Answer:
1.095 AU.
Step-by-step explanation:
To find the average distance of an object from the Sun given the orbital period, we can use Kepler's third law. This law states that the square of the orbital period (T) is proportional to the cube of the average distance (r) between the object and the Sun.
First, let's convert the orbital period of 0.58 years into seconds. There are 365 days in a year and 24 hours in a day, so there are 365 * 24 * 60 * 60 = 31,536,000 seconds in a year.
Now, we can use the formula T^2 = k * r^3, where k is the constant of proportionality. We need to find the value of k, which can be determined by comparing the orbital period and average distance of any known object.
For example, Earth takes about 1 year to orbit the Sun, and its average distance is defined as 1 Astronomical Unit (AU). Substituting these values into the formula, we get 1^2 = k * 1^3, which simplifies to k = 1.
Now, we can find the average distance (r) for the given object. Using the formula T^2 = k * r^3 and substituting the orbital period of 0.58 years (31,536,000 seconds) and the value of k, we get (31,536,000)^2 = 1 * r^3.
Solving for r, we take the cube root of both sides to get r = (31,536,000)^(2/3). Evaluating this expression, we find that the average distance of the object from the Sun is approximately 1.095 AU.