Physics 229 Week 2 Lab this week: 1. The Winter Sky Lab next week: 2. Measuring Things Test 1: Wednesday, 2/8. Homework, due Wednesday, 2/8: Bennett, et al., Chapter 2. Problems 48, 49, 50, 51, 52. I won’t collect these problems, but they are examinable.
Nicholas Copernicus Born 1473 (in Torun, Poland). Died 1543. Proposed heliocentric system, with planets moving in circular orbits. Author of De Revolutionibus (On the Revolutions).
Copernican System Planets move around the Sun in circular orbits. The Earth (and Moon) are third from the Sun. Simple explanation of retrograde motion.
Retrograde Motion: Jupiter and Saturn June 2000-May 2001
Copernican Explanation of Retrograde Motion
Tycho Brahe Born 1546 (in Denmark). Died 1601. Made extensive observations of the motions of the planets. Observed the supernova of 1572 and reasoned that the stars cannot be unchangeable.
Tycho’s tomb in Prague
Johannes Kepler Born 1571 (near Stuttgart, Germany). Died 1630. Assistant to Tycho Brahe. Originated three laws of planetary motion. Realized that planetary orbits must be ellipses.
Kepler: “Why Six Planets?” Perfect Solids: Tetrahedron: 4 triangles (Fire) Cube: 6 squares (Earth) Icosahedron: 20 triangles (Water) Octahedron: 8 triangles (Air) Dodecahedron: 12 pentagons (Heavens)
Kepler’s First Law Planets move in ellipses, with the Sun at one focus.
How to Draw an Ellipse
Astronomical Unit Length of the semimajor axis of Earth’s orbit = 1.49597 × 108 km Planet Semimajor axis (a) in AU Mercury 0.387 Venus 0.723 Earth 1.000 Mars 1.524 Jupiter 5.203 Saturn 9.539 Uranus 19.19 Neptune 30.06 Pluto 39.48
Kepler’s Second Law The radius line from the Sun to a planet sweeps out equal areas in equal times.
Kepler’s Third Law The square of the sidereal period is equal to the cube of the semimajor axis, or P2 = a3
Kepler’s Third Law Planet Semimajor axis (a) in AU Orbital Period (years) Mercury 0.387 0.2409 Venus 0.723 0.6152 Earth 1.000 Mars 1.524 1.881 Jupiter 5.203 11.86 Saturn 9.539 29.42 Uranus 19.19 84.01 Neptune 30.06 164.8 Pluto 39.48 248.0
Galileo Galilei Born 1564 (in Pisa, Italy). Died 1642. First to use a telescope for astronomical observations. Author of Dialogue Concerning the Two Chief World Systems. Originated concept of Galilean relativity.
Impetus A property transmitted to an object by a mover (e.g. a throwing arm). In most medieval concepts, this property is “used up” as the object moves.
Galileo’s Telescope Observations The phases of Venus. Mountains and craters on the Moon. Sunspots. The four bright satellites of Jupiter. The rings of Saturn. Neptune (although Galileo did not realize it was a planet).
Galileo’s Observations of Venus
Venus phases and size
Mountain and craters on the Moon
Sunspots and the satellites of Jupiter
Galileo’s Heresies Falling bodies move at the same speed, regardless of mass. The 1604 Supernova must be a star. Letter to Christina of Lorraine (1615) Dialogue Concerning the Two Chief World Systems (1632)
Isaac Newton Born 1642 (in Lincolnshire, England). Died 1727. Originated Three Laws of Motion Originated Law of Universal Gravitation. With Leibniz, invented Calculus. Author of the Principia. Invented the first reflecting telescope.
Mass and weight Mass is the amount of matter in an object. We measure it in kg. Weight is the force exerted by gravity on an object. We measure it in N.
Newton’s First Law of Motion An object at rest tends to remain at rest. An object in motion moves at a constant speed in a straight line unless acted upon by a force.
Newton’s Second Law of Motion The acceleration of an object is directly proportional to the force acting on it and inversely proportional to its mass. Force = mass × acceleration F = m a
Newton’s Third Law of Motion For every action there is an equal and opposite reaction.
Law of Universal Gravitation The gravitational force between any two objects is proportional to the product of their masses and inversely proportional to the distance between them.
Expanding our Solar System Uranus: discovered by William Herschel (1781). Neptune: position predicted by Adams and Leverrier; discovered by Galle (1846). Pluto: discovered by Clyde Tombaugh (1930).