The period of revolution of planet A around the sun is 8 times that of B. The distance of A from the sun is how many times greater than that of B from the sun?

The period of revolution of a planet from the Sun is related to its distance from the Sun by Kepler’s third law. This law explains that the square of the orbital period of a planet is proportional to the cube of its average distance from the Sun. Here, planet A takes 8 times longer to complete one revolution around the Sun as compared to planet B.

Using Kepler’s law, the relationship between the orbital period and distance implies that if the period of revolution of planet A is 8 times that of planet B, the cube root of the square of this ratio will give the ratio of their distances from the Sun. Simplifying this relationship, it is determined that the distance of planet A from the Sun is 4 times greater than that of planet B.

This result demonstrates how much more time is taken by the planet to complete its orbit as the distance from the Sun increases. The universality of this principle among all celestial bodies that move in elliptical orbits tells us a lot about planetary systems’ structure and dynamics, bringing to light harmony between orbital period and distance in celestial mechanics.