Final answer:
The correct statement is that both the planet and the star experience the same gravitational force, but due to the planet's smaller mass, it experiences a larger acceleration than the star. This is based on Newton's laws of motion and the concept of a common center of mass around which both bodies revolve. The correct option is option 3.
Step-by-step explanation:
In the case of a planet orbiting a distant star, the correct statement regarding the acceleration and gravitational forces experienced by the star and the planet is: Both the star and the planet feel the same gravitational force, but the planet experiences a larger acceleration than the star. This conclusion stems from Newton's third law of motion, which states that for every action, there is an equal and opposite reaction. Thus, the gravitational force exerted by the planet on the star is equal in magnitude to the force exerted by the star on the planet.
The difference in acceleration between the two bodies is due to their respective masses. According to Newton's second law of motion (F=ma), given that the force is the same, the object with the smaller mass (in this case, the planet) will experience a greater acceleration. Conversely, the star with a larger mass will experience a smaller acceleration for the same magnitude of force.
This dynamic between the two bodies can be observed in the way planets and stars move around their common center of mass. The comparable size of a planet's orbit to a star's motion around the center of mass is greatly determined by their mass ratio. This principle also applies when calculating the effects of gravity on orbits in the solar system and the motions of satellites and spacecraft.