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Scientists discover two planets orbiting a distant star. The average distance from the star to Planet A is 8 AU, and it takes 710 Earth days for Planet A to orbit the star. If it takes 1170 Earth days for Planet B to complete an orbit, what is the average distance from Planet B to the star? AU

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cjrodriguez89

Answer: 11.2 AU

Explanation:

Applying Kepler's 3rd law, we can find out the average distance of planet B to the star.

This Law states that for planets orbiting a same star, there exists a fixed relationship between the average distance to  the star, and the period of his orbit  around it, as follows:

K = T² / d³

So , in this case, we can write:

(da)³ / Ta² = (db)³ / (Tb)²

Solving for db:

db = ∛8³.(1170)² / 710² = ∛1390.4 = 11.2 AU

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