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Chapter 4 - Planet Holloway
Chapter 4 - Planet Holloway

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... Whenever one body exerts a force on a second body, the second body exerts an equal and opposite force on the first. This is often stated: For every action, there is an equal and opposite reaction. In Newton's 1st Law, we looked at the sum of forces on a single object, which could sum to zero. Here w ...
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... b) Find the time that has elapsed when the body is moving parallel to the vector i. (3 marks) 3. A boy of mass 40 kg stands in a lift. Find the force exerted by the floor of the lift on the boy when a) the lift is moving upwards with constant speed, (2 marks) b) the lift is moving downwards with acc ...
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... high symmetry, gravitational calculations are often much easier if GAUSS’S LAW is used! a. Calculate the gravitational field g outside the sphere, a distance r  R from the center. (6 points) b. Calculate the gravitational field g inside the sphere, a distance r  R from the center. (6 points) c. Ca ...
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... • Sir Isaac Newton (1643-1727) an English scientist and mathematician famous for his discovery of the law of gravity also discovered the three laws of motion. He published them in his book Philosophiae Naturalis Principia Mathematica (mathematic principles of natural philosophy) in 1687. Today thes ...
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Newton's theorem of revolving orbits



In classical mechanics, Newton's theorem of revolving orbits identifies the type of central force needed to multiply the angular speed of a particle by a factor k without affecting its radial motion (Figures 1 and 2). Newton applied his theorem to understanding the overall rotation of orbits (apsidal precession, Figure 3) that is observed for the Moon and planets. The term ""radial motion"" signifies the motion towards or away from the center of force, whereas the angular motion is perpendicular to the radial motion.Isaac Newton derived this theorem in Propositions 43–45 of Book I of his Philosophiæ Naturalis Principia Mathematica, first published in 1687. In Proposition 43, he showed that the added force must be a central force, one whose magnitude depends only upon the distance r between the particle and a point fixed in space (the center). In Proposition 44, he derived a formula for the force, showing that it was an inverse-cube force, one that varies as the inverse cube of r. In Proposition 45 Newton extended his theorem to arbitrary central forces by assuming that the particle moved in nearly circular orbit.As noted by astrophysicist Subrahmanyan Chandrasekhar in his 1995 commentary on Newton's Principia, this theorem remained largely unknown and undeveloped for over three centuries. Since 1997, the theorem has been studied by Donald Lynden-Bell and collaborators. Its first exact extension came in 2000 with the work of Mahomed and Vawda.
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