The mean distance of planet from the sun is approximately 1/4 times that of earth from the sun. Find the number of years required

Q: The mean distance of planet from the sun is approximately 1/4 times that of earth from the sun. Find the number of years required for planet to make one revolution about the sun.

Sol: Given r_p = (1/4 ) r_e and T_e = 1 yr

From kepler’s third law,

$\large T^2 \propto r^3 $

$\large (\frac{T_p}{T_e})^2 = (\frac{r_p}{r_e})^3 $

$\large T_p = T_e(\frac{r_p}{r_e})^{3/2} $

$\large T_p = 1(\frac{r_e}{4 r_e})^{3/2} = (\frac{1}{4})^{3/2}$

= 0.125 yrs .