Question

The ratio of the distance of two planets from the sun is 1.38 .the ratio of the period of revolution around sun is:
A 1.38 B .1.38 2

Answer 1

$\huge\underline\blue{\sf Answer:}$

$\large\red{\boxed{\sf {\frac{T_1}{T_2}}=(1.38)^{3/2}}}$

$\huge\underline\blue{\sf Solution:}$

$\large\underline\pink{\sf Given: }$

• Ratio of distance of two planets from sun ($\bf{\frac{a_1}{a_2}}$)=1.38

$\large\underline\pink{\sf To\:Find: }$

• Ratio of the period of revolution around sun is ($\sf{\frac{T_1}{T_2}}$)=?

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According to Kepler's Third law of Planetary motion :

The square of the period of revolution of any planet around the sun is directly proportional to the cube of the semi-major axis of its elliptical orbit.

$\large{♡}$$\large{\boxed{\sf T^2=a^3}}$

Here in our Question :

$\large\implies{\sf {\frac{T_1}{T_2}}={\frac{a_1}{a_2}}^{3/2}}$

$\large{\sf {\frac{a_1}{a_2}}=1.38 }$ (Given)

So ,

$\large\implies{\sf {\frac{T_1}{T_2}}=(1.38)^{3/2}}$

$\huge\red{♡}$$\large\red{\boxed{\sf {\frac{T_1}{T_2}}=(1.38)^{3/2}}}$

Hence ,

Ratio of the period of revolution around sun is $\large{\sf (1.38)^{3/2}}$