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  • Please help! What would be the duration of the year if the distance between the earth and the sun gets doubled?

What would be the duration of the year if the distance between the earth and the sun gets doubled?

  • Option 1)

    1032 days

  • Option 2)

    129 days

  • Option 3)

    365 days

  • Option 4)

    730 days

 

Answers (2)

best_answer

As we learnt in 

Kepler's 3rd law -

T^{2}\: \alpha\: a^{3}

From fig.

AB=AF+FB

2a=r_{1}+r_{2}

\therefore\; a=\frac{r_{1}+r_{1}}{2}

a= semi major Axis

r_{1}= Perigee

- wherein

Known as law of periods

r_{2}= apogee

T^{2}\: \alpha \: \left ( \frac{r_{1}+r_{2}}{2} \right )^{3}

{r_{1}+r_{2}= 2a

 

 T^{2}\propto R^{3}

If r get double  \Rightarrow }R_{2}=2R_{1}

\frac{T_{2}}{T_{1}}=\left ( \frac{R_{2}}{R_{1}} \right )^{\frac{3}{2}}=2^{\frac{3}{2}}

\Rightarrow T_{2}=\left ( 2\sqrt{2} \right ) T_{1}=\left ( 2\sqrt{2} \right ) 365\ days = 1032\ days


Option 1)

1032 days

This is correct option

Option 2)

129 days

This is incorrect option

Option 3)

365 days

This is incorrect option

Option 4)

730 days

This is incorrect option

Posted by

divya.saini

View full answer

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