Question

What is the average distance from the Sun (in astronomical units) of an asteroid with an orbital period of 8 years?

Answer 1

To solve this problem we will use Kepler's third law, which tells us that the square of the orbital period of a planet is differently proportional to the cube of the average distance from the planet to the sun, mathematically that is,

$P^2 = a^3$

Here,

P = Period

a = Average distance

If we rearrange the equation to find the average distance we have that

$a = P^{ \frac{2}{3}}$

Replacing the period given of 8 years we have that

$a = 8^{ \frac{2}{3}}$

$a = 4 AU$

Therefore the average distance of the asteroid from the Sun is 4 Astronomical Units