The figure shows the elliptical orbit of a planet m around the Sun S. The shaded region SCD has twice the area of the shaded region SAB. If t1 is the time taken to go from C to D and t2 the time from A to B, then

t1 = t2
t1 = 8 t2
t1 = 4 t2
t1 = 2 t2

Correct answer: t1 = 2 t2

Solution

By Kepler's second law, areal velocity dA/dt is constant, so time is proportional to area swept. Since area SCD = 2 * area SAB, t1 = 2 t2.

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