# How do you know you have reached North or South Pole without GPS?

Having read about the recent foot traverse of Antarctica by Colin O'Brady I was wondering which means the polar explorers of former, pre-GPS times used to determine that they had reached the North or South Pole. Obviously, you cannot use a compass since it would guide you to magnetic north or south and not to the pole itself.

So what means did they use or (to make it a bit more open) could they have used?

• Same question on Astronomy.SE: How would I measure that I'm at a pole? Jan 14, 2019 at 8:45
• GPS only tells you your location with respect to a reference geoid, which is just an approximation of the shape of the earth. GPS locations can be up to a mile off in very mountainous areas. Jan 14, 2019 at 22:43
• I thought that the only reason for wrong readings is when GPS is not able to get signals from three satellites which it needs to triangulate. @Jasper any reference for this fact? Jan 15, 2019 at 19:19
• @Ashutosh, Jasper's comments make no sense. Multilateration can work in any terrain and the usual errors are due to poor line of sight to satellites, multipath signal reflections, and poor satellite distribution at time of measurement. The problem with GNSS near the poles is that satellite orbits are between 55-65° inclination, which means satellites will always be low on the horizon. No satellite will ever pass directly above a pole. Positions are a bit lower accuracy than at lower latitudes because of this. Jan 24, 2019 at 19:07

## 3 Answers

I'll expand a bit on how one would use a sextant to locate the north or south pole.

The basic arrangement needs a horizontal reflective plane, for which Amundsen used a pool of mercury. A precisely weighted mirror could work also, but a pool of mercury is more robust and doesn't go out of calibration. Sextant measures the angular distance between two visible objects, in this case between the sun and its reflection in the horizontal surface.

This angle is twice the elevation of sun above the horizon. If you are standing at exactly the north (or south) pole, sun will remain at the same elevation all through the day. There will be a small linear change due to earth's orbit around the sun, but no cyclic 24-hour change because you are on the earths rotational axis.

Now, you can take multiple measurements over the day and draw a graph. Even though sun remains at the same elevation, it will still move in a circle around you, so each measurement corresponds to a different direction.

If the elevation graph is flat, you have found the pole. If it however resembles a sine wave, you can use the information to move closer to the pole. The direction where the sun's elevation is lowest is towards the pole, and the distance to the true pole can be calculated from the difference between lowest and highest elevation.

• Unless you're taking the reading at the equinox, the sun will not stay at the same elevation throughout the day because on other than those dates the Earth's axis will not be aligned at right angles to the sun. Amudsen arrived on December 14th, which was a week before the solstice and thus around the time when the sun would show the maximum variation in elevation throughout the 24 hour day. However, knowing what the sun's elevation should be on a given date at a given location is easily given on a table, so they could compare the readings with what they should have been at the pole. Jan 14, 2019 at 18:26
• @KeithMorrison Hmm, I can't really see what would cause the variation, considering you are on the axis of rotation - the tilt of Earth's axis will determine the elevation of the Sun, but it will not vary in 24 hour cycles but only in 1-year cycle at the pole. I tried to check with an online skymap and at least visually, Sun's elevation stays the same throughout the day: in-the-sky.org/…
– jpa
Jan 14, 2019 at 19:15
• @KeithMorrison At the pole the Sun is about (90-23.5)° above the horizon at solstice all "day" long. Before/after solstice the sun is lower, but still (almost) constant during a 24 h period. As the "constant" elevation angle of the preceding and next day is slightly different, there actually is a (small) variation over the 24h interval. However, at (or near) solstice, this variation is in fact lowest. Jan 14, 2019 at 23:20
• @KeithMorrison I was a bit surprised when I read jpa's answer as well. However, I think he's right... Imagine standing on the North Pole in summer. The Earth's Axis goes up between your feet and through your head. As the Earth turns (neglecting orbital motion) you are just turning on the spot so the Sun's elevation doesn't change. Also think about where the terminator is; as Earth turns, you don't change your position relative to the terminator. Contrast this with being at a distance from the pole - you get closer and further from the terminator so the Sun goes up and down. Jan 15, 2019 at 11:49
• @gerrit Not a problem: en.wikipedia.org/wiki/Sunstone_(medieval) Jan 15, 2019 at 21:40

Amundsen's team used a meter on their sledges to get close (dead reckoning) and then sextants to confirm the position.

Using Amundsen's diary, Roland Huntford (in The Amundsen Photographs) describes the photo as "Shooting the sun at the South Geographical Pole. Amundsen (left) is holding a sextant. Helmer Hanssen (right) is bending over the artificial horizon, which is a tray of mercury. Amundsen is lining up the direct image of the sun with its reflection in the surface of the mercury."

Amundsen's original South Pole Station

When their sledge meters indicated they should be at the right place, they stopped at the location marked "Sledge" on the map at right (from The South Pole) to determine their position more accurately from sun shots. Amundsen then sent three men out on sledges at 90° intervals. Each went about 10 statute miles; in this way he assured that his party had encircled the Pole.

...

At Polheim the team took a series of hourly observations for a 24-hour period to confirm their location

Amundsen's original South Pole Station

For the next three days the men worked to fix the exact position of the pole; after the conflicting and disputed claims of Cook and Peary in the north, Amundsen wanted to leave unmistakable markers for Scott.[139] After taking several sextant readings at different times of day, Bjaaland, Wisting and Hassel skied out in different directions to "box" the pole; Amundsen reasoned that between them they would bracket the exact point.[140] Finally the party pitched a tent, which they called Polheim, as near as possible to the actual pole as they could calculate by their observations. In the tent Amundsen left equipment for Scott, and a letter addressed to King Haakon which he requested Scott to deliver

Wikipedia

People still use sextants today, and they are still the best way to find latitude/longitude without GPS so it seems like is what one would use.

• Is it necessary to directly look into the sun using this method? Jan 14, 2019 at 12:41
• @M.Herzkamp If you want to be technical, he is looking directly at the sun's reflection, but yes it is necessary. Jan 14, 2019 at 18:57
• @M.Herzkamp Undoubtedly they used dark filters. Don't panic about ocular damage. Jan 15, 2019 at 15:53

Take a time-lapse photo of the sky directly overhead at night. The moving stars will form circles in your photo, and if the center of the circles is directly overhead, you are there.

• In theory, this would work. In practice, an error of just one second of arc in aiming your camera upwards will result in an error of more than 300 meters in position. Sextants are designed for high-precision aiming; camera tripods aren't.
– Mark
Jan 13, 2019 at 7:14
• A comment on Mark's answer (above). An arcsecond corresponds to about 100 feet at the Earth's surface, not 300 meters. But his point is perfectly valid of course. Jan 13, 2019 at 14:09
• All pre-GPS expeditions tried hard to be outta there before night. Jan 13, 2019 at 16:42
• To clarify kubanczyk's comment: The poles are the lands of the midnight sun. If there are any stars visible, that means it is winter; you really don't want to walk to the South Pole in winter. Jan 14, 2019 at 10:06
• @Bruce: Night is six months long at the pole, the worst time to explore it :) I don't know if either film or digital cameras will work in the super cold at night (i.e. in winter) at a pole Jan 15, 2019 at 11:15