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Physics 320: Astronomy and Astrophysics – Lecture II

Physics 320: Astronomy and Astrophysics – Lecture II. Carsten Denker Physics Department Center for Solar–Terrestrial Research. Celestial Mechanics. Elliptical Orbits Newtonian Mechanics Kepler’s Laws Derived The Virial Theorem. Elliptical Orbits.

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Physics 320: Astronomy and Astrophysics – Lecture II

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  1. Physics 320: Astronomy and Astrophysics – Lecture II Carsten Denker Physics Department Center for Solar–Terrestrial Research

  2. Celestial Mechanics • Elliptical Orbits • Newtonian Mechanics • Kepler’s Laws Derived • The Virial Theorem NJIT Center for Solar-Terrestrial Research

  3. 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: NJIT Center for Solar-Terrestrial Research

  4. 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: NJIT Center for Solar-Terrestrial Research

  5. Conic Sections NJIT Center for Solar-Terrestrial Research

  6. 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 NJIT Center for Solar-Terrestrial Research

  7. 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 NJIT Center for Solar-Terrestrial Research

  8. 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. NJIT Center for Solar-Terrestrial Research

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

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

  11. Potential Energy NJIT Center for Solar-Terrestrial Research

  12. Work–Kinetic Energy Theorem NJIT Center for Solar-Terrestrial Research

  13. Total mechanical energy: Conservation of mechanical energy: Minimal launch speed: Escape Velocity NJIT Center for Solar-Terrestrial Research

  14. Group Problem • What is the minimum launch speed required to put a satellite into a circular orbit? • How many times higher is the energy required to to launch a satellite into a polar orbit than that necessary to put it into an equatorial orbit? • What initial speed must a space probe have if it is to leave the gravitational field of the Earth? • Which requires a a higher initial energy for the space probe – leaving the solar system or hitting the Sun? NJIT Center for Solar-Terrestrial Research

  15. Center of Mass NJIT Center for Solar-Terrestrial Research

  16. Reduced mass Binary Star System in COM Reference Frame NJIT Center for Solar-Terrestrial Research

  17. Energy and Angular Momentum In general, the two–body problem may be treated as and equivalent one–body problem with the reduce mass moving about a fixed mass M at a distance r. NJIT Center for Solar-Terrestrial Research

  18. Kepler’s 2nd Law The time rate of change of the area swept out by a line connecting a planet to the focus of an ellipse is a constant. NJIT Center for Solar-Terrestrial Research

  19. Virial Theorem Kepler’s 3rd Law NJIT Center for Solar-Terrestrial Research

  20. Kepler’s 3rd Law (cont.) Virial Theorem: For gravitationally bound systems in equilibrium, it can be shown that the total energy is always one–half of the time averaged potential energy. NJIT Center for Solar-Terrestrial Research

  21. Exhibition Science Audience Class Project NJIT Center for Solar-Terrestrial Research

  22. Homework Class Project • Read the Storyline hand–out • Prepare a one–page document with suggestions on how to improve the storyline • Choose one of the five topics that you would like to prepare in more detail during the course of the class • Homework is due Wednesday September 23rd, 2003 at the beginning of the lecture! NJIT Center for Solar-Terrestrial Research

  23. Homework Solutions NJIT Center for Solar-Terrestrial Research

  24. Homework • Homework is due Wednesday September 16th, 2003 at the beginning of the lecture! • Homework assignment: Problems 2.3, 2.9, and 2.11 • Late homework receives only half the credit! • The homework is group homework! • Homework should be handed in as a text document! NJIT Center for Solar-Terrestrial Research

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