Question

mars has two moons, phoebos and deimos, shown in the image below. rank the length of the two moons periods from longest to shortest. wednesday, 1 august 2018, 1:40am bst, central uk simulated orbit diagram for martian moons phobos and deimos image of mars with two orbits labeled phobos and deimos phobos period > deimos period deimos period > phobos period deimos period = phobos period

Explanation:

Step1: Recall Kepler's Third Law

Kepler's Third Law states that for objects orbiting the same central body, the square of the orbital period \( T \) is proportional to the cube of the semi - major axis \( a \) of the orbit (\( T^{2}\propto a^{3} \)). This means that a larger semi - major axis (the average distance from the central body, Mars in this case) corresponds to a longer orbital period.

Step2: Analyze the Orbit Diagram

From the given orbit diagram of the Martian moons Phobos and Deimos, we can see that Deimos has a larger semi - major axis (its orbit is more extended away from Mars) compared to Phobos.

Step3: Apply Kepler's Third Law

Since \( T^{2}\propto a^{3} \), and Deimos has a larger \( a \) (semi - major axis) than Phobos, the orbital period of Deimos (\( T_{Deimos} \)) will be longer than the orbital period of Phobos (\( T_{Phobos} \)). So, \( T_{Deimos}>T_{Phobos} \) or in other words, Deimos period > Phobos period.

Answer:

Deimos period > Phobos period (the option with "Deimos period > Phobos period")