1	Astro 1050 Mon. Sep. 16, 2002 Today: Finish up Kepler’s Laws, Galileo, and Newton Science Issues
2	Kepler’s Laws, #1 and #2 1609 Published two laws showing: K1 Planets orbit the sun in ellipses, with the Sun at one focus K2 Motion is faster when they are near the Sun, in such a way that a line from the planet to the sun sweeps out equal areas in equal times
3	Properties of Ellipses Ellipse defined by two constants semi-major axis a 1/2 length of major axis eccentricity e 0=circle, 1 = line
4	Kepler’s Laws, #3 1619 Publishes third law, showing that there is a relationship orbital period and semi-major axis: Exact relationship is P² µ a³ . Outer planets orbit more slowly than inner ones Example: Earth P = 365 days, a = 1.00 AU. Mars p = 687 days, a = 1.524 AU Orbital Period of some asteroid with a = 4 AU ?
5	Galileo Galilei 1564 - 1642 Galileo’s earlier work 1590 Masses fall at same rate – heavier do not fall faster (unless affected by air resistance) 1604 Observes a supernova, no parallax Þ beyond Moon Telescopes: 1609 Hears of invention of telescope, which at that point just use eyeglass lenses Works out details of better lenses and lens placement, builds improved ones himself
6	Galileo: First telescopic observations “Sidereus Nuncius” (The Starry Messenger) published in 1610 reporting: Moon isn’t “perfect” (violating Aristotelian principles for heavens) Shows mountains and valleys Uses shadows to estimate heights Milky Way made up of myriad faint stars Doesn’t directly violate Aristotelian principles, but suggests that a few simple phenomena can explain many features of the heavens Discovers 4 moons (Galilean Satellites) orbiting Jupiter Violates idea that all motion is centered on the Earth Shows that orbiting objects can “follow” a moving body 4 moons will also be seen to follow Kepler’s 3^rd law P² µa³ (but with a different proportionality constant)
7	Galileo’s additional observations Detects sunspots and the rotation of the Sun. Further evidence of the “imperfect” heavens Detects the phases of Venus Phases show that Venus must orbit the Sun. “Full” Venus when it is on far side of Sun. “Crescent” Venus when it is on near side of Sun.
8	Galileo’s critical observations Jupiter’s moons show orbits which are not earth-centered Venus’ phases show it must circle the Sun Several objects (Moon, Sun) show “imperfections” which are not supposed to be present in the heavens Galileo’s observations clearly support Copernican model, but so far his printed work has mostly been reporting what he sees, rather than directly arguing for Copernican model.
9	Galileo’s critical observations Jupiter’s moons show orbits which are not earth-centered Venus’ phases show it must circle the Sun Several objects (Moon, Sun) show “imperfections” which are not supposed to be present in the heavens Galileo’s observations clearly support Copernican model, but so far his printed work has mostly been reporting what he sees, rather than directly arguing for Copernican model.
10	Galileo and the Church Real issue is one of “Authority”, not Astronomy or Faith Controversy takes place in the context of the Protestant Reformation and the 30 Years War (between Catholic and Protestant Europe) Council of Trent (1546) has rejected right of personal interpretation of the Bible Panel of 11 theologians (lower level group) has decided that the bible favors the Aristotelian description of the Universe Kepler is a German Protestant 1616: Galileo “privately” prohibited from debating Copernican vs. Aristotelian model – but Siderial Messenger not suppressed. 1623: Galileo meets with new Pope Urban VIII (friend of Galileo) who doesn’t lift prohibition, but seems to encourage him. 1629: Galileo publishes the “Dialog Concerning the Two Chief World Systems”.
11	Galileo and the “Dialog” Written as a debate between 3 people Salviati Copernican advocate – (really Galileo) Sagredo Intelligent but uninformed Simplicio Aristotelian philosopher – not very bright Hoped to avoid earlier ruling by not directly advocating Copernican model Actually made things worse by convincing accusers they were “Simplicio” 1633 Inquisition condemns him for violating 1616 order Something like modern “contempt of court” ruling Proceeding not a re-argument of Copernican vs. Aristotelian debate But forced to recant, admitting “errors” Sentenced to life imprisonment –actually “house arrest” Dies in 1642 Pope John Paul II finally makes some amends 350 years later.
12	Newton: 1642-1727 Principia published in 1687 3 Law of motion 1. A body continues at rest or in uniform motion in a straight line unless acted upon by some force. 2. A body’s change of motion is proportional to the force acting on it and is in the direction of the force. 3. When one body exerts a force on a second body, the second body exerts an equal and opposite force back on the first body. Universal gravitation There is an attractive force between all bodies, proportional to their mass, and inversely proportional to the square of their distance.
13	Explanation for Kepler’s Laws Momentum keeps the planets moving – you do not need some force to do this. Gravity provides the force which makes orbits curve Gravity of Sun curves orbits of Planets Gravity of Earth curves orbit of moon (and also makes objects on earth fall downward) “Conservation of Angular Momentum” explains why motion is faster when closer to the sun. The inverse square law of gravity explains P² µ a³ and the details of why the orbits are ellipses.
14	Circular Orbits: Limiting case of an ellipse. Centripetal acceleration (v²/r) caused by Gravity Period found by Kepler’s 3^rd Law just comes from this Given P and a (and G) this gives us a way to find the mass of a planet or star
15	Summary: People and Contributions Nicolaus Copernicus 1473 - 1543 Heliocentric model Explanation of retrograde motion Tycho Brahe 1546 - 1601 Observations of changes in sky Accurate planet positions Johannes Kepler 1571 – 1630 Mathematical description of planetary orbits Galileo Galilei 1564 – 1642 Observations using telescope supporting Copernican model Isaac Newton 1642 – 1727 Physics to explain Kepler’s orbits
16	The Scientific Method Note the alternating “theorists” and “observers” Nicolaus Copernicus 1473 - 1543 Heliocentric model Explanation of retrograde motion Tycho Brahe 1546 - 1601 Observations of changes in sky Accurate planet positions Johannes Kepler 1571 – 1630 Mathematical description of planetary orbits Galileo Galilei 1564 – 1642 Observations using telescope supporting Copernican model Isaac Newton 1642 – 1727 Physics to explain Kepler’s orbits
17	The (idealized) scientific method Hypothesis: An assertion or conjecture that must still be tested. Theory: A system of rules and principles of wide applicability that have been tested. Natural Law: A very well tested theory
18	Falsifiability You never prove a scientific theory “right” If it is so trivial you can test every possible case, it isn’t much of a theory. Useful theories are general theories You can’t test every possible case. All you can really do is try to prove theories wrong When you honestly try and can’t, as least some part of it must be approximately “right”. A “theory” which has been carefully crafted so it cannot be proven wrong isn’t a scientific theory.
19	What makes a good hypothesis? Occam’s Razor: William of Ockham (ca. 1285-1349) “Plurality should not be posited without necessity.” Modern interpretation (not necessarily Occam’s): Don't make any more assumptions than you have to or roughly The simpler explanation is the preferred one In some ways, if “falsifiability” is what makes a scientific hypothesis, then one which is “simpler” (but not trivially so) is more easily “falsifiable” and therefore better.
20	Scientific Revolutions Paradigms: A commonly accepted set of scientific ideas and assumptions: The geocentric paradigm The heliocentric paradigm Most new theories are “modifications” of previous ones. Occasionally a fundamental change in viewpoint is required. Newtonian Gravity vs. General Relativity Newtonian Mechanics vs. Quantum Mechanics Reference Thomas Kuhn: The Structure of Scientific Revolutions
21	Tested vs. Untested Predictions Well tested predictions can’t change much Newton’s “apple” Planetary motion Newton’s sky predictions vs. Ptolemy’s Einstein’s position predictions vs. Newton’s The “why” of events can change radically. Can have radically different predictions in untested areas: Elliptical comet orbits from Newton (Halley’s Comet) Bending of starlight from Einstein Relativity (Black holes) “Orbits” of electrons in atoms from Quantum Mechanics.
22	Human Scientists How the scientific method works with real human scientists The best scientists really do try do “falsify” their own theories It’s the way it “should” work. You look a lot less foolish when you find your own mistakes. But to have a “fair” chance, theories do need someone to defend them. Claims that a theory has been proven wrong can be (and often are) mistaken. The person who proposes a theory is presumably best qualified to defend it. It isn’t just a game – the theories were created to be USED for further work, and that is usually being done first by the people who developed them. Even if the originators are less than vigorous in testing their own theory, others will be trying to do that. Individual scientists do not always follow the full scientific method outlined, but because of competition the “system” as a whole does tend to.
23	For Wednesday: