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NJIT Physics 320: Astronomy and Astrophysics – Lecture II Carsten Denker Physics Department Center for Solar–Terrestrial Research
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September 10, 2003NJIT Center for Solar-Terrestrial Research Celestial Mechanics Elliptical Orbits Newtonian Mechanics Kepler’s Laws Derived The Virial Theorem
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September 10, 2003NJIT Center for Solar-Terrestrial Research Elliptical Orbits Kepler’s 1 st Law: A planet orbits the Sun in an ellipse, with the Sun at on focus of the ellipse. Kepler’s 2 nd Law: A line connecting a planet to the Sun sweeps out equal areas in equal time intervals. Kepler’s 3 rd Law: The average orbital distance a of a planet from the Sun is related to the planets sidereal period P by:
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September 10, 2003NJIT Center for Solar-Terrestrial Research Ellipses Focal points F 1 and F 2 (sun in principal focus) Distance from focal points r 1 and r 2 Semimajor axis a Semiminor axis b Eccentricity 0 e 1 Ellipse defined:
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September 10, 2003NJIT Center for Solar-Terrestrial Research Conic Sections
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September 10, 2003NJIT Center for Solar-Terrestrial Research Distances in the Planetary System Astronomical unit [AU], average distance between Earth and Sun: 1 AU = 1.496 10 8 km Light year: 1 ly = 9.461 10 12 km Light minute: 1.800 10 7 km (1 AU = 8.3 light minutes) Parsec: 1 pc = 3.0857 10 13 km = 3.262 ly
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September 10, 2003NJIT Center for Solar-Terrestrial Research 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
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September 10, 2003NJIT Center for Solar-Terrestrial Research Laws of Motion Newton’s 1 st 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 2 nd 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 3 rd Law: For every action there is an equal and opposite reaction.
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September 10, 2003NJIT Center for Solar-Terrestrial Research Gravitational Force (Kepler’s 3 rd law, circular orbital motion, M >> m) (constant velocity) (centripetal force)(law of universal gravitation) Universal gravitational constant: 6.67 10 –11 Nm 2 / kg 2
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September 10, 2003NJIT Center for Solar-Terrestrial Research Gravity Near Earth’s Surface
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September 10, 2003NJIT Center for Solar-Terrestrial Research Potential Energy
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September 10, 2003NJIT Center for Solar-Terrestrial Research Work–Kinetic Energy Theorem
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September 10, 2003NJIT Center for Solar-Terrestrial Research Escape Velocity Total mechanical energy: Conservation of mechanical energy: Minimal launch speed:
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September 10, 2003NJIT Center for Solar-Terrestrial Research 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?
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September 10, 2003NJIT Center for Solar-Terrestrial Research Center of Mass
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September 10, 2003NJIT Center for Solar-Terrestrial Research Binary Star System in COM Reference Frame Reduced mass
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September 10, 2003NJIT Center for Solar-Terrestrial Research 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.
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September 10, 2003NJIT Center for Solar-Terrestrial Research Kepler’s 2 nd 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.
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September 10, 2003NJIT Center for Solar-Terrestrial Research Kepler’s 3 rd Law Virial Theorem
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September 10, 2003NJIT Center for Solar-Terrestrial Research Kepler’s 3 rd 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.
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September 10, 2003NJIT Center for Solar-Terrestrial Research Class Project Exhibition Science Audience
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September 10, 2003NJIT Center for Solar-Terrestrial Research 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 23 rd, 2003 at the beginning of the lecture!
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September 10, 2003NJIT Center for Solar-Terrestrial Research Homework Solutions
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September 10, 2003NJIT Center for Solar-Terrestrial Research Homework Homework is due Wednesday September 16 th, 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!
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