The following figure shows the elliptical path of a planet about the Sun. The two shaded parts, S1 and S2, have equal areas. If t1 and t2 be the time taken by the planet to go from A to B and from C to D respectively, then:
A
t1>t2
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B
t1<t2
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C
t1=t2
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D
t1 and t2 cannot be compared.
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Solution
The correct option is Ct1=t2 According to Kepler’s law, the line joining a planet and the Sun sweeps equal areas in equal intervals of time during the rotation of the planet around it. Here, the regions S1 and S2 have the same area. Thus, the time taken for the planet to go from C to D is equal to the time taken for the planet to go from A to B. Hence, t1=t2