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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

A
Anonymous

Dec 04, 2024

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)

A
Anonymous

Dec 01, 2024

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.

A
Anonymous

Nov 23, 2024

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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