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?

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.

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

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.

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

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

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

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

Simple, ingenious idea – hard measurement  

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

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

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

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

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!

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!

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.

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