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Consider a star with 2 planets. The mass of planet A is the same as the mass of planet B. The orbit of Planet A is on average, closer to the star than the orbit of Planet B. Which of the following statements is true?

1) Planet A has a larger orbital period than Planet B
2) Planet A has a smaller orbital period than Planet B
3) Planet A has a larger orbital radius than Planet B
4) Planet A has a smaller orbital radius than Planet B

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Final answer:

Planet A has a smaller orbital period and a smaller orbital radius than Planet B as it is closer to the star, according to Kepler's third law, which relates orbital periods to distances from the star.

Step-by-step explanation:

The main answer to the student's question is that Planet A has a smaller orbital period than Planet B. Since Planet A is on average closer to the star than Planet B, according to Kepler's third law, which states that the square of the orbital period (P) of a planet is directly proportional to the cube of the semi-major axis (a) of its orbit, it can be inferred that Planet A, being closer, will also have a shorter period. The third law is expressed as P² ≈ a³, highlighting that a tighter orbit (smaller a) leads to a quicker journey around the star (smaller P).Thus, this directly answers the first part of the question. As for the second part, it is indeed correct that Planet A has a smaller orbital radius than Planet B, because being closer to the star implies a smaller average distance from the star, which is essentially the orbital radius for a planet in an elliptical orbit.In conclusion, of the statements provided, the correct ones regarding Planet A compared to Planet B are that it has smaller orbital period and smaller orbital radius because of its proximity to the star, as dictated by Kepler's laws of planetary motion.

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