After Galileo

When we Left Galileo• Inquisition 1633:

– “vehemently suspect of heresy”– that the Sun lies motionless at the center of

the universe, that the Earth is not at its center – required to “abjure, curse and detest”– sentenced to house arrest

• Many scientists did not support Galileo– Difficult to see through primitive telescope– Earth obviously not moving

• No overwhelming evidence

Kepler 1571-1630• Astronomer and Mathematician• Assistant to Tycho Brahe• Astrologer to

Holy Roman Emperor• Mystic – 5 Regular Solids– 5 Planets

• Tycho’s Data• Modern Science• Einstein - “God does not play dice.”

KeplerThree Laws:• The orbit of a planet is an ellipse

with the Sun at one of the two foci.

• A line segment joining a planet and the Sun sweeps out equal areas during equal intervals of time.

• The square of the orbital period of a planet is proportional to the cube of the semi-major axis of its orbit. Prob Set 10C

Newton 1642-1727

• Mathematical Genius• Manic-Depressive

No Social Life• Invented Calculus• Professor at Cambridge• At the Royal Society rumor of a

mathematician at …• “What path would a planet follow if

the sun attracted it with an inverse square force?”

• Newton Answered: “An ellipse”

Inverse Square

• Legend has it that Newton was looking at an apple• aapple = 9.8 m/s2

• amoon = .0027 m/s2

• Ratio = 9.8 / .0027 ≈ 3600

• Radius of earth = 6.38 * 106 m• Radius of moon’s orbit = 3.84 *108 m• Ratio = 3.84x108 / 6.38x106 = 60.2• 60 x 60 = 3600• The moon is 60 times farther away• It’s acceleration is 3600 times less

a ~ 1 / r2 F ~ 1 / r2

• 10 times farther away, the earth’s gravity is 100 times weaker• Here we are 4,000 miles from the center of the earth.• If you weight 200 pounds here, 40,000 miles into space you

will weigh 2 pounds

• a = k / r2

• a r∙ 2 = k

• a1 r∙ 12 = a2 r∙ 2

2

• a1 / a2 = r22 / r1

2

• a1 / a2 = (r2 /r1) 2

Prob Set 15G