1. Birth of Modern Astronomy OR How Nerds Changed the World!!!
The Motion of Planets
Birth of Modern Astronomy OR
How Nerds Changed the World!!!
Theory?
Hypothesis?
Law?
Scientific Method?

2. How is science done? Observations Experiments Explanations Repeat
Theories
Laws
Repeat

3. Assumptions of Early Models
Geocentric - Earth in the middle
Everything orbits the Earth
Stars are located on the Celestial Sphere
Everything moves in uniform circular motions

4. The Greeks Anaximander Pythagoras Eudoxus Aristotle Apollonius
Celestial sphere rotates around the earth
Pythagoras
Earth is a sphere
Eudoxus
Planet motion accounted for by separate spheres
Aristotle
Complete model of the universe (4 elements)
Perfect heavens
Apollonius
epicycles

5. The Time of Aristotle

6. Model of the Universe
All things in the universe go to their Natural Place
Element
Natural Motion
Properties
Earth
Falls down
Dry, Cold
Air
Rises up
Wet, Hot
Water
Cold, Wet
Fire
Hot, Dry

7. Hellenistic (Greek) Periodic Table

8. Retrograde Motion

9. The problem of Retrograde Motion: Apollonius
The motion of these spheres did not account for retrograde motion.
Apollonius introduces ‘epicycles’
Roughly meaning ‘cycles within’

10. What is an epicycle?
Epicycle
The Center of of epicycle revolves around the earth
The planet spins along the epicycle at the same time.
Mars
Earth
Deferent

11. Enter the Roman: Ptolemy
Brought it all together
Added the equant to adjust the model to match observations
Wrote “The Mathematical Compilation”
Destruction of Library of Alexandria
(Europe lost almost all it’s written knowledge)
The Arab Scholars called it “Almagest” (“the greatest”)
This is how they came to know it once the work returned to Europe.

12. Epicycle
Mars
Equant
Claudius Ptolemy (87-165)
Earth
Deferent

13. The Dark Ages

14. Nicolaus Copernicus (1473-1543)
Errors building up
Must be a better way!
Let’s try a Heliocentric system!
Not any better though

16. Tycho Brahe (1546-1601) Comet – beyond the Moon Supernova – far away
Naked eye observations of planets
Accuracy through repetition
Best observations of planetary positions
Hired “nerd” to help calculate model
Died….

17. Three Laws of Planetary Motion
Johannes Kepler ( )
Worked for Brahe
Took data after his death
Spent years figuring out the motions of the planets
Came up with…
Three Laws of Planetary Motion

18. 1. Planets move in elliptical orbits with the Sun at one foci
Perihelion
Aphelion
Foci (sing. Focus)
Average distance from the Sun = 1 Astronomical Unit (1 A.U.)

19. 2. Planets move faster at perihelion than at aphelion.
1 Month
1 Month

20. 3. Period is related to average distance
P = period of the orbit
a= average distance
P2 = k a3
Longer orbits - greater average distance
Need the value of k to use the formula
k depends upon the situation
Can be used for anything orbiting anything else

21. P2 = a3 Special version of Kepler’s third Law –
If the object is orbiting the Sun
P – measured in years,
a – measured in A. U., then….
P2 = a3

22. Galileo Galilei (1564-1642) Knew of Copernicus’s & Kepler’s work
Used a telescope to look at the sky
What did he see?

23. The Moon was an imperfect object
Venus has phases

24. Jupiter has objects around it
Saturn is imperfect
The Sun is imperfect

25. Isaac Newton (1642-1727) The Three Laws of Motion The ultimate “nerd”
Able to explain Kepler’s laws
Had to start with the basics -
The Three Laws of Motion

26. 1. Law of Inertia - Objects do whatever they are currently doing unless something messes around with them.

27. 2. Force defined
F=ma
F=force
m=mass
a=acceleration (change in motion)

28. 3. For every action there is an equal and opposite reaction.
The three laws of motion form the basis for the most important law of all (astronomically speaking)
Newton’s Universal Law of Gravitation

29. F=force of gravity
G=constant
M1, M2 = masses
R=distance from “centers”
Gravity is the most important force in the Universe

30. Newton’s Revisions to Kepler’s Laws of Planetary Motion:
Kepler’s 1st and 2nd Laws apply to all objects (not just planets)
3rd Law rewritten:
4π2 and G are just constant #s (they don’t change)
M1 and M2 are any two celestial bodies (could be a planet and Sun)
Importance: if you know period and average distance of a planet, you can find mass of Sun (2 x 1030 kg) or any planet!
Mass of Sun is kg
Mass of Earth is kg
Mass of Mr. J is 100 kg! WOW! 30