1/23/12 1 3. The Copernican Revolution Announcements • HW1 is due Thursday. You have to be registered at MasteringAstronomy to do the homework! • TA Qufei Gu will be in RH111 4:00-5:00PM Wednesday to help with homework. Email: zyx88@unm.edu • Feb 3 is the last day to drop with refund • If your clicker is not registered and you are not set up in MasteringAstronomy by Feb 3 you will be dropped from this course From Aristotle to Newton • The history of our knowledge about the Solar System (and the universe to some extent) from ancient Greek times through the beginnings of modern physics. Clicker Question Who was the first person to use a telescope to make astronomical discoveries? A. Aristotle B. Brahe C. Kepler D. Galileo E. Newton 1/23/12 2 “Geocentric Model” of the Solar System • Ancient Greek astronomers knew of Sun, Moon, Mercury, Venus, Mars, Jupiter and Saturn • Aristotle vs. Aristarchus (3rd century B.C.) • Aristotle: Sun, Moon, planets and stars rotate around fixed Earth • Aristarchus: Used geometry of eclipses to show Sun bigger than Earth (and Moon smaller), so guessed that Earth orbits the Sun. Also guessed Earth spins on its axis once a day => apparent motion of stars • Aristotle: But there’s no wind or parallax! • Aristarchus: Yes, there is! • Difficulty with Aristotle’s “Geocentric” model: Retrograde motion of the planets. Planets generally move in one direction relative to the stars, but sometimes they appear to loop back. This is called retrograde motion. If you support a geocentric model, you must attribute retrograde motion to actual motion of planets, leading to loops called epicycles. Ptolemy’s geocentric model (A.D. 140) Planets generally move in one direction relative to the stars, but sometimes they appear to loop back. This is "retrograde motion". 1 2 3 4 5 6 7 1 2 3 4 5 6 7 Earth Mars Apparent motion of Mars against "fixed" stars * * * * * * January July 1/23/12 3 Heliocentric model • Re-discovered by Copernicus in 16th century • Put Sun at the center of everything • Much simpler, almost got rid of epicycles • But orbits circular in his model. In reality they are elliptical, so it didn’t fit the data perfectly • Not generally accepted at the time Copernicus 1473-1543 Illustration from Copernicu’s work showing heliocentric model Copernican model was a triumph of the Scientific Method Scientific Method: a. Make high quality observations of some natural phenomenon b. Come up with a theory that explains the observations c. Use the theory to predict future observations d. Make further observations to test the theory e. Refine the theory, or if it no longer works, make a new one Occam’s Razor: Simple Theories are better You can prove a theory WRONG but not RIGHT Observation Theory Prediction Galileo (1564-1642) • Built his own telescope. • Discovered four moons orbiting Jupiter => Earth is not center of all things! • Discovered sunspots. Deduced Sun rotated on its axis. • Discovered phases of Venus, inconsistent with geocentric model. 1/23/12 4 Kepler (1571-1630) • Used Tycho Brahe's precise data on apparent planet motions and relative distances. • Deduced three laws of planetary motion. Kepler’s First Law The orbits of the planets are elliptical (not circular) with the Sun at one focus of the ellipse. Ellipses: Eccentricity = distance between foci / major axis length Describes ‘flatness’ of ellipse. Kepler’s Second Law A line connecting the Sun and a planet sweeps out equal areas in equal times. This means: Planets move faster when closer to the Sun. Kepler’s Third Law The square of a planet’s orbital period is proportional to the cube of its semi-major axis. P: Period, a: semi-major axis P2 is proportional to a3 P2αa3 For circular orbits, a=b=radius This means: The larger a planet’s orbit, the longer the period a b 1/23/12 5 Solar System Orbits Orbits of some planets/dwarf planets Planet a (AU) P (Earth years) Venus 0.723 0.615 Earth 1.0 1.0 Jupiter 5.2 12 Pluto 39.5 249 At the time of the Copernican Revolution, the actual distances of planets from the Sun were not known, but were later measured. One technique is parallax. Earth-baseline parallax uses measurements on either side of Earth to measure planet distances. Clicker Question A flaw in Copernicus’s model for the Solar system was: A. It didn’t explain retrograde motion B. He used circular orbits C. The Earth was still at the center D. He used the same mass for all the planets E. All of the above 1/23/12 6 Clicker Question An asteroid orbiting the Sun at a distance in between Earth and Mars will be moving: A. Faster than the Earth but slower than Mars B. Faster than Mars but slower than the Earth C. Faster or Slower than Earth depending on its mass D. At the same speed as the asteroid belt Newton (1642-1727) • Kepler’s laws were basically playing with mathematical shapes and equations and seeing that it worked. • Newton’s work based on experiments of how objects interact. • His three laws of motion and law of gravity described how all objects interact with each other. Newton’s First Law of Motion Every object continues in a state of rest or a state of uniform motion in a straight line unless acted on by a force. Newton’s Second Law of Motion When a force, F, acts on an object with a mass, m, it produces an acceleration, a, equal to the force divided by the mass. Acceleration is a change in velocity or a change in direction of velocity. a = FmF = ma 1/23/12 7 Newton’s Third Law of Motion To every action there is an equal and opposite reaction. Or, when one object exerts a force on a second object, the second object exerts an equal and opposite force on the first object. Newton’s Law of Gravity For two objects of mass m1 and m2 , separated by a distance R, the force of their gravitational attraction is given by: F is the gravitational force. G is the ‘gravitational constant’. An example of an inverse-square law. Your weight is just the gravitational force between the Earth and you. F = Gm1m2R2 Newton’s Correction to Kepler’s First Law The orbit of a planet around the Sun has the common center of mass (instead of the Sun) at one focus. Clicker Question Suppose Matt weighs 120 lbs on his bathroom scale on Earth, how much will his scale read if he is standing on a platform 6400 km high (1 earth radius above sea level)? A. 12 lbs B. 30 lbs C. 60 lbs D. 120 lbs E. 240 lbs 1/23/12 8 Escape Velocity Velocity needed to completely escape the gravity of a planet. The stronger the gravity, the higher the escape velocity. Examples: Earth 11.2 km/s Jupiter 60 km/s Deimos (moon of Mars) 7 m/s Consider Helium gas at room temperature (300 K) So v = 1 km/s on average, but sometimes more. E = kT = 4.1×10−21 JE = mHev22 = 4.1×10−21 ⇒ v = 2 × 4.1×10−212 ×1.67 ×10−27 = 1574m / s Timelines of the Big Names Copernicus Galileo Brahe Kepler Newton 1473-1543 1546-1601 1564-1642 1571-1630 1642-1727 Reading Assignment 1/26 • Chapter 2.1-2.4 – Radiation and the Electromagnetic Spectrum Ylva Pihlstrom 03_CopernicanRevolution.pptx