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Physics 202: Introduction to Astronomy – Lecture 4

Physics 202: Introduction to Astronomy – Lecture 4. Carsten Denker Physics Department Center for Solar–Terrestrial Research. Jupiter. The Jovian Moons Io Europa Ganymede Callisto. Laws of planetary motion Kepler’s laws Elliptical orbits Astronomical unit

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Physics 202: Introduction to Astronomy – Lecture 4

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  1. Physics 202: Introduction to Astronomy – Lecture 4 Carsten Denker Physics Department Center for Solar–Terrestrial Research

  2. Jupiter • The Jovian Moons • Io • Europa • Ganymede • Callisto Center for Solar-Terrestrial Research

  3. Laws of planetary motion Kepler’s laws Elliptical orbits Astronomical unit Dimensions of the solar system Radar measurements of Earth/Venus distance Newton’s laws Mechanics Force Mass Inertia Acceleration Gravity Gravitational force Inverse-square law Chapter 1.4 – 1.5 Center for Solar-Terrestrial Research

  4. Collection of 20 years of accurate planetary positions by Tycho Brahe (1546 – 1601) Johannes Kepler (1571 – 1630) 1609: Astronomia Nova 1619: Harmonice Mundi 1627: Rudolphine Tables Orbital Paths of Planets Center for Solar-Terrestrial Research

  5. Elliptical Orbits • Kepler’s 1st Law: A planet orbits the Sun in an ellipse, with the Sun at on focus of the ellipse. • Kepler’s 2nd Law: A line connecting a planet to the Sun sweeps out equal areas in equal time intervals. • Kepler’s 3rd Law: The average orbital distance a of a planet from the Sun is related to the planets sidereal period P by: Center for Solar-Terrestrial Research

  6. Ellipses • Focal points F1 and F2(sun in principal focus) • Distance from focal points r1 and r2 • Semimajor axis a • Semiminor axis b • Eccentricity0 e  1 • Ellipse defined: Center for Solar-Terrestrial Research

  7. Distances in the Planetary System • Astronomical unit [AU], average distance between Earth and Sun: 1 AU = 1.496  108 km • Light year: 1 ly = 9.461  1012 km • Light minute: 1.800  107 km (1 AU = 8.3 light minutes) • Parsec: 1 pc = 3.0857  1013 km = 3.262 ly Center for Solar-Terrestrial Research

  8. Isaac Newton (1642 – 1727) • 1686: Principia Mathematica, universal law of gravitation • Stable planetary orbits result from a balance between centripetal and gravitational acceleration • Sun–to–Earth mass ratio (MEarth/MSun= 28700 instead of 332945), wrong value for solar parallax, better estimate in later edition of the Principia (within factor of two) Center for Solar-Terrestrial Research

  9. Newtonian Physics • Galileo Galilei (1564–1642) • Heliocentric planetary model • Milky Way consists of a multitude of stars • Moon contains craters  not a perfect sphere • Venus is illuminated by the Sun and shows phases • Sun is blemished possessing sunspots • Isaac Newton (1642–1727) • 1687 Philosophiae Naturalis Principia Mathematica mechanics, gravitation, calculus • 1704 Optiks  nature of light and optical experiments Center for Solar-Terrestrial Research

  10. Laws of Motion • Newton’s 1st Law:The law of inertia. An object at rest will remain at rest and an object in motion will remain in motion in a straight line at a constant speed unless acted upon by an unbalanced force. • Newton’s 2nd Law: The net force (the sum of all forces) acting on an object is proportional to the object’s mass and it’s resultant acceleration. • Newton’s 3rd Law: For every action there is an equal and opposite reaction. Center for Solar-Terrestrial Research

  11. Gravitational Force (Kepler’s 3rd law, circular orbital motion, M >> m) (constant velocity) (centripetal force) (law of universal gravitation) Universal gravitational constant: 6.67  10–11 Nm2 / kg2 Center for Solar-Terrestrial Research

  12. Gravity Near Earth’s Surface Center for Solar-Terrestrial Research

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