Final answer:
The question involves using Kepler's Third Law of Planetary Motion to compare the orbital periods of two satellites or planets by calculating the ratio of their periods' squares and distances' cubes.
Step-by-step explanation:
The question relates to the comparison of orbital periods of two satellites (or planets), which are determined by Kepler's Third Law of Planetary Motion. This law states that the ratio of the squares of the periods (T2) of two planets is equal to the ratio of the cubes of their average distances (r3) from the Sun. Therefore, to find the ratio approximation of the periods (planet1period and planet2period) within a given tolerance (ratiotolerance), we would need to compare their r3/T2 ratios and adjust them to the closest acceptable integers within the specified tolerance, assigning the resulting numerator to approxnum and the denominator to approxden.
According to the provided text, the constant ratio of r3/T2 holds true across the solar system, allowing us to make these calculations. Small deviations from this ratio may occur due to measurement uncertainties or orbital perturbations. This comparison is a practical application of Newton's universal law of gravitation, which has been used historically to predict the existence of new celestial bodies. However, this law is descriptive and does not explain the underlying causes of this orbital behavior.