1.[Mathematical Insight 4.3, Section 4.5]Imagine there is a solar system where only two planets are orbiting in circle around a star. The star has the same mass as the Sun; one of the planets, planet A, has smaller orbital radius than the other one, planet B. The two planets both have the same mass as the Earth.-

a. Using Newton's version of Kepler's third law, find out which planet (A or B) has a longer period. If planet A is twice as heavy (massive) as planet B, will you change your answer? Explain.

b. Using Newton's version of Kepler's third law, find out which planet (A or B) has a faster orbital velocity. (Hint, orbital velocity = 2a/p). If planet A is twice as heavy as planet B, will you change your answer? Explain.