Q.According to Kepler's Second Law, the radial vector to a Planet from the Sun sweeps out equal areas in equal intervals of time. This law is a consequence of Conservation of ____.
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Start your 14-day free trial to unlock the full solution →Kepler's Second Law (the radius vector sweeps equal areas in equal times) follows from conservation of angular momentum, because the Sun's gravitational pull on a planet is a central force with zero torque about the Sun.
The gravitational force the Sun exerts on a planet always points along the line joining the planet to the Sun. A force that always points toward (or away from) a fixed point is called a central force.
Torque about the Sun is tau = r x F. Since F is always parallel (or antiparallel) to r for a central force, the cross product r x F = 0. Zero torque means the angular momentum L = r x p about the Sun does not change with time -- it is conserved.
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