Final answer:
The claim is false; knowing the orbital period, semimajor axis, and star's mass is not enough to determine a planet's mass because the mass equation combines both the star and planet masses, and without additional data, individual masses cannot be specified.
Step-by-step explanation:
The statement is false: knowing the period and semimajor axis of the orbit of a planet circling a nearby star, as well as the mass of the star, is not sufficient to determine the mass of the planet. According to Newton's reformulation of Kepler's third law, which is D³ = (M₁ + M₂)P², the mass measurement is a combination of the two objects in mutual orbit (in this case, the star's mass and the planet's mass).
Since the equation gives the sum of the masses, without additional information about either the mass of the star or planet, the individual masses cannot be determined. Kepler's third law, P² is proportional to a³, was originally derived for the motion of planets around the Sun, where the planets' masses are negligible compared to the Sun's mass. In the case of a star-planet system, if the planet is much less massive than the star, which is usually the case, the mass of the planet does not significantly affect the total mass used in the calculation. As a result, the mass of the planet remains indeterminate from the given information alone.