Final answer:
In a circular orbit, the planet's distance from the star remains constant, and the planet's speed remains constant as well, adhering to the conditions of uniform circular motion.
Step-by-step explanation:
The correct statement for a planet orbiting a star in a circular orbit at a constant orbital speed is that the planet's distance from the star remains constant. In a circular orbit, the force of gravity is balanced by the centripetal force required to keep the planet moving in a circle, resulting in a constant speed and radius. This satisfies the condition of uniform circular motion, where neither the speed nor the orbital radius changes. However, Kepler's laws of planetary motion indicate that in elliptical orbits, planets will indeed have varying speeds; they move faster when closer to the star and slower when farther away. But these laws apply to elliptical orbits, not circular ones. Therefore, referring to the initial question, the correct statement is (1) The planet's distance from the star remains constant, and (4) The planet's speed remains constant.