Tangents to a sphere

Commercial Internet signals are relayed by satellites that are over the equator. Because they are in low-earth orbits, they are only 2° above the horizon at 79° North latitude. Any farther north of that & they disappear from view. Since most of our voyage was above 79°, the ship had no Internet connection most of the time. Fortunately, the iPhone stores draft messages until the next connection.
The most well-known tangent is, of course, that of the sun's rays. The Arctic Circle, at 66.5° North Latitude, is that point on the sphere of the Earth where the sun is visible for 24 hours on June 21. At 79 to 81°, the sun never sleeps in July so we had 24 hours of bright sunlight. By convention the pace of the day was kept on Norway time but it was necessary to force sleep at 10 or 11 in order to get some rest every day before breakfast wake up at 7. Some days there was an even earlier wake up because of a bear sighting so I found myself tired or at least sleepy most of the time. The frequent shore excursions were good because 3 to 4 hours of hiking in the 40° cold was enough to make me sleep very well. This was particularly true when the footing was loose gravel or ankle-deep water or mud. In addition, every shore trip was a "wet landing" from the zodiac & this added to the exposure to the elements.