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ASTRONOMY 202 Spring 2007: Solar System Exploration Instructor: Dr. David Alexander Web-site: www.ruf.rice.edu/~dalex/ASTR202_S07 Class 11: Newton’s Laws [2/9/07] Announcements Gravitational acceleration Mass, weight and fun on elevators One good apple • Newton’s 3 Laws of Motion • Conservation of Momentum • Conservation of Angular Momentum Chapter 4 Newtonian Gravitation • Universal Law of Gravitation • ‘Falling’ Orbits • Generalizing Kepler’s Laws • Tricking gravity Tidal Forces and Orbital Energy Announcements Homework 4 available online – due Mon Feb 12 Guidelines for Discussion papers online • Discussion paper due Mon Feb 19 Observing night planned for sometime next week, weather permitting Gravitational Potential Energy The amount of gravitational potential energy released as an object falls depends on its mass, the strength of gravity, and the distance it falls. On the surface of the Earth: P = mgh Mass-Energy E = mc2 The energy produced in the center of stars is generated entirely from matter. Conservation of Energy We can change the form of energy from one to another but the total quantity of energy never changes. This is called the law of conservation of energy and is one of the cornerstones of science. Gravitational Acceleration Acceleration due to gravity: g = 9.81 m/s2 This value holds at the surface of the Earth. a15_ham_feather1.mov Momentum and Force Momentum – the product of an objects mass and velocity: p = mv Force – the thing that causes a change of momentum: F = ma - strictly speaking this should be net force Mass and Weight Mass on Earth = 100 kg Weight at surface of Earth = 100 kg Mass on Moon = 100 kg Weight at surface of Moon = 16 kg Newton’s Laws of Motion If I have seen further it is by standing on the shoulders of giants. Letter to Robert Hooke, February 5, 1675 Philosophiae Naturalis Principia Mathematica (1687), Sir Isaac Newton (1642-1727) Newton invented calculus several years prior to Leibniz but did not publish his results. Newton modified the conventional telescope to provide an off-axis focus. 2.5 m Isaac Newton Telescope La Palma, Canary Islands Newton’s First Law I. In the absence of a net (overall) force acting upon it an object moves with constant velocity Thus, objects at rest will tend to stay at rest while an object in motion stays in motion with no change in velocity. This is called an object’s inertia. Newton’s Second Law II. The acceleration of an object as produced by a net force is directly proportional to the magnitude of the net force, in the same direction as the net force, and inversely proportional to the mass of the object. Units? Force = rate of change of momentum or Force = mass x acceleration (F=ma) Thus, objects of different mass will accelerate differently when subjected to the same force. Also applies to angular motion Inward force implies inward acceleration Newton’s Third Law III. For any force, there is an equal and opposite reaction force or For every action there is an equal and opposite reaction Thus, forces always come in equal and opposite pairs.