30-gravitation II

# 30-gravitation II - Phys 211 Chapter 13 Gravitation Review...

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Phys 211 4/8/09 Chapter 13 Gravitation

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Review Kepler’s First Law: All planets move on elliptical orbits with the Sun at one focus. Kepler’s Second Law: The line that connects a planet to the Sun sweeps out equal areas in equal time. (Conservation of angular momentum.) Kepler’s Third Law: The square of the period of any planet is proportional to the cube of the semi-major axis of its orbit. T 2 R 3 = const F = G m 1 m 2 r 2 ˆ r Newton’s Law of Gravitation:
Symmetry and Superposition Find the net gravitational force on m 1 . F 1 NET = F 12 + F 13 + F 14 + F 15 F 1 NET = 2 F 13 cos( θ ) F 1 NET = 2 G m 1 m 3 a 2 cos( θ ) F 12 and F 12 cancel out F 13x and F 15x cancel out

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Checkpoint 2 The figure has three arrangements of particles of equal mass. Rank the arrangements according to the magnitude of the net gravitational force on the particle labelled “m”, greatest first.
Extended Objects Shells: m 1 m 2 r F 1 Outside the shell, the force is the same as if all the mass were located at the center of the shell.

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