Question

The average distance of the sun from a planet is 9times in comparison to average distance of sun from earth Find the time period of revolution of the planet​

Answer 1

Answer:

“The square of the orbital period of a planet is directly proportional to the cube of the semi-major axis of its orbit.”

Putting it simply, if the time taken for a planet to rotate once in its orbit is T and the radius of the orbit is R (assuming a circular orbit, as must do in such questions), then, T 2 is proportional to R 3 .

=>(T1/T2) 2 = (R1/R2) 3

Here, let T1, R1 be the time period and radius of Earth’s current orbit. Let T2, R2 be the same quantities for the planet’s orbit.

Given, R2 = 4*R1

=> R1/R2 = 1/4

Substituting in the above equation,

=> (T1/T2) 2 = (1/4) 3 = 1/64

=> T1/T2 = (1/64) 0.5 = 1/8

=> T2 = 8*T1

Since T1 is one Earth year or 365 Earth days,

The time period of revolution of the planet is 8 Earth year or 2920 Earth days.

P.S. ‘=>’ means ‘which implies’.

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