The mean distance of Mars from the Sun is$\mathbf{1}\mathbf{.52}$times 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; compare your answer with the value given in Appendix C.

The mean distance of Mars from the sun is $1.52$ times that of Earth from the sun.

Using Kepler’s law of period, find thenumber of years required for Mars to make one revolution around the sun and compare the answer with the given value in Appendix C. According to Kepler’s third law, the squares of the orbital periods of the planets are directly proportional to the cubes of the semi major axes of their orbits.

Formula is as follow :

${\left(\frac{{\mathrm{T}}_{\mathrm{M}}}{{\mathrm{T}}_{\mathrm{E}}}\right)}^2={\left(\frac{{\mathrm{r}}_{\mathrm{M}}}{{\mathrm{r}}_{\mathrm{E}}}\right)}^3$

where, T is corresponding time and ris corresponding radius.

Now,

${\left(\frac{{\mathrm{T}}_{\mathrm{M}}}{{\mathrm{T}}_{\mathrm{E}}}\right)}^2={\left(\frac{{\mathrm{r}}_{\mathrm{M}}}{{\mathrm{r}}_{\mathrm{E}}}\right)}^3$

As,

${\mathrm{r}}_{\mathrm{M}}=1.52{\mathrm{r}}_{\mathrm{E}}$and${\text{T}}_{\text{E}}=\text{1year}$

${\text{T}}_{\text{M}}=1.87\text{years}$

Hence, thenumber of years required for Mars to make one revolution around the sun is1.87 years.

The given value in the appendix is 1.88 years which is quite close to the obtained answer.

Therefore, using Kepler’s law of period, the time of revolution of the mars around the sun can be found.