Final answer:
By applying Kepler's third law of planetary motion and given the known period and radius of Deimos's orbit, we can calculate the orbital period of Phobos to be 0.16 days.
Step-by-step explanation:
The question is asking to calculate the orbital period of Mars's moon Phobos using Kepler's third law of planetary motion. To find the period of Phobos's orbit, we can use the relationship from Kepler's third law that the square of the orbital period (T) is proportional to the cube of the radius of the orbit (r). Since the radius of Deimos's orbit and its period are given, and we have the radius for Phobos, we can set up a ratio based on Kepler's law where TDeimos2/rDeimos3 = TPhobos2/rPhobos3. We can solve for the period of Phobos (TPhobos) and find that the correct answer is Option a. 0.16 days.