Question

Two planets A and B are revolving around the Sun have time period in the ratio of 27 : 2√2, then the ratio of their radius of revolution is​

Answer 1

Answer:

The relation b/w time period and radius is

R³ = k T²

R = k T⅔

Required Ratio:

R1/R2 = (T1/T2)⅔ = (27/2√2)⅔ = 9/2

Answer 2

HELLO DEAR,

GIVEN:-Two planets A and B are revolving around the Sun have time period in the ratio of 27 : 2√2, then the ratio of their radius of revolution is

SOLUTION:-

R1 / R2 = 9 / 2.

Let time period [T1] of planet A = 27x

And time period[T2] of planet B = 2√2x.

So, [T1/T2] = (27/2√2)

By using the relation of time period and radius in Kepler's Laws.

[R³ = KT²]

So, [T1/T2]² = [R1/R2]³

[R1/R2] = [T1/T2]⅔

[R1/R2] = [27/2√2]⅔

[R1/R2] = 9/2

Therefore the relation of their radius is 9:2.

There are three laws of Kepler's law of planetary motion.

1) every planets orbit is an ellipse with the sun at focus.

2) a line joining the sun and planet sweeps equal area in equal time interval.

3)the square of a planets orbital period is proportional to the cube of the semi major axis of it.

THANKS.