Question

(6) Moons of Mars.
In 1727, Jonathan Swift wrote Gulliver's Travels in which he described two moons orbiting Mars. About 150 years later, the American astronomer Asaph Hall used a large telescope to discover two moons of Mars and they were named Phobos ("fear") and Diemos ("terror"). Their motions were surprisingly close to Jonathan Swift's description. The orbital period of Phobos is 8 hours and that of Diemos about 30 hours.

(2 pts.) (a) Using the information given above and one of Kepler's laws (which one?), explain which moon, Phobos or Diemos, is farther from Mars.

(2 pts.) (b) Describe the motions of Phobos and Diemos as seen by an inhabitant of Mars at, say, 40° north martian latitude.

(Note: Phobos and Diemos both orbit Mars close to Mars' equatorial plane and in the same (counterclockwise) direction that Mars spins. Mars' spin period is close to 24 hours. Drawing diagrams would probably help).

PLEASE EXPLAIN YOUR ANSWERS CLEARLY

Answer 1

a) Kepler's third law says - The time period squared () of a body revolving around another is proportional to the cube of the semi major axis () of the orbit.

                                          

Therefore, larger the time taken to complete one revolution (), larger the size of the orbit.

That is, Diemos () is farther from Mars on an average than Phobos ().

b) To an observer in Mars, whose time period of spinning on its own axis is 24 hrs, Phobos will be seen moving in an anticlockwise direction (because the time period of Phobos is shorter than of Mars and so it will fly past the rotating Mars). It will be observable three times a day to the man (24/8 = 3) and at an inclined angle of towards the south (this means it would not be overhead ever and pass through an inclined path in the sky).

     Whereas Diemos will be seen moving in a clockwise direction (since it has a greater time period) at an inclined angle of southwards. But it will be seen only once in a day and that too in different times of the day with a period of 5 days (LCM of 24 and 30 = 120 hrs = 5 days). This means that on the 5th day, the time when it is observable coincides with that of the 1st day (since both of them reaches, after going through 5 rotations and 4 revolutions respectively, at the respective positions at which they started on the 1st day).