I heard in a documentary that, in Svalbard (Spitsberg), Norwegian archipelago in the Arctic Ocean, the Moon never sets. Why? A drawing would certainly help.
You must have misheard it, or the documentary you watched wasn't presenting very precise information. It does set but it also stays on the night sky for several days during the polar winter (polar night) when the Moon if full. This is relatively simple to imagine, so I'll describe it;
So what's happening is that the Earth's axial tilt during the polar winters leans the whole Northern hemisphere towards the night side, away from the Sun. This tilt is big enough (~ 23.4°) that the night sky objects aligned with the Earth's equatorial plane stay visible relatively low on the horizon. With those regions being either relatively flat and/or with a view towards the sea, there's not many obstructions limiting the viewing angle, so the Moon (and analogous also the Sun during polar summers) stays "locked" low above the horizon. To help a bit with imagining this, here's an animation of the Earth's axial tilt, courtesy of Wikipedia:
If we imagine this animation of the Earth with the Sun in the distant left of the image, so during Northern hemisphere's winter (winter solstice to be precise), and the Moon to the distant right of the image (roughly 25 widths of the image away), so when it's either full or close to this lunar phase, it's not too difficult to appreciate that the northernmost polar regions have a direct line of sight of the Moon during Earth's full rotation on its axis, or a day. If you keep in mind that other celestials, including the Moon, are oblivious to the Earth's axial tilt (well, not exactly, but let's not nitpick about tidal effects that might take millions of years to make a difference), as the Moon moves farther in its orbit, in our case towards the viewer, this observation angle decreases further still and those northernmost latitudes hide to us for some part of the day. At lunar last quarter, it would be directly towards us relative to the image, so this direct line of sight relationship between the Earth and the Moon becomes reciprocal to how we're seeing places on the Earth on the animation.
Why when the Moon is full? Simply because that's when the Moon is also behind the Earth (but not in its shadow), so the relative angle between the observation point and the Moon would stay high enough to observe it. As it moves in lunar phase and in orbit around the Earth farther, this angle becomes lower and the Moon indeed does set also in the arctic region. For what is worth, this goes exactly the same for South pole, only with a half a year difference.
One other effect that plays a role here is the Earth's atmospheric refraction which also adds to the duration during which the Moon appears not to set. Meaning, that even when the Moon wouldn't be in direct line of sight, but only marginally so, it would still appear low on the skies due to optical effect (displacement) of the atmosphere. This effect would somewhat offset observing the Moon from lowlands with possibly shallower observation angle when compared to higher altitude observation points with less direct line of sight obstructions, due to denser atmosphere and thus higher refraction index.
For the practical side of TidalWave's excellent answer, here's a moon almanac for the place: http://www.timeanddate.com/moon/norway/longyearbyen
In 2014 the moon is above the horizon for a maximum of about 9 days at a time.
Why does the Moon never set in Svalbard, Norway?
As can be deduced from the diagram or knowing that the Moon's orbit is inclined by only 5 degrees with respect to the ecliptic while the Earth's axis is inclined by more than 23 degrees, the moon can not always be above the horizon, nor always be below it. Over the course of about 20 years all combinations are possible, and so whatever is possible at Svalbard must also be possible at the antipodal point Adelaide Antartica, and the Moon can't "never set" at both places unless it's always visible from one and simultaneously never visible from the other, and that's some kind of symmetry breaking.
For more on this see answers to:
Here's a calculation for the year 2020 and for August 2020 only, adapted from this answer. The Moon oscillates between periods of being up for days, being down for days, and rising/setting daily, depending on it's position along its orbit. It cycles through these states a little more than 13 times a year. You can take your pick from the long list of types of lunar months in this answer. For something simple like the sidereal month of 27.3 days there are about 13.4 of those in a year.
from skyfield.api import Loader, Topos import numpy as np import matplotlib.pyplot as plt from skyfield.api import load halfpi, pi, twopi = [f*np.pi for f in (0.5, 1, 2)] to_degs, to_rads = 180/pi, pi/180 load = Loader('~/Documents/fishing/SkyData') # avoids multiple copies of large files ts = load.timescale() # include builtin=True if you want to use older files (you may miss some leap-seconds) eph = load('de421.bsp') earth, sun, moon = [eph[x] for x in ('earth', 'sun', 'moon')] AS = earth + Topos('90.0 S', '0.0 E', elevation_m = 2835) Svalbard = earth + Topos('79.0 N', '18.4 E', elevation_m = 1000.) # elevation is variable days = np.arange(0, 366, 0.1) times = ts.utc(2020, 1, days) malt, maz = [thing.radians for thing in Svalbard.at(times).observe(moon).apparent().altaz()[:2]] salt, saz = [thing.radians for thing in Svalbard.at(times).observe(sun).apparent().altaz()[:2]] days31 = np.arange(0, 31, 0.02) times31 = ts.utc(2020, 8, days31) malt31, maz31 = [thing.radians for thing in Svalbard.at(times31).observe(moon).apparent().altaz()[:2]] salt31, saz31 = [thing.radians for thing in Svalbard.at(times31).observe(sun).apparent().altaz()[:2]] plt.figure() plt.subplot(2, 1, 1) plt.plot(days, to_degs * malt, '-', linewidth=0.5) plt.xlim(0, 366) plt.xlabel('days in 2020') plt.ylabel('Moon evel (deg)') plt.suptitle('from Svalbard') plt.subplot(2, 1, 2) plt.plot(days31, to_degs * malt31, '-') plt.plot(days31, np.zeros_like(days31), '-k') plt.xlim(0, 30) plt.xlabel('days since Aug. 1, 2020') plt.ylabel('Moon evel (deg)') plt.show()