Question

The semi major axis of palmer a is four times of planet b then ratio of time period of revolution of planet around the sun is

Answer 1

Given:

The semi major axis of planet a is four times of planet b.

To find:

Ratio of time period of revolution around sun?

Calculation:

It is best to use KEPLER'S 3RD LAW OF PLANETARY MOTION:

• T² = x³ , T is time period and x is average orbital radius (can be considered as semi-major axis).

Taking appropriate ratios:

$\dfrac{ {(T_{a})}^{2} }{ {(T_{b})}^{2} } = \dfrac{ {(x_{a})}^{3} }{ {(x_{b})}^{3} }$

$\implies \bigg(\dfrac{ T_{a}}{T_{b}} \bigg)^{2} = { \bigg(\dfrac{ x_{a} }{ x_{b}} \bigg)}^{3}$

$\implies \bigg(\dfrac{ T_{a}}{T_{b}} \bigg)^{2} = { \bigg(4 \bigg)}^{3}$

$\implies \bigg(\dfrac{ T_{a}}{T_{b}} \bigg)^{2} = 64$

$\implies \dfrac{ T_{a}}{T_{b}} = \sqrt{64}$

$\implies \dfrac{ T_{a}}{T_{b}} = 8$

So, ratio of time period is 8 : 1.