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Prograde motion (west-to-east) Leo Retrograde motion (east-to-west) Cancer Mars Jupiter Mercury Sun Venus Earth Moon Saturn Visual Parallax Nicholas Copernicus (15th century) •universe is heliocentric •planets orbit Sun in perfect circles Tycho Brahe (16th century) • Naked-eye astronomer • Documented planet motions to within 4 minutes of arc. • Could not detect stellar parallax Johannes Kepler (1573-1631) • Succeeded Tycho • Used Tycho’s data tables to fit planetary motions to Copernican model Kepler’s first law: Planetary orbits are ellipses, with Sun at one focus Kepler’s second law: A line drawn from the planet to the Sun sweeps out equal areas in equal time intervals Kepler’s third law: The square of a planet’s orbital period is proportional to the cube of its average distance from the sun p2 = constant 3 a Earth: ( 1.00 year)2 2/au3 = 1.00 yr (1.00 AU) 3 Kepler’s third law: The square of a planet’s orbital period is proportional to the cube of its average distance from the sun p2 = constant 3 a Mars: ( 1.88 year)2 2/au3 = 1.00 yr (1.52 AU) 3 Kepler’s third law: The square of a planet’s orbital period is proportional to the cube of its average distance from the sun p2 = constant 3 a Jupiter: (11.87 year)2 2/au3 = 1.00 yr (5.20 AU) 3 Hohmann transit orbital Earth 1.00 AU 2.52 AU 1.52 AU Mars Hohmann transit orbital Earth at launch (spacecraft perihelion) 0.98 AU 2.50 AU 1.52 AU 1.20 AU Mars at arrival (spacecraft aphelion) Hohmann transit orbital (1.25 au)3 = 1.95 yr2 1.00 au3/yr2 Earth at launch (spacecraft perihelion) Mars at arrival (spacecraft aphelion) Hohmann transit orbital (1.25 au)3 = 1.95 yr2 1.00 au3/yr2 Earth at launch (spacecraft perihelion) = 1.40 years Mars at arrival (spacecraft aphelion) Hohmann transit orbital (1.25 au)3 = 1.950 yr2 1.00 au3/yr2 Earth at launch (spacecraft perihelion) = 1.40 years = 510 days (full orbit) = 255 days (half orbit) Mars at arrival (spacecraft aphelion) Hohmann transit orbital (1.25 au)3 = 1.95 yr2 1.00 au3/yr2 Mars at launch Earth at launch: Nov. 26,2011 (spacecraft perihelion) = 1.40 years = 510 days (full orbit) Earth at arrival = 255 days (half orbit) Mars at arrival: August 06, 2012 (spacecraft aphelion) Galileo Galilei (1564 - 1642) • “Father of modern science” • First to use telescope for astronomy • Observations supported a Heliocentric solar system • Experiments with gravity, inertia Galileo Galilei (1564 - 1642) • “Father of modern science” • First to use telescope for astronomy • Observations supported a Heliocentric solar system • Experiments with gravity, inertia Galileo Galilei (1564 - 1642) • “Father of modern science” • First to use telescope for astronomy • Observations supported a Heliocentric solar system • Experiments with gravity, inertia Galileo Galilei (1564 - 1642) • “Father of modern science” • First to use telescope for astronomy • Observations supported a Heliocentric solar system • Experiments with gravity, inertia Galileo’s Moon Appenine Mountains described sunspots and their movement, showing that the Sun rotates. described the phases of Venus Ptolemaic system couldn’t explain full phases Galileo was the first to observe the moons of Jupiter and record their motion Up to this point it was assumed that the motion of a planet around the Sun would leave a moon behind Total distance covered by ball is proportional to time squared For any steepness or starting height the ball always approaches the same elevation on the opposite ramp (ignoring friction)… …if we remove the opposite ramp the ball can never reach the same elevation and so should continue to roll forever in a straight line (again ignoring friction). Inertia: a body at rest remains at rest while a body in motion remains in motion at a constant velocity, unless acted upon by an outside force (such as gravity or friction). Issac Newton (1642-1727) • Universal Law of Gravitation • Calculus • Wave nature of light Issac Newton (1642-1727) • Universal Law of Gravitation • Calculus • Wave nature of light Speed: distance/time Issac Newton (1642-1727) • Universal Law of Gravitation • Calculus • Wave nature of light Speed: distance/time Velocity: distance/time in a specific direction Issac Newton (1642-1727) • Universal Law of Gravitation • Calculus • Wave nature of light Speed: distance/time Velocity: distance/time in a specific direction Acceleration: any change in velocity with time (requires an outside force) Issac Newton (1642-1727) • Universal Law of Gravitation • Calculus • Wave nature of light Speed: distance/time Velocity: distance/time in a specific direction Acceleration: any change in velocity with time (requires an outside force) Force: Mass x Acceleration (weight is an example) Newton’s Law of Universal Gravitation: The force of attraction between two bodies is proportional to the product of their masses and inversely proportional to the square of the distance between them. T 0 1 2 3 4 5 T 0 1 2 3 4 5 T 0 0 1 2 3 4 5 1 2 3 4 5 Horizontal velocity (v) is constant V3 V2 V1 Acceleration (g) is constant projectile falls to the ground in exactly the same time. CM Ve = √2GM/r Where: Ve = escape velocity G = gravitational constant M = mass of planet or other body r = radius of planet or other body Geocentric or Geostationary orbit EARTH SATELLITES GPS SATELLITES Space Elevator Lagrange Points Gravity according to Einstein Gravity according to Einstein Gravity according to Einstein Gravity according to Einstein In a “flat” universe, light travels in a straight line Earth Sun Distant star In Einstein’s universe, light follows curvature created by massive objects Sun Distant star Earth Light sources located behind massive objects will appear in different positions in the sky Sun Distant star (apparent position) Distant star (actual position) Earth Actual position of star Apparent position of star Einstein Cross Distant galaxy Multiple images of the same (more distant) quasar Einstein Ring Distant blue galaxy, distorted into ring LRG 3-757 (foreground galaxy)