Answer: So, the average distance from the Sun of a planetary object with an orbital period of 325 years is approximately 40.0 AU.
Step-by-step explanation:
The average distance from the Sun (in astronomical units) of a planetary object with an orbital period of 325 years can be estimated using Kepler's Third Law of Planetary Motion. This law states that the square of the orbital period (T) of a planet is proportional to the cube of its average distance from the Sun (r):
T^2 = k * r^3
where k is a constant. We can rearrange this equation to solve for r:
r = (T^2 / k)^(1/3)
The value of k depends on the units used for T and r, so it is important to make sure that the units are consistent. If T is in years and r is in astronomical units (AU), then k has a value of approximately 4π^2.
Using this formula, we can estimate the average distance from the Sun of a planetary object with an orbital period of 325 years:
r = (325^2 / (4 * π^2))^(1/3)
r ≈ 40.0 AU
So, the average distance from the Sun of a planetary object with an orbital period of 325 years is approximately 40.0 AU.