For Newton seized them and, with trembling hands,Began to work his problem out anew.)Then, then, as on the page those figures turnedTo hieroglyphs of heaven, and he beheldThe moving moon, with awful cadences\Falling into the path his law ordained,Even to the foot and second, his hand shookAnd dropped the pencil...Work it out for me,"He cried to those around him; for the weightOf that celestial music overwhelmed him;And, on his page, those burning hieroglyphsWere Thrones and Principalities and Powers. ..For far beyond, Immeasurably far, Beyond our sun, he saw that river of sunsWe call the Milky Way, that glittering hostPowdering the night, each grain of solar blazeDivided from its neighbour by a gulfToo wide for thought to measure; each a sunHuger than ours, with its own fleet of worlds,Visible and invisible. Those bright throngsThat seemed dispersed like a defeated host,Through blindly wandering skies, now, at the wordOt one great dreamer, height o'er height revealedHints of a vaster order, and moved onIn boundless intricacies of harmonyAround one centre, deeper than all SUIlS,The burning throne of God.

TidesTidesSeveral thinkers in the past guessed that the Several thinkers in the past guessed that the Moon had some connection with the tidesMoon had some connection with the tides

Posidonius (Alexandria), Roger Bacon, Kepler, Posidonius (Alexandria), Roger Bacon, Kepler, DescartesDescartes

What was the reason for their guess?What was the reason for their guess?The tides are especially high during full moon The tides are especially high during full moon and new moon. and new moon. They based their guess on observations:They based their guess on observations:– The tides occur about one hour later each day.The tides occur about one hour later each day.– If you look at the time of moon-rise, you find that it If you look at the time of moon-rise, you find that it

also occurs roughly one hour later each day. Poemalso occurs roughly one hour later each day. Poem

Galileo (mistakenly) believed that tides arise Galileo (mistakenly) believed that tides arise from the rotation of the earth.from the rotation of the earth.

What measurable evidence helped What measurable evidence helped support Newton’s detailed theory support Newton’s detailed theory

of gravitation (1/Rof gravitation (1/R22)?)?

Tides Tides – Caused by sun and moonCaused by sun and moon

Shape of the earth is not an exact sphereShape of the earth is not an exact sphere– Precession of the equinoxesPrecession of the equinoxes– Value of g is not the same at the poles and Value of g is not the same at the poles and

equatorequator

Comets are predictableComets are predictable

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

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

(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 forgetEven to eat and drink, when he was wrappedIn those miraculous new discoveriesAnd, under this wild maze of shadow and sunBeheld-though not the Master Player's hand-The keys from which His organ music rolls,Those visible symphonies of wild cloud and lightWhich clothe the invisible world for mortal eyes.

Fools have saidThat 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 lawsForetell that knowledge one day shall be song,And those whom Truth has taken to her heartFind that it beats in music.

Even this ageHas glimmerings of it. Newton never sawHis own full victory; but at least he knewThat 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...

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

Tides

The Shepherdess of the SeaReproach 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 moonShall lead us into harbor soon

Dear, when you see her glory shine,Between your fragrant boughs of pineKnow there is but one hour to waitBefore her hands unlock the gate,And the full flood of singing foamFollow her lovely footsteps home.

Then waves like flocks of silver sheepCome rustling inland from the deep,And into rambling valleys pressBehind their heavenly shepherdessYou cannot see them? Lift your eyesAnd see their mistress in the skies

She rises with her silver bow,I feel the tide begin to flowAnd every thought and hope and dreamBorne on the universal tide,The wanderer hastens to his bride.The sea’s white shepherdess, the moon,Shall lead him into harbor soon.

Detail Behavior of Tides Detail Behavior of Tides Provided Confirmation of Provided Confirmation of

Newton’s Gravitational TheoryNewton’s Gravitational Theory

Newton was the first to explain that tides Newton was the first to explain that tides occur because the force of gravity of the occur because the force of gravity of the Moon on the Earth gets weaker with Moon on the Earth gets weaker with increasing distance.increasing distance.

The water closest to the Moon is attracted The water closest to the Moon is attracted toward the Moon with greatest force.toward the Moon with greatest force.

Therefore, as the earth rotates, we have a Therefore, as the earth rotates, we have a high tide when the water comes closest to high tide when the water comes closest to the moon.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.

Why does the moon’s gravity play a Why does the moon’s gravity play a bigger role than the sun’s gravity ?bigger role than the sun’s gravity ?

Force of sun on earthForce of sun on earth

F sun-on-earth = G mF sun-on-earth = G mearthearth x m x msunsun/R/Rearth-sunearth-sun 22

= 6.7 x 10= 6.7 x 10-11-11 x (6 x 10 x (6 x 102424)(2 x 10)(2 x 103030)/(150 x 10)/(150 x 1099))22

= 35.6 x 10= 35.6 x 102121 Newtons Newtons

Force of the Sun is Much Greater)

1/R2

1/R2

Change in F Change in F moon-across-earthmoon-across-earth = =

= 2 x 10 = 2 x 10 2020 - 2.14 x 10 - 2.14 x 10 2020

=0.2 x 10 =0.2 x 10 2020 Newtons Newtons

Change in F Change in F sun-across-earthsun-across-earth = =

35.57 x 10 35.57 x 10 2121 – 35.56 x 10 – 35.56 x 10 2121

=0.1 x 10 =0.1 x 10 2020 Newtons Newtons

G mearthmsun

(Re-s - Re)2

- G mearthmsun

(Re-s + Re)2

G mearthmmoon

(Re-m - Re)2

- G mearthmmoon

(Re-m + Re)2

But there are two tides in a 24-But there are two tides in a 24-hour periodhour period

When are tides the highest?When are tides the highest?

A) half-moonA) half-moon

B) Full-moonB) Full-moon

C) New-moonC) New-moon

D) B & CD) B & C

E) All of the aboveE) All of the above

Strong Tides and Weak TidesStrong Tides and Weak Tides

Why the earth’s axis Why the earth’s axis precesses?precesses?

Because the earth Because the earth is not exactly is not exactly

sphericalspherical

The moon pulls harder on the bulge closer to the moon causing the spinning earth to precess like a top

Shape of the earth is not an exact sphere!Shape of the earth is not an exact sphere!

Why? - Because of rotation, it deformed in early Why? - Because of rotation, it deformed in early stages of formationstages of formation

Newton: How much does it have to be out of shape Newton: How much does it have to be out of shape for the precession to be out of shape for the for the precession to be out of shape for the precession to be 26,000 year period?precession to be 26,000 year period?

Newton: Difference is about 50 km (actually 43 km)Newton: Difference is about 50 km (actually 43 km)

Measure it!!!Measure it!!!

Which of the following is false?Which of the following is false?

A) the value of g is is lower at the equator A) the value of g is is lower at the equator than at the poles due to the rotation of the than at the poles due to the rotation of the earthearth

B) the value of g is is lower at the equator B) the value of g is is lower at the equator than at the poles due to the non-spherical than at the poles due to the non-spherical shape of the earthshape of the earth

C) the value of g is the same all over the earthC) the value of g is the same all over the earth

D) The value of g is less at the top of a D) The value of g is less at the top of a mountain than at sea level.mountain than at sea level.

Also since the earth is not spherical…Also since the earth is not spherical…

g is different at poles and equatorg is different at poles and equator

Measure period with pendulum Measure period with pendulum and determine g from and determine g from

g = 9.832 m/secg = 9.832 m/sec22 at Poles at Poles

g = 9.814 m/secg = 9.814 m/sec22 at Equator – due to at Equator – due to

shape of earth aloneshape of earth alone

g = 9.780 m/secg = 9.780 m/sec22 at Equator due to at Equator due to

rotation rotation andand shape of earth shape of earth

T = 2π L/g

CometsComets

1681-1682 Halley’s Comet1681-1682 Halley’s Comet

““Lo! From the dread Lo! From the dread immensity of space, immensity of space,

Returning, with accelerated Returning, with accelerated course, course,

The rushing comet to the sun The rushing comet to the sun descends:descends:

And, as he shrinks below the And, as he shrinks below the shading earth, With awful shading earth, With awful

train projected o’er the train projected o’er the heavens’ heavens’

The guilty nations tremble.”The guilty nations tremble.”

Appearances of Halley’s Comet in HistoryAppearances of Halley’s Comet in History

684 Nuremberg Chronicles- 164 Mentioned in Babylonian Tablet

1066 Bayeux Tapestry

1145 Eadwine Psalter

Giotto 1301

1456 Sketch of path

1531 Apian (orientation tail)

1682 Spotted by Halley and Newton

Moving Moving awayaway from Sun from Sun

Newton: Eccentric Newton: Eccentric closedclosed orbit orbit

Halley’s Historical RecordsHalley’s Historical Records

1757 …. 1682, 1607, 1531, 1456

? 75 76 75

The appearance of Comets The appearance of Comets can be predicted!!!can be predicted!!!

1759 Halley’s Comet Returns as Predicted - 1759 Halley’s Comet Returns as Predicted - Newtonian TriumphNewtonian Triumph

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…..