Question

The distance of two planet from the sun are 10^13 and 10^12 respectively the radio of time period of planet is

Answer 1

From Kepler's Third law of planetary motion 

T₁²/T₂²  =  R₁³/R₂³

BY TAKING ROOT ON BOTH SIDES 
WE GET,

T₁/T₂ =  √(R₁³/R₂³)


T₁/T₂ =  √(10^13)³/(10^12)³

Answer 2

$10\sqrt{10}$ would be the ratio of the time period of the planets.

Explanation:

Given that,

The distance of the two planets from the sun = $10^{13} , 10^{12}$

To find,

The ratio of the time period of the planets = ?

Procedure:

Using Kepler's law, we know that

$T^{2}$ ∝ $r^{3}$

or

$T^{1} /T^{2}$ = $(r^{1} /r^{2} )^{3/2}$

so,

$T^{1} /T^{2}$ = $(10^{13} /10^{12} )^{3/2}$

∵ $T^{1} /T^{2}$ = $10\sqrt{10}$

Thus, the ratio is $10\sqrt{10}$

Learn more: Find the ratio

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