lec21 - Physics 140 Fall 2007 15 November lecture#21...

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Physics 140 – Fall 2007 15 November: lecture #21 Approximating the earth as a sphere of uniform density, at what radius inside the earth is the gravitational acceleration equal to the value that would be felt a height of 3 R E above Earth s surface ? 1. R E / 2 2. R E / 3 3. R E / 4 4. R E / 9 5. R E / 16
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1) Planets move in ellipses of semi-major axis a with the sun at a focus. An ellipse has eccentricity e, where ea is the distance from the center to a focus. perihelion - R p = a (1– e ) closest point in sun-planet orbit aphelion - R a = a (1+ e ) farthest point in sun-planet orbit Kepler’s laws of planetary motion 2) Planetary orbits sweep out equal areas in equal times . This law reflects the fact that gravity is a central force . Since gravity acts along the radial direction connecting two bodies, it produces no torque on either. For a planet of mass m , the angular momentum of the orbit is conserved and determines the rate of area A swept out by its orbit 3) The square of the orbital period
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lec21 - Physics 140 Fall 2007 15 November lecture#21...

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