Here I am claiming to be at The South Pole of the World. I take it on faith, because someone put a bunch of markers out there claiming to be at The South Pole of the World. I’m good at faith. How could I prove to myself I was really on that spot?
Well first, there’s the high-tech way. My phone talks to GPS satellites, and if I meander around, I can get it to say I’m at 90-degrees South, and it claims 10-meter accuracy. And I happen to be standing near one of those markers.
Set the Wayback Machine to 1912. How did Amundsen and Scott and those folks take a stab at knowing they were at 90-degrees South? They used strong Surveyor-fu is what they did. Hey as long as you’re over by the Wayback Machine, hit the “Simplified Earth” button, please.
Okay, that’s better. We’re now on the fictional Earth that’s a perfect sphere, has a perfectly circular orbit, and has an axis of rotation that’s straight up and down from the plane of the orbit. This will save us a lot of pencils. On this planet, it’s easy to tell when you’re at the South Pole: the sun stays exactly on the horizon at all times. If you’re standing some place and want to get to the South Pole, just walk in the direction where the sun dips under the horizon. Since a Nautical Mile is about one minute of arc [That’s 1/60th of a degree. Heck, here on Simplified Earth let’s make it exactly so.] just walk in the direction away from where the sun is highest in the sky, and walk 60 Nautical Miles for each degree the sun is above the horizon. If you find yourself at the North Pole instead of the South Pole, either rename them, since it’s arbitrary, or turn around and walk back across the equator and try again, or just dig straight down until you strike sky.
There’s a large degree of assumed precision here. You can be a mile away from a pole, and the sun is only 1/60th of a degree out of true. The sun itself is about a half of a degree across, so you have to measure that whole “stays exactly the same level” thing to within 1/30th of the sun’s diameter to be within a mile or so. That implies that you do need some seriously precise instruments. Amundsen established his Polheim camp around 89 57 30, about two and a half miles from the pole.
A few other pesky details will get into the way when we leave Simplified Earth. That whole “perfect sphere” thing isn’t working for us. If we are measuring the distance between the sun and the horizon but the horizon isn’t level all the way around our field of view, we won’t get the right place. A slope of one minute would put us off a mile. If I’ve done the math right, for a person standing on the ground, the horizon is about three miles away, and that’s a slope of about four and a half feet over a mile distance. In fact, the local geography around the real South Pole is flatter than that, so let’s ignore the slope. We also have to actually see the horizon. When the horizon is obscured or not flat, there are interesting work-arounds but none of those are available.
Unlike Simplified Earth, our axis of rotation isn’t perpendicular to the orbit; that’s why we have seasons. So while we are taking the measurements throughout the day to try to see if the sun is staying the same distance above the horizon, the earth is moving in its orbit around the sun, and the sun is getting higher in the sky if we’re moving towards the summer solstice, like now. Tomorrow the sun will be about 0.2 degrees higher in the sky than it was today. since the sun is about half a degree across, that means that the sun will be half a sun higher, and we should take that into account. We could try to arrange to do our measurement on the day of the Summer solstice, and then we could ignore this issue; on the solstices, the sun’s apparent altitude changes the least, and on the Winter solstice we can’t see the sun from the South Pole.
We are assuming that the optical effects of looking through the atmosphere at the sun are the same in every direction. I don’t know if there are lensing effects from different temperatures that could bend the apparent position of the sun differently through the day. I don’t think that the irregularity of Earth’s orbit around the sun will be an issue, considering what issues we already have.
The last perturbation of our measurements I’m going to mention is that Amundsen-Scott Station is not on solid ground; it is on an ice sheet moving roughly East, at the rate of about an inch a day. On New Years Day, the so-called Geographical South Pole will be marked with a new ornamental marker, and on January 2nd it will be an inch off.
At my going-away party Pablo said, “You should take a sextant with you and prove you’re at the pole.” And Chris said, “You can have mine.” I have wacky friends. I told that story here, and one of my new friends here at the Pole said, “oh, I know how to use a sextant; I’m an Ensign in the NOAA Corps.” [.. he said violating all the rules of use of quotation marks in journalism.] I hope a future post will feature Ensign Bliss and the Sextant at the Pole.