6. Newton - Newtonian Mechanics and Gravity Outline Our...

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7- Newtonian Mechanics and Gravity Our 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 derived from basic arguments in Newtonian mechanics To learn about the different types of orbits (shapes, bound vs. unbound) Outline Monday, October 5, 2009
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7- 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 spectrum of different colours of light Isaac Newton (1642-1727) was a British mathematician who is often said to be the most brilliant scientist in history Monday, October 5, 2009
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7- “If I have been able to see further, it was only because I stood on the shoulders of giants.” --Isaac Newton Nature and Nature’s Laws lay hid in night God said, Let Newton be! and all was light. --Alexander Pope Monday, October 5, 2009
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7- Newton’s Laws of Motion Newton’s Laws of Motion 1. 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, Σ F, acting on it via: Σ F = ma 3. For every applied force, there is a reaction force which is equal in magnitude but opposite in direction. Monday, October 5, 2009
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7- Kepler’s laws explain how planets move, but not why they move that way Newton came up with a general theory of gravity which gives rise to Kepler’s laws (as a special case) and provides a physical explanation for gravity Newton’s Theory of Gravity Newton’s Universal Law of Gravitation The gravitational force between any two bodies of masses m 1 and m 2 is 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 -11 N m 2 /kg 2 Monday, October 5, 2009
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7- Let’s use Newton’s law of gravity to estimate the mass of Earth Recall: gravitational acceleration felt by bodies very near Earth’s surface is g = 9.80 m/s 2 Thus, if we drop a baseball of mass m b near 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 Earth Monday, October 5, 2009
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7- 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 R earth , the radius of Earth We can set the two forces equal and solve: Monday, October 5, 2009
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