# The orbital radius of Mars is 1.52 times larger than that of Earth. What is the orbital period of Mars 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.

• Don’t you have a calculator?

1.52¹·⁵ = 1.873982

Even if you don’t have a calculator, there are ways to find square roots with a pencil and a piece of paper. You should find out how to do that. Most school kids learn the method in high school. Or, at least, they used to.

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