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
simulated orbit diagram
for martian moons
phobos and deimos
wednesday, 1 august 2018,
1:40am bst,
central uk
mars
deimos
phobos
deimos period > phobos period
phobos period > deimos period
deimos period = phobos period

Explanation:

Step1: Apply Kepler's third law

Kepler's third law states that \( T^{2}\propto r^{3}\), where \(T\) is the orbital period and \(r\) is the orbital radius.

Step2: Compare orbital radii

From the diagram, Deimos has a larger orbital radius (\(r\)) around Mars than Phobos.

Step3: Determine period relationship

Since \(T^{2}\propto r^{3}\), a larger \(r\) means a larger \(T\). So Deimos has a longer period than Phobos.

Answer:

Deimos period > Phobos period