Orbital period of planets
The above graph shows the relationship between the orbital period (T) and the semi major axis (a) of the eight planets of the sun. Which of the following explanations is correct?
a) The orbital period is proportional to the semi major axis.
b) The orbital period is inversely proportional to the semi major axis.
c) The square of the orbital period is proportional to the semi major axis.
d) The square of the orbital period is proportional to the cube of the semi major axis.
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1 solution
Kepler's 3rd law of planetary motion (also known as harmonic law) states that, "The square of the orbital period is directly proportional to the cube of semi-major axis of an orbit." This can be represented mathematically as P 2 = k R 3 , where k is a proportionality constant. Even better, k can be equal to k = G ( M 1 + m 2 ) 4 π 2 , where M and m are masses of sun and planets, respectively.