# Chapter 13: Gravitation. Newton’s Law of Gravitation A uniform spherical shell shell of matter attracts a particles that is outside the shell as if all.

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Chapter 13: Gravitation

Newton’s Law of Gravitation A uniform spherical shell shell of matter attracts a particles that is outside the shell as if all the shell’s mass is concentrated at its center! G = 6.67  10 –11 N m 2 /kg 2 Superposition Principle

Gravitation Near Earth’s Surface Gravitational acceleration 1. 1.Earth is not uniform. 2. 2.Earth is not a sphere. 3. 3.Earth is rotating. Mean Earth surface (0 km, 9.83 m/s 2 ), Mt. Everest (8.8 km, 9.80 m/s 2 ), highest manned balloon ( 36.6 km, 9.71 m/s 2 ), Space Shuttle orbit (400 km, 8.70 m/s 2 ), and communications satellite (35,700 km, 0.225 m/s 2 )

Kepler’s Laws 1. 1.The Law of Orbits: All planets move in elliptical orbits, with the Sun at one focus. 2. 2.The Law of Areas: A line that connects the planet to the Sun sweeps out equal areas in the plane of the planet’s orbit in equal times, i.e., the rate dA/dt at which it sweeps out area A is constant. 3. 3.The Law of Periods: The square of the period is proportional to the cube of the semimajor axis of its orbit.

Potential and Kinetic Energy Potential Energy Kinetic Energy Total Energy

Einstein and Gravitation

 Sample Problems 13-4, 13-5, 13-6

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