1. Exam Wednesday September 21
PHYS Astronomy
Exam Wednesday September 21
The exam will cover anything that was covered in the notes
The exam will be closed book.
You will be allowed to have one 8/12 X 11 sheet of notes for the exam.
Good Luck!

2. placed Earth away from center of perfect spheres
PHYS Astronomy
Hipparchus (c B.C.)
placed Earth away from center of perfect spheres
developed a star catalog
- method to predict positions of sun and moon
- discovered precession of earth’s axis of rotation - estimated precession of equinoxes at 46”/year - actually 50.26”
Ptolemy (c. A.D )
combined all available astronomical information into 13 volume work, the Almagest - a geometrical model of solar system with Earth in center that predicted positions of Sun, Moon and planets - used for 1,500 years
used idea of Apollonius (c B.C.) that planets move on small circle that turns upon larger circle around the Earth explained retrograde motion of planets - fully developed by Hipparchus - accurately predicted planetary positions within a few degrees of arc

3. Retrograde Motion of Planets
PHYS Astronomy
Retrograde Motion of Planets
Apparent retrograde motion - reversal of planetary motion through the zodiac from eastward to westward
Apparent retrograde motion of Jupiter

4. Ptolemaic Model Deferent - main circle of planet path
PHYS Astronomy
Ptolemaic Model
Deferent - main circle of planet path
Epicycle - small circles on deferent along which planet moved

5. Ptolemaic Model Animation
PHYS Astronomy
Ptolemaic Model Animation

6. PHYS Astronomy
Ptolemy's model of the motions of the Sun, Moon, and planets around Earth.

7. Mars Retrograde Motion
PHYS Astronomy
Mars Retrograde Motion
Earth’s orbital speed is faster than Mars’. When Earth catches up with Mars, Mars appears to move backwards against the background of the stars

8. Mars Retrograde Motion Animation
PHYS Astronomy
Mars Retrograde Motion Animation

9. Heliocentric World View - The Copernican Revolution
PHYS Astronomy
Heliocentric World View - The Copernican Revolution
Nicholas Copernicus ( )
- wanted better way to predict planetary positions - adopted Sun-centered planetary system suggested by Aristarchus
- worked out simple geometric relationships that allowed calculation of planet’s true orbital period and distance from Sun in terms of Earth-Sun distance (AU)
- still believed that heavenly motion must be perfect circles - had to add circles upon circles as in the Ptolemaic model - did not make substantially better predictions and was not accepted for another 50 years

10. - observed comet - proved was in the heavens
PHYS Astronomy
Tycho Brahe ( )
- observed alignment of Jupiter and Saturn in occurred two days later than Copernicus prediction - decided to compile precise measurements of stellar and planetary positions
- compiled best set of naked-eye observation ever made - to within 1 arcminute (thickness of a fingernail at arm’s length)
- observed supernova of proved it was farther away than the Sun - called it a nova (“new star”)
- observed comet - proved was in the heavens
- believed planets must orbit Sun but never succeeded in explaining planetary motion. Inability to detect stellar parallax led him to believe that Sun orbited Earth while all other planets orbited Sun

11. A Complete Reformation of Astronomy
PHYS Astronomy
A Complete Reformation of Astronomy
Johannes Kepler ( )
- hired by Tycho Brahe to explain observations
- years of calculations trying to find circular orbit for Mars that matched Tycho’s observations - succeeded in matching Mars’ position in ecliptic - could not match position north or south of ecliptic
- finally realized planetary orbits were not circular but elliptical - developed three laws of orbital motion - accurately predicted planetary motions and matched Tycho’s data

12. Kepler’s Laws of Planetary Motion
PHYS Astronomy
Kepler’s Laws of Planetary Motion :
Law 1: Law of elliptical orbits
Each planet moves in an elliptical orbit.
Law 2: Law of areas
The imaginary line connecting any planet to the sun sweeps over equal areas of the ellipse in equal intervals of time.
Law 3: Law of periods
The square of any planet's period of orbital revolution is proportional to the cube of its mean distance from the sun.

13. PHYS Astronomy
Kepler’s First Law
The orbit of each planet around the Sun is an ellipse with the Sun at one focus

14. Drawing a circle. (b) Drawing an ellipse. (c) Eccentricity
PHYS Astronomy
Drawing a circle.
(b) Drawing an ellipse.
(c) Eccentricity
describes how much an ellipse deviates from a perfect circle -ratio between distance from the center of the ellipse to the focus of the ellipse and the semi-major axis.

15. PHYS Astronomy

16. PHYS Astronomy
Kepler’s Second Law
As a planet moves around its orbit, it sweeps out equal areas in equal times.

17. Area and Time Animation
PHYS Astronomy
Area and Time Animation

18. PHYS Astronomy
Kepler’s Third Law
The square of any planet's period, P, of orbital revolution is proportional to the cube of its mean distance, r, from the sun. I.e., the more distant a planet, the slower it moves on average. Example: For earth, r E= 1 AU, PE = 1 year. For Mars, r M= 1.52 AU, PM = 1.88 years

19. A plot of the cube of the average planetary distance vs the square
PHYS Astronomy
A plot of the cube of the average
planetary distance vs the square
of the orbital period is a straight
line
The average orbital speed is
inversely proportional to the
average distance from the sun

20. Planet Semimajor Axis (1010 m) Period (T yr) T2/a3 (10-34 y2/m3)
PHYS Astronomy
Planet
Semimajor
Axis (1010 m)
Period
(T yr)
T2/a3
(10-34 y2/m3)
Mercury
5.79
0.241
2.99
Venus
10.8
0.615
3.00
Earth
15.0 1
2.96
Mars
22.8
1.88
2.98
Jupiter
77.8
11.9
3.01
Saturn
143
29.5
Uranus
287 84
Neptune
450
165
Pluto
590
248

21. PHYS Astronomy
Note:
- Kepler's third law needs to be modified when the orbiting body's mass is not negligible compared to the mass of the body being orbited.
- Kepler's laws assume a two-body system - particularly bad approximation in the case of the Earth-Sun-Moon system
for calculations of the Moon's orbit, Kepler's laws are far less accurate than the empirical method invented by Ptolemy.
- Kepler's laws do not consider the emission of radiation or relativity
- Because electrical forces, like gravity, obey an inverse square law, Kepler's laws also apply to bodies interacting electrically.
Kepler did not understand why his laws were correct - Isaac Newton discovered the answer more than fifty years later. For instance, the second law also a statement of conservation of angular momentum.

22. The Death of the Earth Centered Universe
PHYS Astronomy
The Death of the Earth Centered Universe
Galileo Galilei ( )
- demonstrated that a moving object remains in motion unless acted on by an outside force (Newton’s 1st law) - contradicted Aristotle’s claim that the natural tendency of any moving object is to come to rest. Birds, falling stones, clouds, etc.. would stay with the Earth unless knocked away by some force
- used telescope that he built (invented by Hans Lippershey) saw sunspots on the Sun, craters and valleys on the moon - proved that the heavens were not perfect and unchanging
- observed moons orbiting Jupiter
- observed the phases of Venus
- showed that Milky Way resolved into countless individual stars - argued stars far more numerous and distant than imagined - reason stellar parallax not observed
- recanted before Church inquisition in Rome in formerly vindicated by the Church in 1992

23. Major Discoveries of Galileo
PHYS Astronomy
Major Discoveries of Galileo
Moons of Jupiter
(4 Galilean moons)
(What he really saw)
Rings of Saturn
(What he really saw)

24. PHYS Astronomy
Surface structures on the moon - shadows; first estimates of the height of mountains on the moon

25. Sun spots (proving that the sun is not perfect!)
PHYS Astronomy
Sun spots (proving that the sun is not perfect!)

26. PHYS Astronomy
Phases of Venus (including “full Venus”) - In the Ptolemaic system, phases would only range from new to crescent. Proved that Venus orbits the sun, not the Earth!

27. Phases of Venus Animation
PHYS Astronomy
Phases of Venus Animation

28. A New View of Nature Sir Isaac Newton (1642 - 1727)
PHYS Astronomy
A New View of Nature
Sir Isaac Newton ( )
- followed Galileo’s lead - developed fundamental laws of motion - revolutionized mathematics and science
- experienced moment of inspiration at 24 years old - saw apple fall from tree and suddenly understood gravity
- published most famous book in science in Philosophiae Naturalis Principia Mathematica - Principia for short
- built first reflecting telescope
- invented calculus
- discovered three laws of motion
- discovered universal law of mutual gravitation

29. Newton's Three Laws of Motion
PHYS Astronomy
Newton's Three Laws of Motion
First law:
A body remains at rest or moves along a straight line with constant velocity so long as no external force acts upon it.
Second law:
A body (m) acted upon by a force (f) will accelerate (a) in the direction of the applied force. The greater the force or the smaller the mass, the greater will be the acceleration .
F =ma
Third law:
A body subjected to a force reacts with an equal counter force to the applied force:
That is, action and reaction are equal and oppositely directed, but never act on the same body.

30. For every force, there is an equal and opposite force 2nd Law
PHYS Astronomy
1st Law
A body moves along a straight line with constant velocity so long as no external force acts upon it.
3rd Law
For every force, there is an equal and opposite force
2nd Law
Force equals mass times acceleration

31. Velocity and Acceleration
PHYS Astronomy
Velocity and Acceleration
Newton showed that acceleration (a) is the change of a body’s velocity (v) with time (t): a
a = Dv/Dt
Differential calculus!
Velocity and acceleration are vectors. v
Different cases of acceleration:
Acceleration in the conventional sense (i.e. increasing speed)
Deceleration (i.e. decreasing speed)
Change of the direction of motion (e.g., in circular motion)

32. Feather and Hammer Movie
PHYS Astronomy
Galileo demonstrated that acceleration of gravity is independent of the mass of the falling object - supposedly dropped balls of different mass from Leaning Tower of Pisa - Newton showed why.
Feather and Hammer Movie