Chapter_13_Keplers_Laws_and_Universal_Gravitation

# Chapter_13_Keplers_Laws_and_Universal_Gravitation - Motion...

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Motion of a Top The only external forces acting on the top are the normal force and the gravitational force The direction of the angular momentum is along the axis of symmetry The right-hand rule indicates that the torque is in the xy plane M τ= × = × r F r g r r r r r

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Kepler’s Laws and Universal Gravitation!
Johannes Kepler 1571 – 1630 German astronomer Best known for developing laws of planetary motion Based on the observations of Tycho Brahe

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Kepler’s Laws Kepler’s First Law All planets move in elliptical orbits with the Sun at one focus Kepler’s Second Law The radius vector drawn from the Sun to a planet sweeps out equal areas in equal time intervals Kepler’s Third Law The square of the orbital period of any planet is proportional to the cube of the semimajor axis of the elliptical orbit
Notes About Ellipses F 1 and F 2 are each a focus of the ellipse They are located a distance c from the center – The sum of r 1 and r 2 remains constant Use the active figure to vary the values defining the ellipse The longest distance through the center is the major axis a is the semimajor axis

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Notes About Ellipses, cont The shortest distance through the center is the minor axis b is the semiminor axis The eccentricity of the ellipse is defined as e = c / a For a circle, e = 0 The range of values of the eccentricity for ellipses is 0 < e < 1 The higher the value of e, the longer and thinner the ellipse
Notes About Ellipses, Planet Orbits The Sun is at one focus Nothing is located at the other focus Aphelion is the point farthest away from the Sun The distance for aphelion is

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Chapter_13_Keplers_Laws_and_Universal_Gravitation - Motion...

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