Amie Lindgren DDS
Oct 15, 2024
The orbital radius of Mars is 1.52 times larger than that of Earth. What is the orbital period of Mars in Earth years?
Given that the orbital radius of Mars is 1.52 times larger than that of Earth, what is the orbital period of Mars expressed in Earth years?
3 Answers
Kepler once said (T_E)^2 / (r_E)^3 = (T_M)^2 / (r_M)^3
E stands for Earth, M for Mars.
Substitute the info r_Mars = 1.53 * r_Earth.
(T_E)^2 / (r_E)^3 = (T_M)^2 / (1.53r_E)^3
Cancel r_E^3 from both fractions.
(T_E)^2 = (T_M)^2 / (1.53)^3
(T_M)^2 = 1.53^3 * (T_E)^2
Take the square root of both sides
T_M = 1.89 T_E = 1.89 years (duh)
1.52³/²= 1.87398 years.
it is the Sidereal year (in terms of stars) for Mars. Its synodal years is
1 – (1/1.87398) = 0.4663659 = 1/2.1441885,
or 2.1441885 years = 783 days … is the time between two consecutive oppositions.
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