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When I was teaching a class why the earth has seasons today, I mentioned how the poles of the earth experience months of daylight and darkness. Then one of my students asked whether the moon disappears as well.

Using an orrery and a string, we looked at the orbit of the moon around the earth and tried to find a place where the moon was below the horizon for an entire orbit. In our attempts, we could find no such place, though some students speculated that if you were in the right place at the right time, the moon could make a full orbit while partially obscured by the horizon.

Is there a place on the earth where the moon cannot be seen on for long periods of time, like the sun in northern latitudes? Or does the fact that it orbits around the earth make this impossible?

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You can find a moonrise/moonset calendar for the South Pole here: timeanddate.com/moon/antarctica/south-pole. You can see that the moon never stays down for more than a couple of weeks. – David H Jul 15 '14 at 4:29
    
I would say the longer you can avoid it is exactly half the moons sidereal period, and that's about 13.5 days. – harogaston Jul 15 '14 at 8:27
    
In a cave :-) I realize this doesn't answer the "intent" of the question, so I left it as a comment instead. – Jonathan Jul 16 '14 at 15:51

Depends on the interpretation of your question... The best places not to observe the moon are the north and south pole. On the north pole you will only be able to see objects above the celestial equator. As the moon orbits the Earth in one month its orbit is inclined from the celestial equator. This inclination is almost the same as the inclination of the ecliptic (path of the Sun) with the celestial equator. The ecliptic crosses the equator at two opposite points on the celestial sphere. This means that for about half its orbit, the Sun, and as the moon's orbit is near the ecliptic, also the Moon, will be above the ecliptic and therefore visible from the north pole.

That being said, the Moon does not follow the ecliptic precisely as the moon's orbit is inclined from the ecliptic by about 5°. The inclination of the ecliptic is 23°, so during very special circumstances the maximum altitude of the Moon above the horizon on the North pole will be 18° during one month. The duration that the Moon will be above the horizon on the north pole will be about 10 days (a guess) about 13.6 days (edit:see comments below).

So if we interpret your question as: Is there a place where the Moon will be below the horizon for a long period of time (> 1 month), then the answer is NO.

But if this happens near June, then the Sun will also be above the horizon at the north pole (for six months), and as the Moon will be close to the Sun (as it follows more or less the ecliptic), it will be very hard to see the Moon during that time. So if you specifically ask whether the Moon will not be visible for an extended period of time, then the answer is YES.

And there are of course also places with perpetual cloud cover ;-)

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1  
Great answer, but I'd like to add that the guess you made of 10 days is incorrect. The moon's orbit will always intersect the celestial equator at two diametrically opposite points (since both are great circles), and as seen from the earth, the period between those two points will always be around 13-14 days (roughly half of ~27.2 days which is its Draconic period, 'roughly' because of eccentricity of the moon's orbit and its size effects on rising and setting times etc.). – Takku Jul 16 '14 at 7:36
    
@Takku Yes you are right! Didn't think that one through I'm afraid.I've edited the answer accordingly. – Dieudonné Jul 16 '14 at 11:32
    
This assumes the moon is a point (not a disk) and there is no refraction. If you take both of those into account, the answer might, just coincidentally, be closer to 10 days. – barrycarter Jul 3 '15 at 2:51

If you go far enough north or south, you will reach a latitude where the moon can be below the horizon for several days, just like the 'midnight sun'. It can also be above the horizon for several days for the same reason.

At the north or south poles, the moon may be either continuously above or below the horizon for nearly 2 weeks at a time.

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At 87 degrees south latitude on the prime meridian (0 degrees east longitude), the moon set at 0121 UTC on Nov 22 2012, and didn't rise again until 2356 on Dec 6 2012, for a total moonless period of 14 days, 22 hours, and 35 minutes. See caveats below.

You can "verify" this calculation by visiting http://aa.usno.navy.mil/data/docs/RS_OneYear.php and entering these parameters:

enter image description here

to get this result:


Sun or Moon Rise/Set Table for One Year
             o  ,    o  ,                                                                              Astronomical Applications Dept.
Location:  000 00, S87 00                         Rise and Set for the Moon for 2012                   U. S. Naval Observatory        
                                                                                                       Washington, DC  20392-5420     
                                                            Universal Time                                                            


       Jan.       Feb.       Mar.       Apr.       May        June       July       Aug.       Sept.      Oct.       Nov.       Dec.  
Day Rise  Set  Rise  Set  Rise  Set  Rise  Set  Rise  Set  Rise  Set  Rise  Set  Rise  Set  Rise  Set  Rise  Set  Rise  Set  Rise  Set
     h m  h m   h m  h m   h m  h m   h m  h m   h m  h m   h m  h m   h m  h m   h m  h m   h m  h m   h m  h m   h m  h m   h m  h m
01  ---- ----  ---- ----  ---- ----  ---- ----  1821       **** ****  **** ****  **** ****       0649  ---- ----  ---- ----  ---- ----
02  ---- ----  ---- ----  ---- ----  ---- ----  1255 0021  **** ****  **** ****  **** ****  ---- ----  ---- ----  ---- ----  ---- ----
03  ---- ----  ---- ----  ---- ----  ---- ----  **** ****  **** ****  **** ****  **** ****  ---- ----  ---- ----  ---- ----  ---- ----
04  ---- ----  ---- ----  ---- ----  1718       **** ****  **** ****  **** ****  1900 1121  ---- ----  ---- ----  ---- ----  ---- ----
05  ---- ----  ---- ----  ---- ----  1030 0834  **** ****  **** ****  **** ****       0634  ---- ----  ---- ----  ---- ----  ---- ----
06  ---- ----  ---- ----  ---- ----  **** ****  **** ****  **** ****  **** ****  ---- ----  ---- ----  ---- ----  ---- ----  2356     
07  ---- ----  ---- ----  2222       **** ****  **** ****  **** ****  **** ****  ---- ----  ---- ----  ---- ----  ---- ----  **** ****
08  ---- ----  ---- ----  1634 0339  **** ****  **** ****  **** ****       1038  ---- ----  ---- ----  ---- ----  ---- ----  **** ****
09  ---- ----  2057       **** ****  **** ****  **** ****  **** ****  0200 0451  ---- ----  ---- ----  ---- ----  0427 1338  **** ****
09                                                                                                                2341                
10  ---- ----  1425 1149  **** ****  **** ****  **** ****  2154 1518  ---- ----  ---- ----  ---- ----  ---- ----  **** ****  **** ****
11  ---- ----  **** ****  **** ****  **** ****  **** ****       1029  ---- ----  ---- ----  ---- ----  ---- ----  **** ****  **** ****
12  ---- ----  **** ****  **** ****  **** ****  **** ****  ---- ----  ---- ----  ---- ----  ---- ----  ---- ----  **** ****  **** ****
13  2049       **** ****  **** ****  **** ****  **** ****  ---- ----  ---- ----  ---- ----  ---- ----  0357       **** ****  **** ****
14  **** ****  **** ****  **** ****  **** ****       1502  ---- ----  ---- ----  ---- ----  ---- ----  **** ****  **** ****  **** ****
15  **** ****  **** ****  **** ****  **** ****  0304 1024  ---- ----  ---- ----  ---- ----  0824 1654  **** ****  **** ****  **** ****
16  **** ****  **** ****  **** ****  **** ****  ---- ----  ---- ----  ---- ----  ---- ----  0325       **** ****  **** ****  **** ****
17  **** ****  **** ****  **** ****       1533  ---- ----  ---- ----  ---- ----  ---- ----  **** ****  **** ****  **** ****  **** ****
18  **** ****  **** ****  **** ****  ---- ----  ---- ----  ---- ----  ---- ----  ---- ----  **** ****  **** ****  **** ****  **** ****
19  **** ****  **** ****  **** ****  ---- ----  ---- ----  ---- ----  ---- ----  0754       **** ****  **** ****  **** ****  1143 0118
19                                                                                                                                2046
20  **** ****  **** ****       2102  ---- ----  ---- ----  ---- ----  ---- ----  **** ****  **** ****  **** ****  **** ****  ---- ----
21  **** ****  **** ****  0252 1604  ---- ----  ---- ----  ---- ----  ---- ----  **** ****  **** ****  **** ****  **** ****  ---- ----
22  **** ****       2040  ---- ----  ---- ----  ---- ----  ---- ----  1324 1819  **** ****  **** ****  **** ****       0121  ---- ----
23  **** ****  0810 1556  ---- ----  ---- ----  ---- ----  ---- ----  0758       **** ****  **** ****  **** ****  ---- ----  ---- ----
24  **** ****  ---- ----  ---- ----  ---- ----  ---- ----  ---- ----  **** ****  **** ****  **** ****  **** ****  ---- ----  ---- ----
25  **** ****  ---- ----  ---- ----  ---- ----  ---- ----  1253 2338  **** ****  **** ****  **** ****  1214 0649  ---- ----  ---- ----
26       2026  ---- ----  ---- ----  ---- ----  ---- ----  0757       **** ****  **** ****  **** ****       0154  ---- ----  ---- ----
27  ---- ----  ---- ----  ---- ----  ---- ----  ---- ----  **** ****  **** ****  **** ****  **** ****  ---- ----  ---- ----  ---- ----
28  ---- ----  ---- ----  ---- ----  ---- ----  ---- ----  **** ****  **** ****  **** ****  1659 0645  ---- ----  ---- ----  ---- ----
29  ---- ----  ---- ----  ---- ----  ---- ----  1303       **** ****  **** ****  **** ****       0213  ---- ----  ---- ----  ---- ----
30  ---- ----             ---- ----  ---- ----  **** ****  **** ****  **** ****  **** ****  ---- ----  ---- ----  ---- ----  ---- ----
31  ---- ----             ---- ----             **** ****             **** ****  **** ****             ---- ----             ---- ----

(**** object continuously above horizon)                                                      (---- object continuously below horizon)

NOTE: BLANK SPACES IN THE TABLE INDICATE THAT A RISING OR A SETTING DID NOT OCCUR DURING THAT 24 HR INTERVAL.

Notice that from Nov 22 through Dec 06 (non-inclusive) the rise and set are both "----", indicating "object continuously below horizon".

Caveats/notes:

  • Like the table above, I assume 34 arcminutes of refraction at the horizon. That's reasonable for most locations, but may be unreasonable at 87 degrees south latitude. If refraction was higher during the calculated moonless period above, the moon may have risen briefly.

  • This is the longest moonless period I could fine between 2 Jan 2000 and 12 Mar 2016, the time limits of the program I'm using. There might be longer moonless periods outside this interval.

  • The process I used isn't guarenteed to find the longest moonless period even within the interval above. In other words, there might be a longer moonless period that I missed.

  • It's somewhat surprising that the longest moonless period occurs so far from the poles (ie, 3 degrees from the south pole). This is due in part to refraction and the fact that the moon has an angular diameter and isn't just a geometric point. Also, the moon's elevation can be 3 degrees lower at 87 degrees than it is at the pole, allowing the moon to remain below the horizon just a little longer.

  • The longest moonless period at the south pole (with caveats above) was from 1 Jun 2013 at 1104 to 16 Jun 2013 at 0719, about two and a quarter hours less than the shortest overall moonless period I found.

  • The longest moonless period at the north pole was from 18 Dec 2008 at 2311 to 2 Jan 2009 at 1155, about half an hour shorter than the south pole time.

  • The program I wrote to help me find this:

https://github.com/barrycarter/bcapps/blob/master/ASTRO/bc-solve-astro-5894.c

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