1. Chapter 2
Sections

2. Geocentric Model
The geocentric model was the idea that the Earth is the center of the universe and all celestial bodies revolve around it
This model was pioneered by the ancient astronomer Ptolemy
Ptolemy lived in Alexandria Egypt during the time of the Roman Empire

3. Ptolemy (90 A.D. – 168A.D.)

4. Problems with the Geocentric Model
The problem of retrograde motion
Retrograde motion refers to the motion of the planets with respect to background stars
Planets slowly move eastward among the background stars
Occasionally, they move back west before moving east again

5. Retrograde Motion of Mars

7. Ptolemy’s explanation
Each planet revolves around an epicycle
Each epicycle revolves around a deferent centered on the Earth

9. Copernicus and the Heliocentric Model
Eventually, problems compounded over the years and it was clear that the geocentric model was not correct
This led Copernicus to propose a sun-centered model of the solar system
This is known as the Heliocentric Model of the solar system

10. Copernicus
Polish Astronomer who solved the problem of retrograde motion by proposing the Earth revolved around the sun
He published a book called On the Revolutions of the Heavenly Bodies (1543), which he received a copy of on his deathbed

11. Heliocentric Explanation of Retrograde Motion

12. Galileo Galilei ( )
An Italian who made observations that supported the heliocentric model
Also considered the father of modern physics

13. Phases of Venus
Galileo was one of the first to use a telescope to observe the night sky
Galileo observed that Venus has phases like the moon
He also observed that the apparent size of Venus changes with phase

15. Galileo’s explanation of the phases of Venus

16. Moons of Jupiter
Galileo also observed several objects orbiting the planet Jupiter
This was direct evidence against the Geocentric Model
These are now known as the 4 Galilean moons

17. Galileo’s sketches of Jupiter

18. Galilean Moons

19. Galileo published a book , Dialogue Concerning the Two Chief World Systems, supporting the heliocentric model
He was punished by the Roman Catholic Church and condemned to house arrest for the last 9 years of his life

20. Johannes Kepler ( )
The German Johannes Kepler accepted the heliocentric model
He used the observations of Tycho Brahe to deduce his 3 laws of planetary motion

21. Kepler’s First Law
The orbit of a planet around the Sun is an ellipse with the Sun at one focus

22. Conic Sections

24. An Ellipse

26. Kepler’s Second Law
A line joining a planet and the Sun sweeps out equal areas in equal intervals of time

27. Kepler’s Third Law
Relates the time it takes a planet to revolve around the sun and its average distance from the sun
The time to make one complete revolution is called the period (p)
The average distance of a planet to the sun is approximately the semi-major axis (a) of the elliptical orbit

28. The average distance from the Earth to the sun, 93 million miles, is called an Astronomical Unit (AU)
If period is measures in Earth years, and semi-major axis in AU’s, then Kepler’s third law can be written as:
p2 = a3
The square of a planets sidereal period is equal to the cube of its semi-major axis

30. Isaac Newton (1642-1727) Born in England
Considered one of the greatest mathematicians and physicists of all time
One of the most celebrated scientists of all time

31. Newton’s First Law of Motion
Objects at rest will remain at rest until a force acts on them
Objects in motion in a straight line moving at a constant speed will continue to do so until a force acts on them

32. Newton’s Law of Gravitation
Every object attracts every other object
The more massive the objects are, the larger the force
The farther apart the objects are, the weaker the force
Mathematically:

33. The distance, d, is the distance between the center of mass of each object
The force is inversely proportional to the distance squared
This means if you double the distance between two objects, the force becomes 4 times weaker
If you triple the distance between two objects, the force becomes 9 times weaker