Question

If a planet is 15.0 au from the sun, what is it’s period? (Hint: compare this planet to Earth)

Answer 1

The period of the planet is 58.1 years

Explanation:

We can solve this problem by using Kepler's third law, which states that:

"The square of the orbital period of a planet is proportional to the cube of its semimajor orbital axis"

Translated into equations, we can write:

$\frac{T_x^2}{r_x^3}=\frac{T_e^2}{r_e^3}$

Where, taking the orbits of the planets as almost circular, we have:

$T_x$ is the orbital period of the unknown planet

$r_x = 15.0 au$ is the radius of the orbit of the planet

$T_e = 1 y$ (1 year) is the period of the orbit of the Earth

$r_e = 1 AU$ is the orbital radius of the Earth

Solving for $T_x$, we find the orbital period of the unknown planet:

$T_x = T_e \sqrt{\frac{r_x^3}{r_e^3}}=(1y)\sqrt{\frac{(15.0)^3}{(1.0)^3}}=58.1 y$

Learn more about Kepler's third law:

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