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Question

The period of a planet around sun is 27 times that of the earth. The ratio of radius of planet's orbit to the radius of the earth's orbit is


A

4

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B

9

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C

64

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D

27

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Solution

The correct option is B

9


Step 1: Given Data:

Let the period of the earth is Te

The period of a planet around the sun is Tp

Tp=27Te

Step 2: Formula Used:

According to Kepler’s law of periods,” The square of the time period of revolution of a planet around the sun in an elliptical orbit is directly proportional to the cube of its semi-major axis”.

That is-

T2a3

Step 3: Calculating the ratio of the radius of the planet's orbit to the radius of the earth's orbit:

Let the average radius of the planet from the sun is Rp

The radius of the earth is Re

The ratios can be as follows-

Te2Tp2=Re3Rp3

Tp=27Te

Putting the value

T2e272T2e=R3eR3pR3eR3p=272ReRp=3323Rp=32ReRp=9Re

Hence option B is the correct answer.


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