Question

The mean distance of mars from sun is $1.5$ times that of earth from sun. What is approximately the number of years required by mars to make one revolution about sun ?

• A. 2.35 years
• B. 1.84 years
• C. 3.65 years
• D. 2.75 years

Answer 1

Answer: (B)

According to Kepler's third law $T^2\propto r^3$
or $T\propto r^{3/2}\therefore \frac{T_E}{T_M}={\left(\frac{r_E}{r_M}\right)}^{3/2}$
where $T_E=$ time of revolution of earth around sun $=1$ year
$r_E=$ mean distance of earth from sun
$T_M=$ time of revolution of mars around sun
$r_M=$ mean distance of mars from sun.
or $T_M=T_E{\left(\frac{r_M}{r_E}\right)}^{3/2}=(1)$
${\left[\frac{1.5r_E}{r_E}\right]}^{3/2}=1.84$ years