Lecture 4 : First Discoveries Continued and the Copernican Revolution

Related Reading: Impey/Hartmann Chapter 2 and 3

What causes seasons?

animation

Linear vs. Angular measurements

For more on the small angle formula go here.

All measurements on the sky are in angular units, not in linear units.

Examples of deductive reasoning ...

From Eratosthenes, 200 B.C., Alexandria

• Compare length of shadows at the same time of day at two different locations

• Difference in length of shadows related to the angle at which you are looking at Sun

• Relating the angular difference to the linear distance gives you the circumference of the Earth

How can you measure the Earth's tilt? Eratoshenes again!

• measure difference between noontime elevation of Sun in winter and summer

• divide the difference by two to get the angle of the tilt

What is the distance to the Moon?

• size on the sky is about 1/2 degree (1800 arcseconds)

• the moon's physical size is about 1/3 that of the Earth (measured from eclipses)

  

  

  • Distance to the Moon (D) = 206265 x size of Moon (d)/angle on sky in arcseconds (alpha)

  • D = (2.1 x 10⁵ d)/(1.8 x 10³) = 120d

  • since Moon's diameter, d, is about 1/3 that of Earth's, D = 40 times Earth's diameter

Ptolemy vs. Copernicus
(many sites available for history, here's one)

Observation	Ptolemy (images are links)	Copernicus
Retrograde Motion
Inferior Planets
Superior Planets

One problem was, why don't the stars move or get fainter and brighter as we get farther or closer ?

Defining Parallax

• parallax applet here

  

Brahe and Kepler

• The insight of the elliptic orbit

  

  

  

  Kepler's Laws

  • Planets travel in elliptical orbits with the Sun at one foci

  • Equal areas are swept up in equal time (Applet 1 or Applet 2)

  • P^2 proportional to a^3 (where P is the period of the orbit and a is the semimajor axis) ( Applet 1)

    

Galileo and the Telescope

• Sunspots (and Sun's rotation: click in image to see Sun rotation movie)

  

• 4 Moons of Jupiter (go here for a fuller historical descritpion)

  

  

• Phases of Venus

  

  

• frames of reference

• inertia

• independence of acceleration on the objects mass (movie needs quicktime plug-in)

  Astronaut movie here