Question

15) Mars has two moons, Phobos and Deimos (Fear and Panic, the companions of Mars, the god of war).

Deimos has a period of 30 h 18 min and a mean distance from the center of Mars of 2.3 x 104 km. If the period
of Phobos is 7 h 39 min, what mean distance is it from the center of Mars?

Answer 1

To determine the mean distance of Phobos from the center of Mars, we can use Kepler's third law of planetary motion.

Step-by-step explanation:

The mean distance of Phobos from the center of Mars can be determined using Kepler's third law of planetary motion. This law states that the square of a planet's orbital period is proportional to the cube of its mean distance from the center of its orbit.

Given that the period of Phobos is 7 hours and 39 minutes and the period of Deimos is 30 hours and 18 minutes, we can set up the following equation:

(Period of Phobos)^2 / (Mean distance of Phobos)^3 = (Period of Deimos)^2 / (Mean distance of Deimos)^3

Substituting the given values, we have:

(7.65 hours)^2 / (Mean distance of Phobos)^3 = (30.3 hours)^2 / (2.3 x 10^4 km)^3

Simplifying the equation, we can solve for the mean distance of Phobos: