For Newton seized them and, with trembling hands, Began to work his problem out anew.

1. For Newton seized them and, with trembling hands, Began to work his problem out anew. )Then, then, as on the page those figures turned To hieroglyphs of heaven, and he beheld The moving moon, with awful cadences \Falling into the path his law ordained, Even to the foot and second, his hand shook And dropped the pencil. ..Work it out for me," He cried to those around him; for the weight Of that celestial music overwhelmed him; And, on his page, those burning hieroglyphs Were Thrones and Principalities and Powers. .. For far beyond, Immeasurably far , Beyond our sun, he saw that river of suns We call the Milky Way, that glittering host Powdering the night, each grain of solar blaze Divided from its neighbour by a gulf Too wide for thought to measure; each a sun Huger than ours, with its own fleet of worlds, Visible and invisible. Those bright throngs That seemed dispersed like a defeated host, Through blindly wandering skies, now, at the word Ot one great dreamer, height o'er height revealed Hints of a vaster order, and moved on In boundless intricacies of harmony Around one centre, deeper than all SUIlS, The burning throne of God.

2. Tides • Several thinkers in the past guessed that the Moon had some connection with the tides Posidonius (Alexandria), Roger Bacon, Kepler, Descartes • What was the reason for their guess? • The tides are especially high during full moon and new moon. • They based their guess on observations: • The tides occur about one hour later each day. • If you look at the time of moon-rise, you find that it also occurs roughly one hour later each day. Poem • Galileo (mistakenly) believed that tides arise from the rotation of the earth.

3. What measurable evidence helped support Newton’s detailed theory of gravitation (1/R2)? • Tides • Caused by sun and moon • Shape of the earth is not an exact sphere • Precession of the equinoxes • Value of g is not the same at the poles and equator • Comets are predictable

4. The mass of the sun is 27 million times larger than the mass of the moon, but the sun is also 384 times farther away from earth than the moon. Compare the force of gravity of the sun on the earth with the force of gravity of the moon on the earth A) the moon’s attraction is bigger B) the sun’s attraction is bigger C) they are about the same D) only the sun attracts the earth, the earth attracts the moon

5. Announcements Final Paper Due May 14, 4 pm.. One hard copy Clark 117, One copy email me: hsp3 Copies of Poem by Alfred Noyes Torch Bearers

6. (Halley writes to Newton's niece) He always walked aloof, Treading a deeper, stranger world than ours. Have you not told me how he would forget Even to eat and drink, when he was wrapped In those miraculous new discoveries And, under this wild maze of shadow and sun Beheld-though not the Master Player's hand- The keys from which His organ music rolls, Those visible symphonies of wild cloud and light Which clothe the invisible world for mortal eyes. Fools have said That knowledge drives out wonder from the world: They'll say it still, though all the dust's ablaze With miracles at their feet; vhile Newton's laws Foretell that knowledge one day shall be song, And those whom Truth has taken to her heart Find that it beats in music. Even this age Has glimmerings of it. Newton never saw His own full victory; but at least he knew That all the world was linked in one again: And, if men found new worlds in years to come, These too must join the universal song. That's why true poets love him...

7. Tides There’s a love song too The sailors on the coast of Sweden sing, I have often pondered it. Your courtly poets Upbraid the inconstant moon. But these men know The moon and sea are lovers, and they move In a most constant measure. Hear the words and And tell me if you can, what silver chains Bind them together.

8. The Shepherdess of the Sea Reproach not yet our sails’s delay; You cannot see the shoaling bay, The banks of sand, the fretful bars, That ebb left naked to the stars, The sea’s white shepherdess, the moon Shall lead us into harbor soon Dear, when you see her glory shine, Between your fragrant boughs of pine Know there is but one hour to wait Before her hands unlock the gate, And the full flood of singing foam Follow her lovely footsteps home. Then waves like flocks of silver sheep Come rustling inland from the deep, And into rambling valleys press Behind their heavenly shepherdess You cannot see them? Lift your eyes And see their mistress in the skies She rises with her silver bow, I feel the tide begin to flow And every thought and hope and dream Borne on the universal tide, The wanderer hastens to his bride. The sea’s white shepherdess, the moon, Shall lead him into harbor soon.

9. Detail Behavior of Tides Provided Confirmation of Newton’s Gravitational Theory

10. Newton was the first to explain that tides occur because the force of gravity of the Moon on the Earth gets weaker with increasing distance. The water closest to the Moon is attracted toward the Moon with greatest force. Therefore, as the earth rotates, we have a high tide when the water comes closest to the moon. Since the Moon is also moving with respect to the earth, as it orbits the earth, a point on the Earth’s surface has to rotate longer than 24 hours return to the spot nearest to the Moon. The difference is about 1 hour.

11. Why does the moon’s gravity play a bigger role than the sun’s gravity ? Force of sun on earth F sun-on-earth = G mearth x msun/Rearth-sun2 = 6.7 x 10-11 x (6 x 1024)(2 x 1030)/(150 x 109)2 = 35.6 x 1021 Newtons Force of the Sun is Much Greater)

12. 1/R2 1/R2

13. Change in F moon-across-earth = = 2 x 10 20 - 2.14 x 10 20 =0.2 x 10 20 Newtons Change in F sun-across-earth = 35.57 x 10 21 – 35.56 x 10 21 =0.1 x 10 20 Newtons

14. But there are two tides in a 24-hour period

15. When are tides the highest? • A) half-moon • B) Full-moon • C) New-moon • D) B & C • E) All of the above

16. Strong Tides and Weak Tides

17. Why the earth’s axis precesses?

18. Because the earth is not exactly spherical The moon pulls harder on the bulge closer to the moon causing the spinning earth to precess like a top

19. Shape of the earth is not an exact sphere! Why? - Because of rotation, it deformed in early stages of formation Newton: How much does it have to be out of shape for the precession to be out of shape for the precession to be 26,000 year period? Newton: Difference is about 50 km (actually 43 km) Measure it!!!

21. Which of the following is false? • A) the value of g is is lower at the equator than at the poles due to the rotation of the earth • B) the value of g is is lower at the equator than at the poles due to the non-spherical shape of the earth • C) the value of g is the same all over the earth • D) The value of g is less at the top of a mountain than at sea level.

22. Also since the earth is not spherical… g is different at poles and equator Measure period with pendulum and determine g from g = 9.832 m/sec2 at Poles g = 9.814 m/sec2 at Equator – due to shape of earth alone g = 9.780 m/sec2 at Equator due to rotation and shape of earth

23. Comets

24. 1681-1682 Halley’s Comet

25. “Lo! From the dread immensity of space, Returning, with accelerated course, The rushing comet to the sun descends: And, as he shrinks below the shading earth, With awful train projected o’er the heavens’ The guilty nations tremble.”

26. 684 Nuremberg Chronicles - 164 Mentioned in Babylonian Tablet Appearances of Halley’s Comet in History

27. 1066 Bayeux Tapestry 1145 Eadwine Psalter

28. Giotto 1301

29. 1456 Sketch of path 1531 Apian (orientation tail)

30. 1682 Spotted by Halley and Newton

31. Moving away from Sun Newton: Eccentric closed orbit Halley’s Historical Records 1757 …. 1682, 1607, 1531, 1456 ? 75 76 75 The appearance of Comets can be predicted!!!

32. 1759 Halley’s Comet Returns as Predicted - Newtonian Triumph

33. I do not know what I may appear to the world, but to myself I seem to have been only like a boy playing on the seashore, and diverting myself now and then in finding a smoother pebble or prettier shell than ordinary, whilst the great ocean of truth lay all undiscovered before me…..