Calculate the period T...

Question

Calculate the period T of a planet whose orbit has a semimajor axis of 2.1 AU.

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Answer 1

According to Kepler's 3rd law, the square of the period is proportional to the cube of the semi-major axis.

 

The semi-major axis of this planet is 2.1 times that of the earth.  The cube of 2.1 is 9.261.

 

That means that the square of this planet's period should be the 9.261 times the square of that of the earth. 

 

The square root of 9.261 is 3.043.  So the period of this planet should be 3.043 times that of this earth.

 

The earth's period is 365.25 days, so this planet's period is or 1111.45 days.