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

 

Answers (1)

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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