Chapter 2 continuation...

Thursday, January 24

Spring 2008

Tycho Brahe’s view on planetary motion

Tycho Brahe (1546 – 1601)

The last great naked-eye astronomer

(telescopes did not exist while he was alive)

Constructed a large quadrant to make highly

accurate measurements of the positions of the planets

and stars

The Tychonic System

Tycho Brahe combined the geocentric and

heliocentric systems of the universe into his

own model, the “Tychonic System”

Kepler and the laws of planetary motion

Johannes Kepler (1571 – 1630)

Publicly defends the Copernican system in his first major astronomical work, The

Sacred Mystery of the Cosmos.

Begins work as an assistant to Tycho Brahe in Prague in 1600, analyzing Tycho’s planetary observation data.

Inherits Tycho Brahe’s data after Brahe’s death in 1601.

Kepler’s laws of planetary motion

T 2

r 3constant

(for all planets orbiting the sun)

=

Kepler’s 1st Law: Kepler’s 2nd Law:

Kepler’s 3rd Law :

T = period of orbit

r = orbital radius

Shortly after the invention of the telescope, Galileo made several observations that could not be accounted for by the geocentric system

Galileo and Planetary Motion

Galileo Galilei (1564 – 1642)

Galileo and Planetary Motion

• Galileo observed the moon “...to be uneven, rough, and crowded with depressions and bulges. And it is like the face of the earth itself, which is marked here and there with chains of mountains and depths of valleys.”

• He discovered four moons orbiting the planet Jupiter.

• He observed the phases of the planet Venus.

• He observed sunspots.

Galileo’s Views on Motion

vv

On a sloped surface, a ball rolling down

the slope gains speed, while a ball rolling up the slope

loses speed.

On a flat surface, there is no slope to

cause a rolling ball to slow down or speed up... it continues its

motion forever.

Principle of inertia: constant-speed, straight-line motion is as natural as at-rest motion.

Describing Motion

• speed is distance traveled over time (a scalar)

• velocity is speed with direction (a vector) – velocity is displacement, D, over time

• acceleration is the rate of change of velocity (a vector)

s = d / t

v = D / t

a = (vf – vi) / t

Galileo and the Inclined Plane

Galileo and the Motion of Falling Objects

t (s) d (m) v (m/s)

0

0

1

1

2

4

3

9

4

16

5

25

6

36

1

3

5

7

9

11

Acceleration of falling objects found to be constant:

a = (vf – vi) / t = 2 m/s2 at all time points in Fig. 2-7

Finish reading Chapter 2 in the textbook for next

Tuesday 01/29

Mallard HW quiz for Chapter 2 now available

– due next Thursday 01/31