Earth Set...?

Question

Suppose you lived on the moon. Suppose the earth was directly over your head. How long would it be before you would see the earth set?

a) one day (one earth day, 24 hours)
b) one-fourth of a day (6 hours)
c) one month (the time it takes the moon to orbit the earth)
d) one-fourth of a month
e) you would never see the earth set

Everyone has great thoughts on this question! Thank you!!!

The answer is: e. As seen from earth you always see one side of the moon. That's why ancient astronomers thought the moon was something stuck on the dome of the sky, rather than another world. The back of the moon was a subject of mystery until first photographed by a Russian spacecraft.

If you lived on the side of the moon that faced earth you would never see the earth set because that side of the moon continually faces the earth.

Answer 1

E. Never. The moon always presents the same face to the earth. The only visual information we have about the other, "hidden" side is what we've obtained from orbiting spacecraft such as the USSR's Lunik III (which took the first pictures in 1959; see the ref. 1 web page) and the Apollo lunar orbiters.
It's not unusual for moons to behave this way (ref. 2). The phenomenon is called tidal or gravitational locking, and is caused by the removal from (or more rarely, addition to) the moon of rotational energy by tidal friction until its rotation rate equals its orbital rate.
EDIT: About sun's effects compared to earth's, and moon's libration.
The sun/earth mass ratio is about 333,000 and the r^2 ratio is (93,000,000/238,000)^2 ~= 150,000, so you'd think with twice the m/r^2 the sun would exert the largest tidal forces. However, tidal force depends on the difference between g force on the near side and the far side of the moon. (The rate of change of g with distance is called the gravity gradient, and space shuttle people are familiar with earth's low-orbit GG as a source of disturbance torque that can cost serious amounts of propellant over time.) If you call moon's diameter 2160 mi, the ratio of earth vs. sun near-side to far-side difference is about 175. This because 2160 is a much larger proportion of 238,000 than of 93,000,000. So earth rules!
As Remo's movie shows, the moon does librate some, so over time we on earth can see about 59% of moon's area. So it's not exactly the "same face" being presented, but still the earth will never set in a location on the moon where earth is directly overhead at any time, since the libration only amounts to, it looks like, about 10 degrees or less.

Answer 2

Kirchwey is right, but a picture is worth a thousands words, so here is the answer in a movie (and it's great): http://aa.usno.navy.mil/graphics/Moon_movie.gif

And here is a movie of an earthrise and earthset taken by a satellite orbiting the moon (It's even better): http://www.nanowerk.com/news/newsid=3342.php

But Kirchwey's answer doesn't explain why the moon is tidally locked on the earth. The sun's gravitational effect on the moon is twice that of the earth's. Just pull out the old calculator and plug the numbers into F=Gm1m2/r^2. Shouldn't the moon be tidally locked onto the sun not the earth?

It is the one moon in the solar system that can literally be described as rotating around the sun, not the host planet.

If Kirchwey doesn't come back to explain this paradox, I'll do it after a major coffee break ..................................

P.S. If you are lying down on the moon and the earth is directly over your head, you will see the earth set once a month.

........................................ I'm Back

Linlyon's, you will note that my very first sentence, like yours, concedes that Kirchwey is right. But I thought that the problem was too easy for him (and you too), so I threw in something more by making it a "Ménage à trois" (3 body) question instead of a simple two body question and asking "Why?" I was just stirring the pot. But so far it has made both me and you think (which is good). You did a good qualatative analysis.

As for my "lying down" P.S.: Dr. H was very careful to specify that the moon was over head. This is because the moon's orbit is eccentric. Which means that from the moon's perspective, the earth will change position. Those locations which are on the edge of the line of sight, i.e., the what we view as the moon's circumference, will see rise above and fall below the horizon each month. Watch the moon "gif" carefully and you will see that the moon changes orientation. Of course to be lying down with the earth over your head means that you are on the circumference

Back to my coffee break.................................

........................................................... Back once more

Kirchwey got the complete answer on tidal force, including why the Sun cause less tidal force on the moon (hence the earth is going to cause tidal lock not the sun). Simply put because the sun is sooo much farther away, the difference in its gravity field from one side of the moon to the other is small compared with the earth's. And it is this difference in the gravity field which cause the the tidal force, and the tidal force eventually causes tidal locking. The how to math is here: http://en.wikipedia.org/wiki/Tidal_force#Mathematical_treatment .

Linlyons qualitative answer of stating the earth would have 64x more tidal force than the sun lines up pretty close to Kirchwey's rough estimate of 80x (175 divided by the 2.2: the sun's gravitational force on the moon compared with the earth's on the moon). So, all and all, I say vote for Kirchwey.

*I also learned something from Kirchwey's answer about the Space Shuttle and tidal force. Interesting .... :-)


Source(s):

Here we have a fine and elegant argument for quieting the doubts of those who, while accepting with tranquil mind the revolutions of the planets about the Sun in the Copernican system, are mightily disturbed to have the Moon alone revolve about the Earth and accompany it in an annual rotation about the Sun. Some have believed that this structure of the universe should be rejected as impossible. But now we have not just one planet rotating about another while both run through a great orbit around the Sun; our own eyes show us four stars which wander around Jupiter as does the Moon around the Earth, while all together trace out a grand revolution about the Sun in the space of twelve years.
—Galileo Galilei

Answer 3

d) one-fourth of a month
??