Question

The semi-major axis of planet A is four times the planet B. The ratio of time periods of revolutions of planets around the sun is​

Answer 1

Given:

The semi-major axis of planet A is four times the planet B.

To find:

Ratio of time period around sun ?

Calculation:

In this type of questions, it is best to apply KEPLER'S THIRD LAW OF PLANETARY MOTION:

• T² = a³ , T is the time period, and 'a' can be considered as the mean orbital radius (or semi-major axis).

Taking appropriate ratio, we can say:

${ \bigg( \dfrac{T_{2}}{T_{1}} \bigg)}^{2} = { \bigg( \dfrac{a_{2}}{a_{1}} \bigg)}^{3}$

$\implies { \bigg( \dfrac{T_{2}}{T_{1}} \bigg)}^{2} = { \bigg( 4 \bigg)}^{3}$

$\implies \dfrac{T_{2}}{T_{1}} = { \bigg( 4 \bigg)}^{ \frac{3}{2} }$

$\implies \dfrac{T_{2}}{T_{1}} = { \bigg( 2 \bigg)}^{3}$

$\implies \dfrac{T_{2}}{T_{1}} = 8$

So , the ratio of time period around the sun will be 8 : 1.