1. Models of Motions in Our Sky
(Power Point 02)
Image Credit: Astropix.com

2. Student Learning Objectives
Examine the contributions of ancient and modern astronomy to the understanding of gravity and planetary motion.
Identify the significance of early contributions
Compare and contrast models for the solar system
Apply Kepler’s Laws to our Solar System

3. How did Greek philosophers describe motions in the sky?
Basic Greek theories for the sky were based on an Earth based perspective.
Heavenly bodies are spheres - move in circles
Heavens are unchangeable
Earth is stationary
Earth at center
Geocentric model

4. Early Science
Aristotle (300 BC) used logic to determine Earth must be at the center.
Eratosthenes (200 BC) calculated circumference of Earth using observation and geometry.
Image Credit: sciencebuddies.org

5. Discussion
Use your experience to explain why Aristotle would have assumed Earth was stationary and at the center of the system.

6. Hipparchus & Magnitudes
Hipparchus (150 BC) began mapping the sky, and characterized stars according to their comparative brightness.
Brightest
2nd Brightest
3rd Brightest
Etc.
We now call the comparative brightness apparent magnitude.
Sun
−26.7
Full Moon
−12.6
Venus
−4.4
Vega
Naked Eye Limit +6
Binoculars Limit
+10

7. Practice 1
Which would appear fainter to us when viewed from Earth with our eyes?
−4 magnitude star
+4 magnitude star
0 magnitude star
If two stars have the same energy output, what would make one star appear fainter than the other, when viewed from Earth?

8. The Epicylce Model
Ptolemy (150 AD) developed an epicycle model to explain the “backwards” motion of Mars.
Retrograde Motion

9. Ptolemy’s Epicycle Model

10. Image Credit: slideshare.net
Heliocentric Model
Copernicus (1500’s) used mathematics/geometry to determine the Sun was much larger than Earth.
Logically, the larger object must be at the center
Sun centered system
Image Credit: slideshare.net

11. Key Players & Their Models
Stationary
Earth
Center
Orbits
Circles
Orbital Speeds Same
Method
Aristotle
observation
Ptolemy
Copernicus
mathematics
Discussion
Compare and contrast 2 of these models.
What did all of these model have wrong?

12. One More Geocentric
Tycho Brahe (1500’s) designed and utilized new instruments for measuring precise angles in the sky.
Although Tycho Brahe believed in the geocentric system, his measurements were later used to provide proof for the heliocentric system

13. 1st Telescope Observations
Galileo (1600’s) used a telescope to make observations that provided proof of the Sun centered system.
Venus was seen to go through phases like the moon which provided proof for the location of the Sun relative to Venus.

14. Image Credit: wordpress.com

15. Galilean Moons
Image Credit: commons.wikimedia.org

16. What are Kepler’s Laws?
Kepler’s laws result in accurate predictions of future motion.
Kepler (1600’s) used Tycho Brahe’s observations and measurements of planetary positions to develop three laws of planetary motion based on ellipses.

17. Planets move in elliptical orbits with the Sun at one focus
Ellipses
Kepler’s 1st Law
Planets move in elliptical orbits with the Sun at one focus
Image Credit: study.com

18. Equal Areas Kepler’s 2nd Law
Planets sweep out equal areas of space in equal time intervals.
Credit:

19. Orbital Period Kepler’s 3rd Law
The orbital period of a planet is related to the semi-major axis of it’s orbit. (P2 = a3)
Image Credit: Wikimedia commons

20. How do we measure birthdays?
Practice 2
Apply Kepler’s Laws to our Moon.
Which planet has the longer orbital period?
Saturn: a = 9.54 AU
Jupiter: a = 5.2 AU
How do we measure birthdays?

21. The planets in our solar system follow orbits that are nearly circular.
Image Credit: NASA

22. Circles vs Ellipses
The elongation of the elliptical orbit is calculated as the eccentricity of the ellipse. (e = 0 to 1)
Image Credit: NASA Earth Observatory

23. Credit: Windows to the Universe