

13. 12 If we assume (incorrectly) that the Tower of Pisa is 20m tall, the ball will take 2s to hit the ground.

14. 13 Even if the ball is thrown horizontally from the tower, the acceleration toward the earth is still 10m/s 2. As a result, the ball that is dropped and the ball that is thrown both hit the ground after 2 seconds!!! We will return to this essential idea in a few slides…

15. 14 Sir Isaac Newton Newton’s Laws: 1.All objects at rest shall remain at rest and all objects in motion shall Remain in motion in a straight line, unless compelled by a FORCE to do otherwise. 2.The ACCELERATION of any object is directly proportional to the FORCE applied to it and inversely proportional to its MASS. 3.For every force applied to an object, there is an equal and opposite force applied by the object on the actor. 1642-1727

16. 15 Newton’s Laws Relative to Galileo’s Experiment: 1.When the ball is dropped it ceases to be at rest. Therefore there must be a force, directed downward, to cause the acceleration. 2.The acceleration will be equal to the force that gravity exerts on the ball divided by the mass of the ball, that is, the acceleration is equal to the force per unit mass. 3.If the Earth exerts a gravitational force on the ball, the ball must exert an equal and opposite force on the Earth!!!! Newton v.s. GalileoNewton v.s. Galileo

17. 16 Law of Universal Gravitation Newton knows that the more mass an object has, the greater the force of Gravity on it. F G = m g Where “g” is the special name given to the acceleration that is caused by gravity. 10 m/s 2

18. 17 Inverse square The inverse square law…

19. 18 The Law

20. 19 Example Example:

21. 20 “Weighing” the Earth… A & B have equal masses and therefore equal weights. The rod is balanced.

22. 21 The very small mass is needed to balance the gravitational force of the very large mass. “G” can be calculated! Knowing G and Kepler’s Law’s allows us to calculate the mass of the Earth, Sun and all of the planets moons and asteroids in the solar system

23. 22 Return to Pisa Return to Pisa…The earth is not flat…

24. 23 Curved Earth After one second the projectile has fallen five meters… But the earth has curved away.

25. 24 QuestionQuestion Question… If the earth is curved such that it “curves away” 5 meters for every 8000 meters traveled, how fast would the projectile need to be going so that, after falling 5 meters, it was still 5 meters above the earth? 8000 m/s!!!

26. 25 Summary Newton invents calculus Newton Proves Kepler’s Laws Universal Gravitation used to determine the mass of the earth Tides understood Moon “lock” understood Satellite motion possible Solar system travel made possible

27. 26 Summary IISummary II

28. 27 Chapter 3 (3.3, 3.4, 3.5) Chapter 4 (4.2, 4.4) Electromagnetic Radiation

29. 28 The frequency is measured in Hertz (Hz) and is the number of waves which pass a given point in one second.

30. 29 Time period of mars

31. 30 EndEnd NEXT TIME: Two Laws of RADIATION