1. Chapter 3 Analyzing Scales and Motions of the Universe

2. Eratosthenes and Aristarchus
Using simple tools and basic geometry to measure:
the size of the Earth
Moon and Sun
and the distances to the Moon and Sun

3. The Greek Geocentric Model
An Earth-centered, or geocentric, model of the universe

4. The Problem of Retrograde Motion
The “merry-go-round” model doesn’t explain retrograde motion―periods when the planets appear to move backwards in the constellations.

5. The Ptolemaic System
To explain retrograde motion, Ptolemy created a complicated system of spheres on spheres.

6. The Heliocentric Model and Retrograde Motion

7. Nicolaus Copernicus
Introduced the heliocentric model of the solar system and deduced that Mercury and Venus had interior orbits and Mars, Jupiter, and Saturn had exterior orbits compared to Earth.

8. Copernicus and the Orbits
Elongation: the angle between the Sun and a planet, as viewed from Earth.
Conjunction: a planet and the Sun lining up, as viewed from the Earth.
Elongation can be used to determine the size of the orbit.

9. Galileo Galilei
Used the newly invented telescope to observe the heavens.
He discovered:
Mountains on the Moon
Sunspots on the Sun
Rings around Saturn
Phases of Venus
Moons in orbit around Jupiter
That the Milky Way was innumerable stars

10. The Phases of Venus
Galileo’s discoveries of moons orbiting Jupiter and phases of Venus strongly supported a heliocentric model.

11. Phases of Venus could not occur in the Ptolemaic system.

12. The Moons of Jupiter
Observations of Jupiter and its moons showed that there are objects that do not orbit Earth.

13. Elliptical Orbits and Kepler’s First Law
The orbit of a planet about the Sun is an ellipse with the Sun at one focus.
Mercury has the most eccentric orbit at

14. Orbital Speeds and Kepler’s Second Law
A line joining a planet and the Sun sweeps out equal areas in equal intervals of time.
A planet moves fastest when closest to the Sun.

15. Orbital Periods and Kepler’s Third Law
The greater the distance between the Sun and planet, the slower the planet travels.
P2 = a3
P: planet’s period, in years
a: planet’s semimajor axis, in AU

16. Newton’s Laws
An object remains at rest, or moves in a straight line at a constant speed, unless acted upon by a net outside force.
F = ma
Whenever one object exerts a force on a second object, the second object exerts an equal and opposite force on the first object.

17. Gravity Explains Kepler’s Laws

18. Newton’s Law of Universal Gravitation
F : gravitational force between two objects
m1 : mass of first object
m2 : mass of second object
r : distance between objects
G : universal constant of gravitation

19. An Explanation of Orbits
A: A ball dropped from a great height falls straight down.
B & C: A ball thrown with some horizontal speed.
E: A ball thrown with the “right” speed orbits in a perfect circle.
D & F: Balls thrown with speed a little too slow and a little too fast orbit in an ellipse.