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# Kepler5 - r decreases v-orbit(and v t must increase If r...

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Kepler's Second Law of orbital motion The area swept out by a line connecting an orbiting object and the central point is the same for any two equal periods of times. That line is called a radius vector in the following discussion. The rate of change of the swept-out area does NOT change with time. The line along which gravity acts is parallel to the radius vector. This means that there are no torques disturbing the angular motion and, therefore, angular momentum is conserved. The part of the orbital velocity (v-orbit) perpendicular (at a right angle) to the radius vector ( r ) is v t . The rate of change of the swept-out area = r×v t /2. To calculate the orbital angular momentum use v t for the velocity. So, the angular momentum = mass × v t × r = mass × 2 × (rate of change of area). That value does not change over time. So if
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Unformatted text preview: r decreases, v-orbit (and v t ) must increase! If r increases, v-orbit (and v t ) must decrease. This is just what Kepler observed for the planets! Earth-Moon system The total angular momentum = spin angular momentum + orbital angular momentum. The total angular momentum is CONSTANT. To find the spin angular momentum, subdivide the object into small pieces of mass and find the angular momentum for each of the small pieces. Then add up the angular momentum for all of the pieces. The Earth's spin speed is decreasing so its spin angular momentum is DEcreasing. Therefore, the Moon's orbital angular momentum must compensate by INcreasing. It does this by increasing the Earth-Moon distance....
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