Earth and Mars are 1.0 AU and 1.52 AU away from the Sun,respectively.Given that the period of Earth's orbit around the Sun is 1 yr,calculate the period of the orbit of Mars around the Sun.(1 AU = 150 $\times$ 10⁶ km) A)1.5 yr B)0.53 yr C)0.28 yr D)1.9 yr E)3.5 yr

Question

Quizplus · Accepted Answer

According to Kepler's third law, the square of the period of an orbit is proportional to the cube of the semi-major axis of the orbit. 
Therefore, 
(Tmars)^2/(TEarth)^2 = (amars/aEarth)^3 
where Tmars is the period of Mars' orbit and amars and aEarth are the semi-major axes of Mars and Earth respectively. 
Substituting the given values, 
(Tmars)^2/(1 yr)^2 = (1.52 AU/1.0 AU)^3 
(Tmars)^2 = 3.84 
Tmars = sqrt(3.84) = 1.96 yrs 
Therefore, the best choice is D) 1.9 yr.

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