Question

The mean distance of Mars from the sun is $1.52times$ that of Earth from the Sun. From Kepler’s law of periods, calculate the number of years required for Mars to make one revolution around the Sun.

Answer 1

In order to answer this question, to calculate the number of years required for Mars to make one revolution around the Sun, we will apply the Kepler’s law of periods equation to find it, and then we will discuss more about the mentioned law.

Complete step by step answer:
According to the Kepler’s law of periods, expressed as a ratio is:
${(\dfrac{{{a_M}}}{{{a_E}}})^3} = {(\dfrac{{{T_M}}}{{{T_E}}})^2}$
Here, $\dfrac{{{a_M}}}{{{a_E}}}$ is the mean distance ratio for the semi-major axis ratio.
and, ${T_E}$ is the number of years for Earth to make one revolution around the Sun.
and we have to calculate the number of years for Mars ( ${T_M}$ ) to make one revolution around the Sun.
$\Rightarrow {(1.52)^3} = {(\dfrac{{{T_M}}}{{1yr}})^2} \\\ \Rightarrow {T_M} = 1.87yr \\\$
Hence, the number of years required for Mars to make one revolution around the Sun is $1.87years$.

Note: Kepler's third and final law is the Law of Periods. The rule shows that the time it takes for a planet to complete its orbit is proportional to its average distance from the sun, using complex mathematical equations.