1. Simple observations – profound Questions
Just using eyes & brain can provoke “cosmological” questions:
Is the Earth the center of the Universe?
How far away are Sun and Moon?
How big are they?
How big is the Earth?
How heavy is the Earth?

2. Earth or Sun the Center? Aristotle (384–322 BC)
Argued that the planets move on spheres around the Earth (“geocentric” model)
Argues that the earth is spherical based on the shape of its shadow on the moon during lunar eclipses
Aristarchus (310–230 BC)
Attempts to measure relative distance and sizes of sun and moon
Proposes, nearly 2000 years before Copernicus, that all planets orbit the Sun, including the Earth (“heliocentric” model)
Aristarchus: measured angle btw sun and moon at first and last quarter moons – right triangle gives relative distance to moon and sun a factor of 20 (actually 390!).
Estimated relative size of earth moon by measuring how long it took the moon to move through the earth’s shadow in a lunar eclipse, got factor of 3 (not too bad). Since sun and moon have same angular size, sun must be ~20 times bigger than the moon.
With Eratosthenes’s measurement of the diameter of the earth, this gave actual distances/sizes for all.

3. Counter Argument or not?
Objection to Aristarchus’s model: parallax of stars is not observed (back then)
Aristarchus argued that this means the stars must be very far away

4. Measuring the Size of the Earth
Eratosthenes (ca. 276 BC)
Measures the radius of the earth to about 20%
Hellenistic period: follows AtG’s conquests of Persia, Egypt, parts of India. Greek the international language of learning. Lasts until the Roman conquests (44BC—100AD)
At summer solstice. Angle measured to be about 7 deg = 1/50 circle, hence dist from Syene to Alex about 1/50 the circumference of the earth.

5. Documentation discerns subtle Effects
Hipparchus (~190 BC)
His star catalog a standard reference for sixteen centuries!
Introduces coordinates for the celestial sphere
Also discovers precession of the equinoxes
Declination measured in degrees north (+) or south (-) of celestial equator
Right ascension (hrs, minutes) increases eastward from the location of the sun at the Vernal equinox

6. How far away is the Moon?
The Greeks used a special configuration of Earth, Moon and Sun (link) in a lunar eclipse
Can measure EF in units of Moon’s diameter, then use geometry and same angular size of Earth and Moon to determine Earth-Moon distance

7. That means we can size it up!
We can then take distance (384,000 km) and angular size (1/2 degree) to get the Moon’s size
D = 0.5/360*2π*384,000km = 3,350 km

8. How far away is the Sun? This is much harder to measure!
The Greeks came up with a lower limit, showing that the Sun is much further away than the Moon
Consequence: it is much bigger than the Moon
We know from eclipses: if the Sun is X times bigger, it must be X times farther away

9. Simple, ingenious idea – hard measurement

10. Graphs Making a graph Example: y = 3x - 1
Create a table with values of the independent variable and the function
Draw the coordinate system on a piece of paper
Put in (x,y) pairs
Connect the dots
Example: y = 3x - 1

11. Daily Rising and Setting
Due to the rotation of the Earth around its axis
Period of rotation: siderial day= 23h56m4.1s
1 solar day (Noon to Noon) =24h
Stars rotate around the North Star – Polaris
Circumpolar – never rise or set 11

12. What time is it? Depends on where you are on the Earth!
Time zones ensure that the noon is really noon, i.e. sun is at highest point
To avoid confusion, use universal time (UT), the time at the meridian in Greenwich
UT = EST + 5 hrs
Daylight savings adds one hour in spring, so UT = EDT+ 4 hrs

13. The Time Zones
Established to insure that sun is at highest point approximately at noon in the middle of the time zone

14. Daily and yearly motion intertwined
Solar vs Siderial Day
Earth rotates in 23h56m
also rotates around sun
 needs 4 min. to “catch up”
Consequence: stars rise 4 minutes earlier each night (or two hours per month, or 12 hours in ½ year)
After 1/2 year we see a completely different sky at night!

15. Carl Sagan Article: Baloney Detection Kit
Occam's Razor
Authorities do NOT carry a lot of weight
Ask whether the hypothesis can be falsified
Use MANY hypotheses to explain experimental facts
There must be an independent confirmation of the facts
Quantify!

16. Bacon: The subtlety of Nature is greater than the subtlety of argument.
Often Nature is much weirder than we think (or are used to from our every day experiences)
At very large speeds (Relativity)
For very small objects (Quantum Mechanics)
For very dense objects (Black Holes)
Etc.

17. Fallacies of logic and rhetoric
Ad hominem
Non sequitur
Appeal to ignorance
Begging the question
Observational selection
 You may influence public opinion, but for scientific progress, all that matters is agreement with observations