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

1 Answer
Ananda Dasgupta
May 22, 2018

#~~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#

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