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NEET PHYSICSEasy

The figure shows elliptical orbit of a planet m about the sun S. The shaded area SCD is twice the shaded area SAB. If t1t_1 is the time for planet to move from C to D and t2t_2 is the time to move from A to B, then:

A

t1>t2t_1 > t_2

B

t1=4t2t_1 = 4t_2

C

t1=2t2t_1 = 2t_2

D

t1=t2t_1 = t_2

Step-by-Step Solution

According to Kepler's Second Law of planetary motion (Law of Areas), the line joining the Sun and the planet sweeps out equal areas in equal intervals of time. This implies that the areal velocity is constant (dAdt=constant\frac{dA}{dt} = \text{constant}), meaning the area swept (AA) is directly proportional to the time taken (tt). Mathematically, A1t1=A2t2\frac{A_1}{t_1} = \frac{A_2}{t_2}. Given that the Area SCD (A1A_1) is twice the Area SAB (A2A_2), i.e., A1=2A2A_1 = 2A_2, we have: 2A2t1=A2t2\frac{2A_2}{t_1} = \frac{A_2}{t_2} t1=2t2\Rightarrow t_1 = 2t_2.

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