Question

A comet has an orbital period of 87 years. What is its average distance in AU) from the Sun?

AU=

Answer 1

To calculate the average distance from the Sun of a comet with an 87-year orbital period, Kepler's Third Law is used, leading to an average distance of approximately 21.89 AU.

Step-by-step explanation:

The student has asked to calculate the average distance from the Sun of a comet with an orbital period of 87 years, expressed in astronomical units (AU). To find this distance, we apply Kepler's Third Law of planetary motion, which states that the square of the orbital period (P) is directly proportional to the cube of the semi-major axis (a) of the orbit, where P is in years and a is in AU. The formula is often written as P² = a³.

For the comet with an orbital period of 87 years, we organize the given information and our goal as follows:

1. Given orbital period P = 87 years
2. We want to find the average distance a in AU

We can rearrange Kepler's Third Law to solve for a:

a³ = P²

Therefore:

a = (P²)^(1/3)

Substituting the given value:

a = (87²)^(1/3)

A simple calculation yields:

a ≈ 21.89 AU

This is the average distance of the comet from the Sun in astronomical units.