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## Physics 320: Astronomy and Astrophysics – Lecture II

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**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 NJIT Center for Solar-Terrestrial Research**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**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**Conic Sections**NJIT Center for Solar-Terrestrial Research**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**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**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**(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**Gravity Near Earth’s Surface**NJIT Center for Solar-Terrestrial Research**Potential Energy**NJIT Center for Solar-Terrestrial Research**Work–Kinetic Energy Theorem**NJIT Center for Solar-Terrestrial Research**Total mechanical energy:**Conservation of mechanical energy: Minimal launch speed: Escape Velocity NJIT 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? NJIT Center for Solar-Terrestrial Research**Center of Mass**NJIT Center for Solar-Terrestrial Research**Reduced mass**Binary Star System in COM Reference Frame NJIT 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. NJIT Center for Solar-Terrestrial Research**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**Virial Theorem**Kepler’s 3rd Law NJIT Center for Solar-Terrestrial Research**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**Exhibition**Science Audience Class Project NJIT 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 23rd, 2003 at the beginning of the lecture! NJIT Center for Solar-Terrestrial Research**Homework Solutions**NJIT Center for Solar-Terrestrial Research**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