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  • Need explanation for: The distance of two planets from sun are nearly 1014 and 1012 meters. Assuming that they move in circular orbits, their periodic times will be in the ratio

The distance of two planets from sun are nearly 1014 and 1012 meters. Assuming that they move in circular orbits, their periodic times will be in the ratio

  • Option 1)

    100

  • Option 2)

    10

  • Option 3)

    1000

  • Option 4)

    100\sqrt{10}

 

Answers (1)

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}\Rightarrow \left ( \frac{T_{2}}{T_{1}} \right )^{2}=\left ( \frac{R_{2}}{R_{1}} \right )^{3}=\left ( \frac{10^{12}}{10^{14}} \right )^{3}=10^{-6}

\therefore T_{2}=10^{-3}T_{1}    or     \frac{T_{1}}{T_{2}}=1000


Option 1)

100

This is incorrect option

Option 2)

10

This is incorrect option

Option 3)

1000

This is correct option

Option 4)

100\sqrt{10}

This is incorrect option

Posted by

Plabita

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