At a certain point in an outer planet’s (Mars, Jupiter, Saturn) orbit, the planet’s motion against the starry background reversed, or went retrograde. Easily explained in the Copernican model as the Earth overtaking the other planet on its inside orbit, it was unexplainable on the geocentric model. Ptolemy’s brilliant solution was the introduction of epicycles. Ptolemy’s geocentric model was the standard cosmology for 1500 years. Will the Big Bang model be as robust? Contrary to legend, the Ptolemaic model did not get more complex and unwieldy, but because it did not model planetary motion exactly, its predictions became more and more inaccurate with time.
Helio vs geo 2
The Copernican RevolutionThe Birth of Modern Science 1
What do we see in the sky? • The stars move in the sky but not with respect to each other • The planets (or “wanderers”) move differently from stars – They move with respect to the stars – They exhibit strange retrograde motion • What does all this mean? • How can we explain these movements? 2 • What does the universe look like?
Geocentric vs. Heliocentric• How do we decide between two theories?• Use the Scientific method: – These are both explanations based on the observation of retrograde motion – What predictions do the models make? – How can these predictions 3 be tested?
Geocentric vs. Heliocentric Models of the Solar SystemAncient Greeks knew of Sun, Moon, Mercury, Venus, Mars, Jupiterand Saturn.Aristotle vs. Aristarchus (3rd century B.C.) Aristotle: Sun, Moon, Planets and Stars rotate around fixed Earth. Aristarchus: 1st Heliocentric model Aristotle: But theres no wind - Doesn’t “feel” like we are moving. (Actually orbiting sun at 70,000 mph!)Difficulties with "Geocentric" model - Retrograde motion of planets - Phases of Venus 4
Geocentric Model of Solar System (Earth Centered) What are some reasons that the geocentric model of the universe seems to make intuitive sense? It doesnt feel like we are moving – wouldnt there be a wind or something?Why would things fall down and not towards the center of the universe? Why dont we see stellar parallax? 5
Geocentric Model (Earth Centered)• Fairly good agreement with retrograde motion of planets• Some predictive power• More precise measurements showed errors• To account for unusual planetary motion epicycles were introduced• Fit the Greek model of heavenly perfection – spheres are the perfect shape, circular the perfect motion 8
Ptolemy’s Prediction: Future planetary positionsObservation: retrograde motion of planetsRefine: epicycles Success! For 1500 years 9 cfa-www.harvard.edu/seuforum/mtu/MTUcosmology.ppt
Motion of the other planets Mars Retrograde Motion 10
12Ptolemys geocentric model (A.D. 140) (VIDEO CLIP)
Ptolemy’s system provided the first framework for all discussion of the universe for nearly 1500 years!! But… there was a problemProblems with Geocentric Theory1. This model does not explain all apparent motions of celestial (space) objects2. Cannot explain Foucault’s Pendulum or the Coriolis Effect 13
Geocentric model fails toaccount for phases of Venus 14
Aside: Aristarchus - Written in the second century BC he calculated the ratio of the distance between the Earth and Sun to that between the Earth and the Moon. (His estimate was more than an order of magnitude too small, but the fault was in his lack of accurate instruments rather than in his method of reasoning.) -This image compares the line subtending the arc dividing the light and dark portions of the Moon in a lunar eclipse with the relative diameters of the Moon and Sun. -Aristarchus also found an improved value for the length of the solar year. 15
Geocentric vs. Heliocentric• Against heliocentric – It predicted planetary motions and events no better than the Geocentric system – The earth does not move (things do not fly off) – The earth is different from the heavens (from Aristotle – the heavens are perfect and unchanging) and cannot be part of the heavens• For heliocentric – Simplified retrograde motion, but epicycles were necessary to account for the planets’ changing speed – The distances to the planets could be measured. These distances were ordered, and therefore aesthetically pleasing to the philosophy of the day16
Heliocentric (Copernican) System • Sun at center (heliocentric) • Uniform, circular motion – No epicycles (almost) • Moon orbited the earth, the earth orbited the sun as another planet • Planets and stars still on fixed spheres, stars don’t move • The daily motion of the stars results from the Earth’s spin • The annual motion of the stars 17 results from the Earth’s orbit
Heliocentric model easilyaccounts for phases of Venus 18
Heliocentric Model“Rediscovered” by Copernicus in 16th century. Copernicus 1473-1543Much simpler was the main attraction forCopernicus. Simply explains retrograde motion.Put Sun at center of everything, butstill insisted on circles, therebyretainig unnecessary complexity.Opposed by Catholic ChurchCopernican revolution – criticalrealization that Earth is not at thecenter of the universe, only acceptedafter his death.
• In the heliocentric model, apparent retrograde motion of the planets is a direct consequence of the Earth’s motion
Retrograde Motion of PlanetsEarth overtakes slow outer planet so the outer planet appears toslow down, move in reverse, and then move forward again withrespect to the fixed stars Planets sometimes appear to loop back - retrograde motion Loops are called "epicycles" July Mars 7 Earth * 7 6 6 * 5 Apparent motion of 3 * Mars against 4 4 * * "fixed" stars 3 5 2 2 24 1 * 1 January
Stellar Parallax• Parallax caused by the motion of the earth orbiting the Sun• Not observed with the naked eye• The heliocentric model predicts stellar parallax, but Copernicus hypothesizes that the stars are too far away (much farther than the earth from the Sun) for the parallax to be measurable with the naked eye
Parallax• Triangulation - Measure angles at points A and B• Parallax - Know Baseline. Measure third angle in triangle made by A, B, and object in space – Baseline problem 26The apparent displacement (shift) of a foreground object relative to the background as the observer’slocation changes is known as parallax.
Misconceptions1. The Copernican model has a force between the sun and the planets. Actually, the natural motion of the celestial spheres drove the planetary motions.2. The Copernican model was simpler than the Ptolemaic one. In fact, though Copernicus eliminated circles to explain retrograde motion, he added more smaller ones to account for nonuniformities of planetary motions.3. The Copernican model predicted the planetary motions better. Because both models demanded uniform motion around the centers of circles, both worked just about as well – with errors as large as a few degrees at times.
Tycho Brahe (1546-1601): thegreatest of the pre-telescopeobservers in Europe.20+ years measuring the positionsof the Sun, Moon and planets withgreat accuracy.
Tycho Brahe• Had two sets of astronomical tables: one based on Ptolemy’s theory and one based on Copernicus’.• He found that both tables’ predictions were off by days to a month.• He believed that much better tables could be constructed just by more accurate observations.• Tycho’s homemade instruments improved measurement precision from ten minutes of arc (which had held since Ptolemy) to less than one
The skies changeTycho observed 2 phenomena thatshowed the heavens DO change: – In November 1572, Tycho noticed a new star in the constellation Cassiopeia – Comet of 1577 • Prior to this sighting, comets were thought to be atmospheric phenomena because of the immutability of the heavens • But neither the star nor the comet changed position as the observer moved, as expected for atmospheric phenomena
• Johannes Kepler (1609)• Johannes Kepler was an assistant to Tycho Brahe. He used Brahe’s observations to study the orbit of Mars• Discovered three laws of planetary motion: predict with accuracy the motions of the planets 36
Johannes Kepler• Kepler succeeded Tycho as the Imperial mathematician (but at only 1/3 the salary of the nobleman)• Kepler worked for four years trying to derive the motions of Mars from Brahe’s observations• In the process, he discovered that the plane of the earth’s orbit and the plane of Mars’ (and eventually the other planets) passed through the sun• Suspecting the sun had a force over the planets, he investigated magnetism• While this is not true, it did lead him to the idea of elliptical orbits• “With reasoning derived from physical principles 37 agreeing with experience, there is no figure left for the orbit of the planet except a perfect ellipse.”
Galileo (1564-1642), ExperimentalistBuilt his own telescope.Discovered four moons orbitingJupiter. What does this suggest?Discovered sunspots. What mightwe infer about the Sun from theseobservations?Observed phases of Venus.Was imprisoned for the last 9 years of his life for his scientificdiscoveries.
Galileo Galilei• Turned a telescope toward the heavens• Made observations that: – contradicted the perfection of the heavens • Mountains, valleys, and craters on the Moon • Imperfections on the Sun (sunspots) – Supported the heliocentric universe • Moons of Jupiter • Phases of Venus – shows a full phase
• Galileo (1564-1642) first scientist to use a telescope to observe the sky. He observed the phases of Venus and the moons of Jupiter. Both observations supported the heliocentric model. 41