Reminders

1 No Online Quiz this Week2 Read Chapter 5

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Midterm Results

Mean: 75%Median: 76%Standard Deviation: 10%

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Lecture 14 – Galileo and Newton’sLaws

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Clicker Question

Which properties of light changes in arefractive medium?

(a) wavelength(b) wavelength and speed(c) frequency, speed, and wavelength(d) speed(e) nothing changes

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Clicker Question

Copernicus’ Ideas were revolutionarybecause:

(a) The earth is not the center of the universe(b) The earth goes around the sun(c) We are not special(d) all of the above

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Clicker Question

Kepler’s Laws(a) Explain the motion of the planets(b) Explain the motion of the moon(c) Explain the motion of all orbiting bodies(d) all of the above

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Galileo

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Achievements

Published Sidereius Nuncius in 1609Discovered that the moon had mountains andtherefore wasn’t perfect

Discovered that Jupiter had 4 moons orbiting itThe so-called Galilean Satelites: Io, Europa,Calisto, GanymedeDiscovered that Venus has phases like the moonCan’t be explained in geocentric system

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Moons of Jupiter

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Phases of Venus

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Publications

Wrote Dialog Dei Due Massimi Sistemi(Dialogue concerning the Two Chief WorldSystems). The death knell for Ptolemy’ssystem.Sentenced to house arrest by Inquisition.Pardoned in 1979!E pur si muove (Still it moves)Started new science of mechanics currentview very different from that of Aristotle

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Distance to the Stars I

PtolemyThe scale of the planetary spacing is set bythe earth-moon distance of 60R⊕ and theneverything is spaced so the epicyles just misseach other. This works out to the earth-sundistance of 1200R⊕ found by Aristarchus fromthe “timing” of the half moon. The stars arejust outside Saturn’s orbit.

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Distance to the Stars II

CopernicusHe fudges to keep the earth-sun at 1200R⊕.Things are spaced so the epicycles just cleareach other, but things are tighter nowbecause the epicycles are smaller. The starsmust be at an immense distance to explainthe lack of parallax.

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Distance Tycho and Galileo I

TychoObserves that stars have diameters of ∼ 2arcminutes. To avoid having parallax of asimilar amount the brightest biggest starswould have to be as big as earth’s orbit. Thisleads him to a stationary earth.

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Distance Tycho and Galileo II

GalileoThe telescope makes planets bigger, i.e.,they have resolved disks of a few tens ofarcseconds. But stars are smaller, down tothe limit of his optics (a few arcseconds?).This demolishes Tycho’s objection, and thestars can be at enormous distances asCopernicus wants.

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Newton (1642-1727)

Arguably, greatest scientist who ever lived“If I have seen farther than other men, it isbecause I stood on the shoulders of giants.”Contributions in many branches ofmathematics, physics, and astronomyPublished Principia in 1687

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Newton

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Newton’s Laws

Newton’s Three Laws of Motion1 A body continues at rest or in a state of uniform

motion unless acted on by a force2

F = ma3 For every action there is an equal and opposite

reaction

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Newton’s Law of UniversalGravitation I

Law of Gravity — Inverse square law

F = −Gm1m2

r2

Can derive Kepler’s laws from Newton’s LawsExplains why objects fall toward center of theearth (see Aristotle)

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Newton’s Law of UniversalGravitation II

Explains why planets orbit sun and whymoons orbit planetsCan be used to make and test predictions

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Newton’s Laws

Newton’s Three Laws of Motion1 A body continues at rest or in a state of uniform

motion unless acted on by a force2

F = ma3 For every action there is an equal and opposite

reaction

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Uniform Circular Motion

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Circular Velocity

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Clicker Question

When the string cuts through the bagel, thebagel will:

(a) Move outward due to the centrifugal force(b) Move in a straight line, since there is no longer a

force(c) Move in a random direction(d) Hit someone in the head

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Escape Velocity

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Center of Mass

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