PES 106        Spring 2003
Previous Lecture

General Astronomy II
Next Lecture

Lecture Notes:

Orbits and Kepler's Laws

text: Chapter 1, Section 1.3

History: Copernicus, Brahe and Kepler

  • about 1500 ................... Poland
    • Nicolaus Copernicus
      • developed model with Sun at center of Solar System
      • planets orbit about the Sun in perfect circles
      • Earth rotates
      • stars are very far away
    • Copernican model explained:
      • order of planets from Sun
      • daily motions from Earth's rotation
    • Copernican model still had some problems:
      • predictions of planet positions were no more accurate than Greek models (because of circular orbit assumption)
  • about 1550 .................... Denmark
    • Tycho Brahe
      • great observer (still no telescopes)
      • produced excellent data
  • about 1600 .................... Germany / Austria
    • Johannes Kepler
      • studied Brahe's data
      • modified Copernican model
        • orbits are ellipses - not circles

Kepler's 3 Laws

- expressed for planets but true for any objects that orbit other objects.

1. Planets move in elliptical orbits with the Sun at one focus.

See Figure 1.27 for an exagerated elliptical orbit. Here is a link to the figure. (Fig. 1.28 in the 2nd ed.)

Elliptical orbit of planet

most of the orbits are almost circular

Here is a NASA movie clip (Quicktime with sound) that describes the law. This takes a LONG time to load (Over 2 minutes on my fast, University connection).

2. While in an elliptical orbit, a planet moves faster when nearer the Sun than when further away.

(radial line from Sun to planet sweeps out equal areas in equal times)

Kepler's 2nd law

Here is a simple animation of Kepler's second law.

Here is a link to a Java applet showing Kepler's second law. Click on "red planet" and on "show orbit" if they are not already selected. Then click on the red "start" button in the lower right corner. (You may need to scroll down to see it). Notice how the planet moves in an elliptical orbit and gets faster when it is closer to the planet.

Here is a link to another Java applet showing Kepler's second law. It takes a little while to load. You may need to read the guidelines to really understand how to use this. I like to click the "show orbit" button. It defaults to a circular orbit, so I increase the "eccentricity" to about 0.2 to see something that looks more like an ellipse.

Here is another NASA movie clip (Quicktime with sound) that describes the second law. Again it takes about 2 minutes to load on a fast connection. There is also a Part two to this movie clip.

3. Planets which are farther from the Sun move slower and have a greater distance to travel. Planets which are farther from the Sun have longer orbital periods.

Not a simple ratio: (Period)2 = (Distance)3

 

Kepler's 3rd Law

Here is another NASA movie clip (Quicktime with sound) that describes the third law. Again it takes about 2 minute to load on a fast connection.

Kepler did not know why his laws worked.

History: Galileo

  • about 1600 ............. Netherlands
    • telescope invented
  • about 1609 .............. Italy
    • Galileo Galilei
      • experimentalist
      • built crude telescope (about 20x)
    • Galileo observed:
      • Milky Way is not a cloud - it is stars
      • sunspots => Sun is blemished !

We now have a description of orbits based on observations.

Next we ask WHY ?

The answer will be: GRAVITY.

Previous Lecture Previous Lecture - - - INDEX OF LECTURES - - - Next Lecture Next lecture

RETURN to Lecture Notes Outline