Upload
gabriel-barber
View
213
Download
0
Embed Size (px)
Citation preview
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
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
Questions• Why is the measurement the better, the longer the baseline is? • Estimate your uncertainty: How well can you measure the
angles? • What other sources of error can you think of?• Does your result look reasonable? How do you know? Is it
accurate? • Which instrumental setup is likely to be the most accurate?
Big quadrant, small quadrant, electronic measurement?• What could be changed to improve the accuracy?
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
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
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!
“Strange” motion of the Planets
Planets usually move from W to E relative to the stars, but sometimes strangely turn around in a loop, the so called retrograde motion. (Explanation: next lecture!)
Ptolemy (~140 AD)
• Puts forth a complete geocentric model
• dominates scientific thought during the Middle Ages
• Longest lasting (wrong) theory ever: 1000yrs
Major Work: Almagest