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Q.
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 ?
Gravitation
Solution:
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 $T_{M}=T_{E}\left(\frac{r_{M}}{r_{E}}\right)^{3/2}=(1)$
$\left[\frac{1.5 r_{E}}{r_{E}}\right]^{3 / 2}=1.84$ years