Question

How can I use Kepler's law of harmonies to predict the time Mars takes to orbit the sun?

Answer 1

`~~1.87` years

Explanation:

Kepler's law of harmonies (also known as Kepler's third law) states that the orbital time period `T` is related to the mean distance `R` from the sun by

`T^2 propto R^3`

For Mars `R_"mars" = 2.28times 10^11\ "m"`,
while for earth, `R_"earth" =`1.50times 10^11\ "m"#

Thus

`(T_"mars"/T_"earth")^2 = (R_"mars"/R_"earth")^3 = (( 2.28times 10^11\ "m")/( 1.50times 10^11\ "m"))^3~~3.51`

Hence

`T_"mars"/T_"earth" = sqrt(3.51) ~~ 1.87`