Final answer:
The student's question relates to the effect of increasing the orbital radius of a planet on its orbital period around a star. Increasing the orbital radius would result in a greater orbital period according to Kepler's third law of planetary motion.
Step-by-step explanation:
The question asked by the student concerns the orbital mechanics of a planet around a star. Specifically, it deals with the relationship between the orbital period T, and the radius r of the orbit.
According to Kepler's third law of planetary motion, which can also be expressed with Newton's version of the law, the square of the orbital period of a planet is directly proportional to the cube of the semi-major axis of its orbit, given by the equation T² ≈ r³ (when the mass of the planet is much smaller than the mass of the star).
Therefore, if the orbital radius r were to increase, the orbital period T would indeed also increase. The crucial point to understand here is that the gravitational force between the two bodies, given by GMm/r², acts as the centripetal force necessary to keep the planet in a circular orbit.
When the orbital radius increases, this force decreases, requiring a longer duration for the planet to complete one full orbit, hence a greater orbital period T.