6. Newton - 7-Newtonian Mechanics and GravityOur goals for...

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Unformatted text preview: 7-Newtonian Mechanics and GravityOur goals for this section:•To review Newton’s Laws of Motion•To introduce Newton’s Theory of Gravity•To show that Kepler’s Laws can be derivedfrom basic arguments in Newtonian mechanics•To learn about the different types of orbits (shapes, bound vs. unbound)OutlineMonday, October 5, 20097-Sir Isaac Newton•Newton made many significant contributions to science, of which we will have time to discuss only a few. Among them:– he helped to invent calculus– he formulated the basic laws of mechanics– he formulated the theory of gravity– he contributed greatly to optics; he was the first to show that white light could be split into a spectrumof different colours of light•Isaac Newton (1642-1727) was a British mathematician who is often said to be the most brilliant scientist in historyMonday, October 5, 20097-“If I have been able to see further, it was only because I stood on the shoulders of giants.”--Isaac NewtonNature and Nature’s Laws lay hid in nightGod said, Let Newton be! and all was light.--Alexander PopeMonday, October 5, 20097-Newton’s Laws of MotionNewton’s Laws of Motion1. If no net force acts on it, a body at rest remains at rest, and one in motion continues to move in a straight line with constant speed.2. The acceleration, a, of a body is related to the mass, m, of the body and the net force, ΣF, acting on it via:ΣF = ma3. For every applied force, there is a reaction force which is equal in magnitude but opposite in direction.Monday, October 5, 20097-•Kepler’s laws explain howplanets move, but not whythey move that way•Newton came up with a general theory of gravitywhich gives rise to Kepler’s laws (as a special case) and provides a physical explanationfor gravityNewton’s Theory of GravityNewton’s Universal Law of GravitationThe gravitational force between any two bodies of masses m1and m2is proportional to the product of their masses and inversely proportional to the square of the distance between them, r:where G = 6.67 x 10-11N m2/kg2Monday, October 5, 20097-•Let’s use Newton’s law of gravity to estimate the mass of Earth•Recall: gravitational acceleration felt by bodies very near Earth’s surfaceis g = 9.80 m/s2•Thus, if we drop a baseball of mass mbnear the Earth’s surface, Newton’s second law tells us that the gravitational force on the ball is:•Newton’s law of gravitation tells us that this force is simply the force of gravitational attraction between the ball and the planet:Example--Finding the Mass of the EarthMonday, October 5, 20097-•Note that we are considering the ball to be very close to Earth’s surface at all times, so we assume that the distance between them is approximately Rearth, the radius of Earth•We can set the two forces equal and solve:Monday, October 5, 20097-•The gravitational acceleration...
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This note was uploaded on 03/01/2011 for the course ASTRO 1a03 taught by Professor Samantha during the Spring '11 term at McMaster University.

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6. Newton - 7-Newtonian Mechanics and GravityOur goals for...

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