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Old Sep 21st 2009, 04:22 AM   #1
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kepler's third law

THe radius of planet x's orbit revolving round the sun is four times radius of earth's orbit . If the time taken for the planet x to complete one revolution is taken as one year . What is the age of a man in planet x if he is 80 years old in the earth .

My attempt :

Using kepler's third law , which is $\displaystyle \frac{T^2}{r^3}=k$

Can i say that $\displaystyle \frac{T_1^2}{r_1^3}=\frac{T_2^2}{r_2^3}$ ??

If Yes , then $\displaystyle T_1=80$ , $\displaystyle r_2=4r_1 $

$\displaystyle \frac{80^2}{r_1^3}=\frac{T_2^2}{(4r_1)^3}$

the answer doesn't make sense ?? Thanks for your help !!
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Old Sep 21st 2009, 06:48 PM   #2
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It would actually be:

$\displaystyle \frac {T_1^2}{r_1^3} = \frac {T_2^2}{4r_1^3}$

$\displaystyle T_2 = \sqrt {(64) (T_1^2)}$

$\displaystyle \boxed {T_2 = 8 T_1}$

So, for the aged man:

$\displaystyle T_1 = 80$

.:.,

$\displaystyle T_2 = (8)(80) = 640 \mbox { "x" years}$

Now, that's what you call a quantitative analysis.
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Last edited by Deco; Sep 21st 2009 at 06:52 PM.
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Old Sep 21st 2009, 08:48 PM   #3
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Originally Posted by Deco View Post
It would actually be:

$\displaystyle \frac {T_1^2}{r_1^3} = \frac {T_2^2}{4r_1^3}$

$\displaystyle T_2 = \sqrt {(64) (T_1^2)}$

$\displaystyle \boxed {T_2 = 8 T_1}$

So, for the aged man:

$\displaystyle T_1 = 80$

.:.,

$\displaystyle T_2 = (8)(80) = 640 \mbox { "x" years}$

Now, that's what you call a quantitative analysis.

Thanks Deco , but the answer given is 10 years old and i am not sure how to work towards it .
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Old Nov 11th 2009, 11:15 PM   #4
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From keplers third law, we have the fact that the square of the orbital period is proportional to the cube of the orbit radius. Since the constant of proportinality is the same it cancels when we take a ratio. Thus,

Te ^2 / Tx ^2 = Re ^3 / Rx ^3 or

Tx ^2 = (Te ^2) (Rx ^3)/ Re ^3

= 1^2 (Rx / Re)^3 = 64 or

Tx = 8 years. Thus the planet x takes 8 earth years to complete one revoultuion around the sun.

Thus in 80 earth years, x completes 80/8 = 10 revs around the sun

Thus the age in x years of a man on x will be 10 years.
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Old Nov 12th 2009, 12:58 AM   #5
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Why dont you also find the age of a man on earth who is 80 on x?
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