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)

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%

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

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– 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

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 GreenwichUT = 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