The figure shows the motion of a planet around the sun in an elliptical orbit with sun at the focus. The shaded areas A and B are also shown in the figure which can be assumed to be equal. If t1 and t2 represent the time for the planet to move from a to b and d to c respectively, then Option 1) t1 > t2 Option 2) t1 < t2 Option 3) t1 = t2 Option 4) none of these

As we learnt in

Kepler's 2nd law -

Area of velocity = $\frac{dA}{dt}$

$\frac{dA}{dt}=\frac{1}{2}\frac{\left ( r \right )\left ( Vdt \right )}{dt}=\frac{1}{2}rV$

$\frac{dA}{dt}\rightarrow$ Areal velocity

$dA\rightarrow$  small area traced

- wherein

Simiar to Law of conservation of momentum

$\frac{dA}{dt}= \frac{L}{2m}$

$L\rightarrow$ Angular momentum

Known  as Law of Area

Areal velocity of planet in elliptical path is constant. This implies equal area will be covered in equal time.

$\Rightarrow t_{1}=t_{2}$

Option 1)

t1 > t2

This is incorrect option

Option 2)

t1 < t2

This is incorrect option

Option 3)

t1 = t2

This is correct option

Option 4)

none of these

This is incorrect option

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