Chapter 3
Scientific Theory
-A theory is the highest "honor" that an idea can obtain. -A hypothesis can become a theory after extensive testing, but a theory will never "graduate" to become a fact. It is always subject to revision in light of new evidence.
Ellipses
-An ellipse is the locus of points where the sum of distances from two specified points is the same.
Summary of Renaissance Cast of Characters
-Copernicus - suggested a Sun-centered solar system - still insisted on circular orbits, epicycles -Tycho Brahe - best astronomy observer of his day - hired Kepler to model orbits to data -Kepler - proposed elliptical orbits - Bingo! (paradigm shift) - used Brahe's excellent data - developed 3 laws of planetary motion -Galileo - pointed newly-invented telescope at the night sky - final nail in the coffin of Earth-centered models with his telescopic observations of Moon, Sun, Venus, Jupiter, Milky Way
So how does the Ptolemaic model explain retrograde motion? Planets really do go backward in this (wrong) model...
-Epicycles (circles upon circles) -Needed to mimic retrograde motion -This system predicts the orbits reasonably well if you add enough epicycles to the system.... -Mercury eventually required 11 epicycles in Ptolemaic model to remain sufficiently accurate!-Extremely contrived!
Myth of Fact? Time slows down for objects moving at a high velocity.
-Fact! Einstein's theory of relativity predicts that time dilates and length contracts as velocity increases. -This has been confirmed with atomic clocks flown on commercial airplanes (J.C. Hafele and R. E. Keating, Science 177, 166 (1972)).
Pseudoscience/Non-Science
-Fails to make testable predictions, or does not yield results beyond that expected from chance: Failed Predictions: -Astrology -ESP/psychic ability -Homeopathy -Numerology -Often, these ideas have no theoretical foundation on why they should work. Untestable: -Cryptozoology -Aliens built the pyramids -Anthropomorphic fallacy -These ideas cannot even be tested.
Eratosthenes Measures Earth (c. 240 B.C.)
-First day of summer at noon: Sun shone directly into a well in Syene, but missed the well in Alexandria by 7°. -Measurements: Syene (modern day Aswan) to Alexandria distance ≈ 5000 stadia angle = 7° -Calculate circumference of Earth: 7/360 = (Alexandria-Syene distance)/(circum. Earth) ⇒ circum. Earth = 5000 × 360/7 stadia ≈ 250,000 stadia -Compare to modern value (≈ 40,100 km): Greek stadium ≈ 1/6 km ⇒ 250,000 stadia ≈ 42,000 km -Greeks were quite well aware that the Earth was round.
Big Bang Theory
-Fit the available data at the time it was developed (e.g., velocities of galaxies in the Universe). -Predicted (in the 1950s) that the radiation left over by the Big Bang should be redshifted into the microwave part of the electromagnetic spectrum in the form of a cosmic microwave background. -This is exactly what was detected in 1965 by Penzias and Wilson with a microwave antenna.
How did Galileo solidify the Copernican revolution?
-Galileo overcame major objections to the Copernican view. -Made great discoveries with the newly invented telescope. -Galileo also saw four moons orbiting Jupiter, proving that not all objects orbit Earth.
How did astronomical observations benefit ancient societies?
-Keeping track of time and seasons • for practical purposes, including agriculture • for religious and ceremonial purposes • aid to navigation -However, few cultures used the scientific method to learn about the nature of the Universe (Greeks were an exception), thus they were not truly studying astronomy. -Ancient people of central Africa could predict wet season from the orientation of the crescent Moon.
What are Kepler's three laws of planetary motion?
-Kepler's First Law: The orbit of each planet around the Sun is an ellipse with the Sun at one focus. -perihelion - nearest to Sun -aphelion - farthest from Sun -You will NEVER find an orbit that looks like this! -Kepler's Second Law: As a planet moves around its orbit, it sweeps out equal areas in equal times. -This means that a planet travels faster when it is nearer to the Sun and slower when it is farther from the Sun.
Kepler's Laws
-Kepler's Law's were purely empirical in nature - he had no idea why the planets followed these laws - it was simply what he observed. -It was later shown by Isaac Newton (Chapter 4) that these laws are a natural consequence of gravity.
Kepler's Third Law
-More distant planets orbit the Sun at slower average speeds, obeying the relationship. -p2 = a3 -p = orbital period in years -a = avg. distance from Sun in astronomical units (AUs) - this is the semi-major axis -The ellipticity of the orbit does not matter! -For Earth, P = 1 year, a = 1 AU - it works!
Hallmarks of Science
-The simplest models are usually favored (Occam's Razor). -A good theory must not only explain all known existing observations, but needs to make new predictions that are verifiable (or falsifiable) by anyone. -It is not enough to just explain the previously known facts, a good theory must also predict future observations - important key concept -Example of a good theory: Big Bang Theory
How did the Greeks explain planetary motion?
-Underpinnings of the Greek geocentric model: • Earth at the center of the universe (since no detected parallax) • Heavens must be "perfect": Objects move on perfect spheres or in perfect circles. -The most sophisticated geocentric (Earth-centered) model was that of Ptolemy (A.D. 100-170) — the Ptolemaic model: • Sufficiently accurate to remain in use for 1,500 years. • Arabic translation of Ptolemy's work named Almagest ("the greatest compilation") -Extremely contrived.....
Overcoming the heavenly perfection objection
-Using his telescope, Galileo saw: • Sunspots on Sun ("imperfections") • Mountains and valleys on the Moon (proving it is not a perfect sphere) • Showed that Venus exhibited non crescent phases (e.g., gibbous) • Tycho thought he had measured stellar distances, so lack of parallax seemed to rule out an orbiting Earth. • Galileo showed stars must be much farther than Tycho thought — in part by using his telescope to see the Milky Way is countless individual stars. • Planets resolved into disks through his telescope while stars were still point sources -If stars were much farther away than planets, then lack of detectable parallax was no longer so troubling. (Galileo did not detect stellar parallax though)
A Scientific Theory is...
-an established model repeatedly tested with observations and experiments - quantities involved are well known - abstract explanation of observations -Contrast this with a hypothesis, which is only an unverified educated "guess" that requires testing. -A theory is a comprehensive explanation of a large set of observations or facts. -E.g., Fact: I see a cup fall to the ground. Theory: The gravitational attraction between the cup and the Earth caused the cup to fall to the Earth and vice versa.
The Scientific Method
1 Question 2 Hypothesis -a tentative explanation 3 Prediction 4 Test (again) 5 Result - becomes a theory after repeated confirmation.
A vocabulary in context exercise in which students match words to definitions describing elliptical planetary orbits, applying ideas from Kepler's Laws of Planetary Motion.
1. According to Kepler's second law, Jupiter will be traveling most slowly around the Sun when at aphelion. 2. Earth orbits in the shape of a/an ellipse around the Sun. 3. Earth is located at one focus of the Moon's orbit. 4. The extent to which Mars' orbit differs from a perfect circle is called its eccentricity. 5. According to Kepler's second law, Pluto will be traveling fastest around the Sun when at perihelion. 6. The mathematical form of Kepler's third law measures the period in years and the semimajor axis in astronomical units (AU).
Which of the following is false about a scientific theory?
A theory is essentially an educated guess.
Imagine a hypothetical near-Earth asteroid that has a semi-major axis (average distance from Sun) that is the same as that of the Earth. What is its period around the Sun?
B) One year -Since p2 = a3, and a for this object is about the same as for Earth, its period around the Sun must also be the same as Earth's. Ellipticity is not important!
The Earth is slightly farther away from the Sun in July than it is in January. How does the area swept out by Earth's orbit around the Sun during the 31 days of July compare to the area swept out during the 31 days of January?
Both areas are the same.
Which of the following was not a feature of the Ptolemaic model?
C) The Earth orbited the Sun.
Copernicus' Sun-centered model of the Solar System did not predict the motions of the planets in our night sky any better than the Earth-centered model of the ancient Greeks. Why is this?
Copernicus used perfect circles for the orbits of the planets instead of ellipses.
Which is the most important quality of a good theory?
D) its ability to make testable predictions that are later verified by new observations. -A) and B) are necessary for a good theory and C) is sometimes true, but D) is the most crucial property of a good theory.
Suppose we observe a comet that orbits the Sun on a highly elliptical orbit with an average (semimajor axis) distance of exactly 1 AU. How long would it take for the comet to complete each orbit around the Sun, and how do we know this?
Each orbit takes 1 year, which we know from Kepler's third law.
Earth is farther away from the Sun in July than in January. Kepler's second law tells us:
Earth travels faster in its orbit around the Sun in January than in July, but has the same angular momentum no matter where it is in its orbit.
Who among the following developed the paradigm-shifting idea that the orbits of the planets were ellipses and not circles?
Kepler
All of the following statements are true. Which one can be explained by Kepler's second law?
Mars moves faster in its orbit when it is closer to the Sun than when it is farther from the Sun.
Myth of Fact? In the southern hemisphere, water goes down sinks or toilets in the opposite direction as in the northern hemisphere (because of the Coriolis effect).
Myth! The Coriolis effect only matters on very large (hundreds of km) length scales, not the diameter of your sink.
Who among the following developed a system for predicting the positions of planets that while wrong remained in use for 1,500 years.
Ptolemy
But this model made it difficult to explain apparent retrograde motion of planets...
Review: Over a period of 10 weeks, Mars appears to stop, back up, then go forward again.
In their geocentric model, how did the Greeks explain what was happening when another planet exhibited retrograde motion?
The planet makes small loops called epicycles as the planet orbited the Earth.
What is a geocentric model of the universe?
a model designed to explain what we see in the sky while having Earth located in the center of the universe
From a scientific viewpoint, a comprehensive idea that has been tested repeatedly which gives us confidence that it represents reality is called _________.
a theory
The Greek scientist Eratothenes made a very accurate determination of the size of the Earth back in 240 B.C. despite not having modern technology. How was he able to accomplish this?
by comparing the maximum altitude of the Sun in two cities at different latitudes
What was Nicholas Copernicus' most relevant contribution to astronomy?
create a detailed model of our solar system with the Sun rather than Earth at the center
Tycho Brahe is best known for _________.
observing planetary positions with sufficient accuracy so that Kepler could later use the data to discover the laws of planetary motion
Galileo discovere4d all of the following EXCEPT ___________
stellar parallax
In the ancient Greek Earth-centered models other planets orbited Earth on epicycles ("circles upon circles"), which today seems quite contrived. Why did the Greeks have to introduce such an odd feature to their model?
to explain the fact that planets sometimes appear to move backward relative to the stars in our sky
Tycho Brahe (1546-1601)
• Compiled the most accurate (one arcminute) naked eye measurements ever made of planetary positions. • Still could not detect stellar parallax, and thus still thought Earth must be at center of solar system (but recognized that other planets go around Sun). • Hired Johannes Kepler, who used Tycho's observations to discover the truth about planetary motion.
Ptolemy's Geocentric Model
• Earth is at center • Sun orbits Earth • Planets orbit on small circles (epicycles) whose centers orbit the Earth on larger circles • This view of the Solar System held for 1500 years....
Why does modern science trace its roots to the Greeks?
• Greeks were the first people known to make models of nature. • They tried to explain patterns in nature without resorting to myth or the supernatural.
Johannes Kepler (1571-1630)
• Kepler first tried to match Tycho's observations with circular orbits -- no success • An 8-arcminute discrepancy led him eventually to use ellipses rather than circles
How did Copernicus, Tycho, and Kepler challenge the Earth-centered model?
• Nicolas Copernicus proposed a Sun centered (heliocentric) model (published 1543) • Used model to determine layout of solar system (planetary distances in AU) But . . . • The model was no more accurate and not any simpler than the Ptolemaic model in predicting planetary positions, because it still assumed perfectly circular orbits (and therefore still had to use epicycles). -Copernicus (1473-1543)
