1. Investigating Astronomy Timothy F. Slater, Roger A. Freeman
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
the 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 Ptolemaic System
To explain retrograde motion, Ptolemy created a complicated system of spheres on spheres.

5. 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.

6. ConceptCheck
If Eratosthenes had found that the Sun’s noon-time summer solstice altitude at Alexandra was much closer to directly overhead, would he then assume that Earth was larger, smaller, or about the same size?
If Aristarchus had estimated the Sun to be 100 times farther from Earth than the Moon, how large would he have estimated the Sun to be?
If Mars is moving retrograde, will it rise above the eastern horizon or above the western horizon?
How fast is Earth spinning on its axis in the Greek geocentric model?
What causes the planets to actually stop and change their direction of motion in the Ptolemaic model?

7. The Heliocentric Model and Retrograde Motion

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. ConceptCheck
In the heliocentric model, would an imaginary observer on the Sun look out and see planets moving in retrograde motion?
If Venus is visible high in the evening sky after sunset, is it leading Earth in its orbit or behind Earth?
How many times is Mars at inferior conjunction during one orbit around the Sun?
What causes the planets to stop and change their direction of motion through the sky in the heliocentric model?
Why is Jupiter’s sidereal period longer than its synodic period?
Why was Copernicus’s model more accurate than Ptolemy’s model?

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. ConceptCheck
Which phase will Venus be in when it is at its maximum distance from Earth?
Why had Jupiter’s moons not been observed prior to Galileo’s time?

14. 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

15. 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.

16. 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

17. ConceptCheck
Which orbit is more circular—Venus’s orbit, with e = , or Mars’s orbit, with e = 0.093?
According to Kepler’s second law, at what point in a communications satellite’s orbit around Earth will it move the slowest?
The space shuttle typically orbits Earth at an altitude of 300 km, whereas the International Space Station orbits Earth at an altitude of 450 km. Although the space shuttle takes less time to orbit Earth, which one is actually moving at a faster rate?
If Pluto’s orbit has a semimajor axis of 39.5 AU, how long does it take Pluto to orbit the Sun once?
Do Kepler’s laws of planetary motion apply only to the planets?

18. 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.

19. ConceptCheck
If the 815-kg unmanned Voyager 2 interplanetary space probe was traveling at 60,000 km per hour without any rocket engines firing in 2006, how fast will it be moving in 2012, still without engines?
How fast is the space shuttle traveling 3 seconds after launch if it is accelerating at a rate of about 20 m/s2?
If a door on the International Space Station requires 100 newtons of force to be pushed open and, according to Newton’s third law, the door pushes back on an astronaut with an equal but opposite force of 100 newtons, why is it that an astronaut can successfully open the door?

20. Gravity Explains Kepler’s Laws

21. 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

22. 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.

23. ConceptCheck
How much does the gravitational force of attraction change between two asteroids if the two asteroids drift three times closer together?
How much would a 75-kg astronaut, weighing about 165 pounds on Earth, weigh in newtons and in pounds if he were standing on Mars, which has a mass of 6.4 x 1023 kg and a radius of 3.4 x 106 m?
What keeps the International Space Station from crashing into Earth when it has no rocket engines constantly pushing it around Earth?

24. Chapter 4 Exploring Our Evolving Solar System
Next Chapter:
Chapter 4 Exploring Our Evolving Solar System