Galileo, Tycho,Galileo, Tycho, and Keplerand Kepler

Galileo’s Experiments (1564-1642)

Galileo tried something new – doing experiments!

• Dropping balls to measure gravity

• Rolling balls to examine inertia

• Observing the sky through a telescope

What Galileo Saw

• An imperfect Sun (sunspots)

What Galileo Saw

• An imperfect Sun (sunspots)

• A Moon with mountains and craters

What Galileo Saw

• An imperfect Sun (sunspots)

• A Moon with mountains and craters

• The “ears of Saturn”

What Galileo Saw

• An imperfect Sun (sunspots)

• A Moon with mountains and craters

• The “ears of Saturn”

• Four moons orbiting Jupiter

What Galileo Saw

• An imperfect Sun (sunspots)

• A Moon with mountains and craters

• The “ears of Saturn”

• Four moons orbiting Jupiter

• The phases of Venus

Tycho Brahe Measurements

Tycho Brahe (without a telescope) made extremely accurate measurements of the positions of the stars and planets over the course of 20 years.

Tycho Brahe’s Model

• Earth at the center of the “Universe” (because parallax is not seen)

• The Sun travels about the Earth in a perfect circle

• The planets move around the Sun in perfect circles

Kepler’s Analysis

By working for Tycho Brahe (and then stealing the data after Tycho’s death), Johannes Kepler had access to the most precise data on planetary positions in history.

He fit the data in every way imaginable.

Kepler’s Laws

Kepler’s Laws

1) Planets move in ellipses with the Sun at one focus

First define the distance from the earth to the Sun to be 1 Astronomical Unit (1 A.U.)

Kepler’s Laws

Kepler’s Laws

1) Planets move in ellipses with the Sun at one focus

2) Planets in their orbits sweep out equal areas in equal times

First define the distance from the earth to the Sun to be 1 Astronomical Unit (1 A.U.)

Kepler’s Laws

First define the distance from the earth to the Sun to be 1 Astronomical Unit (1 A.U.)

Kepler’s Laws

1) Planets move in ellipses with the Sun at one focus

2) Planets in their orbits sweep out equal areas in equal times

3) The period, P, of an orbit (in years) squared is equal to a, the semi-major axis of the orbit (in A.U.) cubed. In terms of mathematics, P2 = a3

These laws are empirical – Kepler knew no reason for them

Kepler’s Laws

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Summary• Galileo: Father of experimental science

• Tests of inertia and acceleration• Observed the sky with a telescope: heavens not perfect

• Tycho Brahe• Recorded very precise positions of the planets with naked eye• Wanted Kepler to fit his data with a modified geocentric model

• Kepler• Discovered 3 mathematical laws that could fully describe the

motions of the planets (but without any physical basis)