HISTORY OF ASTRONOMY

REVISED!

Skylab – Stage 2

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DerivationDerivation

• Angle at A: Angle at A: αα=19°=19°

• Angle at B: Angle at B: ββ=22°=22°

• Baseline (b): 12.6mBaseline (b): 12.6m

• Height (H): ???Height (H): ???

• Have triangle with known side and 2 Have triangle with known side and 2 angles: angles: H = D tan H = D tan ββ

H = (D+b) tan H = (D+b) tan αα

2 equations, 2 unknowns2 equations, 2 unknowns

Solve for Solve for

H = b tan H = b tan αα/(1-tan /(1-tan αα/tan /tan ββ))

AA BB

D

Excel Sheet

ExampleExample

• Angle at A: 19°Angle at A: 19°

• Angle at B: 22°Angle at B: 22°

• Baseline: 12.6mBaseline: 12.6m

• Height: 29.4ft = 96 ftHeight: 29.4ft = 96 ft

AABB

Performing Experiments

• Experiments must be repeatable – requires careful control over variables

• Possible outcomes of an experiment:– The experiment may support the theory

• We then continue to make predictions and test them

– The experiment may falsify the theory• We need a new theory that describes both the original data and

the results of the new experiment

• Since we cannot do every possible experiment, a theory can never be proven true; it can only be proven false

Making Measurements• Errors

– Random– Systematic

• With every measurement, it is essential to provide an estimate of the uncertainty – the likely range of errors

• Example:– Using a ruler marked in mm, we round to the nearest marking –

at most off by half a division, or 0.5 mm– Cite a measurement of 15 mm as 15 0.5 mm to indicate that

the real value of the length is likely to be anywhere between 14.5 mm and 15.5 mm– If a theory predicts a value of 15. 2 mm, then a reading of 15 0.5 mm is in agreement with the theory but a reading of 15 0.1 mm is probably not

Is the uncertainty small or big?

• It depends! If you have a small uncertainty and the measured length is also small, you might have a huge uncertainty!

• Use percentages: – Percent error = (estimated uncertainty)/(result) x 100%– Example: 51.3 cm ± 0.2 cm gives

– Percent error = (0.2 cm)/(51.3cm) x 100 % = 0.4 % (This is a pretty small uncertainty)

Is the result precise or accurate or what?• Two different concepts: precision and accuracy!

• High precision means small error

• High accuracy means close to an accepted value

• Examples: * * * * high precision, high accuracy

* * * * high precision, low accuracy

* * * * low precision, high accuracy

* * * * low precision, low accuracy

accepted value

When do results agree?

• Results agree, if they are within the error margins of each other

• Examples:

| O | | O |

values very different, but errors large: agreement!

| O | | O |

values closer, but errors smaller: no agreement!

Triangulating the Size of the Earth• Eratosthenes (ca. 276 BC)

– Measures the radius of the earth to about 20%

Calculation• Angle is measured to be

7.2 = 360/50

• So distance Alexandria-Syene is 1/50 of Earth’s circumference

• Baseline can be measured: 5000 stades

Circumference is 23,330 miles (modern value: 25,000 miles – only 7% off

Distances to the Stars

• Use even bigger baseline by waiting ½ year, not ½ day

• Baseline: 300 million km Parallax can be used out to about 100 light years

• The bigger the parallactic angle, the closer the star!

– A star with a measured parallax of 1” is 1 parsec away

– 1 pc is about 3.3 light years

• The nearest star (Proxima Centauri) is about 1.3 pc or 4.3 lyr away

The most important measurement in Astronomy: Distance!

• The distances are astronomical – of course

• The distance scales are very different– Solar system: light minutes– Stars: light years– Galaxies: 100,000 ly– Universe: billions of ly

• Need different “yardsticks”

A Short History of Astronomy• Ancient (before 500 BC)

– Egyptians, Babylonians, Mayans, Incas, Chinese

• Classical Antiquity (500 BC-500 AD) – Greeks, Romans: Plato, Aristotle, Ptolemy

• Middle Ages (500-1450 AD)– Arabic astronomers

• Renaissance (1450-1550 AD)– Copernicus

• Baroque (1550-1700 AD)– Brahe, Kepler, Galilei, Newton

Ancient Astronomy

Stonehenge, England

Pyramids, Gizeh near Cairo, Egypt

Aristotle (384 – 322 BC)• Arguably the first genuine scientist in

history

• Aristotle's views on physical science shaped medieval scholarship Scholasticism

• His views on motion of the objects was deeply flawed but compelling

• Thomas Aquinas made Aristotle compatible with Christian beliefs

Physics and Metaphysics

• Aristotle’s “Physics” (Greek: Φυσικὴ ἀκρόασις or physikes akroasis; Latin: Physica) is one of the foundational books of science and philosophy

• His book on philosophy is called Metaphysics (Greek: τὰ μετὰ τὰ φυσικά) – beyond physics

How do things move?Aristotle (c. 350 B.C.)

Aristotle observed how things move, and constructed the following theory:

• Things have a tendency to stay stationary.

• If you push something, it will move, then return to it’s natural state: stationary.

• Actually, it will try to return to it’s natural place: smoke and gas will go up, rock and water will go down.

• If you fire an arrow from a bow, you give it impetus: it will travel until this impetus runs out, at which time it will fall to to ground and return to it’s natural state.

This was stated in a series of books called ‘Physics’, and gives us the name of the science. This theory makes intuitive sense, and allows us to make a prediction: rocks won’t move unless they are pushed. People took this as truth for ~1900 years.

Wrong, i.e. falsified by experiments!

Aristotle easily falsified by experiment – but emphasis was not on observation

How people thought about projectiles up until the Renaissance: the cannonball moves in almost a straight line, until it runs out of impetus and falls on the house. WRONG!

Aristotle: On the

Heavens• Aristotle On

astronomy

• Read in Latin throughout the middle ages

• Renaissance: Greek original

Two realms – eternally separated

• Sublunar: ever changing, complicated, chaotic, human (i.e. lowly)

• Supralunar: eternal, no changes other than “perfect” (i.e. complete) circular motion, divine

Prescientific Explanations - Alchemy

• See online reading

• Casual observation of patterns in nature – Bubbles of air in water go

up, etc.

• Wrong theory/elements

• This leads to wrong world views

The Grand Mystification of the Cosmos

• Aristotle’s thoughts ossified and prevented progress

• Disempowerment of the inquisitive mind– Trapped in a realm of chaos, what can we do?

– There is no connection of what goes on on Earth and in the heavens, so how can we find out?

– We are lowly, how can we ask divine questions or question the word of God?

Sun, stand thou still!• King James Bible (Joshua 10:12)

Then spake Joshua to the LORD in the day when the LORD delivered up the Amorites before the children of Israel, and he said in the sight of Israel, Sun, stand thou still upon Gibeon; and thou, Moon, in the valley of Ajalon.

• Logic: So the Sun usually moves!

The Bible, Plato, Aristotle, Ptolemy, Aquinas

• Everyone and the Scripture agree on the explanation of the cosmos since over one thousand years

• And you want to doubt that ?! How DARE you!