A planet moving around sun sweeps area A1 in 2 days, A2 in 3 days and A3 in 6 days. Then the relation between A1, A2 and A3 is

Q: A planet moving around sun sweeps area A1 in 2 days, A2 in 3 days and A3 in 6 days. Then the relation between A1, A2 and A3 is

Numerical

(a) 3A1 = 2A2 = A3

(b) 2A1 = 3A2 = 6A3

(c) 3A1 = 2A2 = 6A3

(d) 6A1 = 3A2 = 2A3

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Ans: (a)
Sol: From Kepler’s 2nd Law (Law of Area )

$\displaystyle \frac{dA}{dt} = constant$

$\displaystyle \frac{A_1}{2} = \frac{A_2}{3} = \frac{A_3}{6} $

On multiplying by 6 ,

A1 = 2A2 = A3