Kepler's third law

\dfrac{T^2}{a^3}=\text{const}

Result unit: — (constant for a given system)

What it describes

Kepler's third law — the square of the orbital period is proportional to the cube of the semi-major axis of the orbit.

T

orbital period

[s]

a

semi-major axis of the orbit

[m]

Kepler's third law — planets farther from the Sun orbit more slowly, and the ratio

T^2/a^3

is the same for all bodies orbiting the same centre. It follows from setting gravity equal to the centripetal force.

Comparing the orbits of bodies circling the same central body (planets, satellites).

A planet has an orbit 4 times larger than Earth's. How long is its year?

Substitution

a=4a_Z

T^2\propto a^3

Result

T=\sqrt{4^3}=8

years.

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