If the radius of earth's orbit is made 1/16, the duration of an year will become

  • Option 1)

    16 times

  • Option 2)

    1/64 times

  • Option 3)

    1/16 times

  • Option 4)

    1/8 times

 

Answers (1)

As we learnt in 

Kepler's 3rd law -

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

From figure

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}\Rightarrow T\propto R^{\frac{3}{2}}

\Rightarrow \frac{T_{2}}{T_{1}}=\left ( \frac{R_{2}}{P_{1}} \right )^{\frac{3}{2}} =\left ( \frac{1}{16} \right )^{\frac{3}{2}}=\frac{1}{64}

\therefore T_{2}=\frac{T_{1}}{64}

 


Option 1)

16 times

This is incorrect option

Option 2)

1/64 times

This is correct option

Option 3)

1/16 times

This is incorrect option

Option 4)

1/8 times

This is incorrect option

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