GPS accuracy at the South Pole, circa 1911-1912

[DPRK]

I do not think the issue was with sextant accuracy. Here is the report from the book:

Captain Roald Amundsen,

At your request I shall here give briefly the result of my examination of the observations from your South Pole Expedition. My calculations are based on the longitude for Framheim given to me by Lieutenant Prestrud, 163° 37’ W. of Greenwich. He describes this longitude as provisional, but only to such an extent that the final result cannot differ appreciably from it. My own results may also be somewhat modified on a final treatment of the material. But these modifications, again, will only be immaterial, and, in any case, will not affect the result of the investigations given below as to the position of the two Polar stations.

At the first Polar station, on December 15, 1911, eighteen altitudes of the sun were taken in all with each of the expedition’s sextants. The latitude calculated from these altitudes is, on an average of both sextants, very near 89° 54’, with a mean error of ±2’. The longitude calculated from the altitudes is about 7t (105°) E.; but, as might be expected in this high latitude, the aberrations are very considerable. We may, however, assume with great certainty that this station lies between lat. 89° 52’ and 89° 56’ S., and between long. 90° and 120° E.

The variation of the compass at the first Polar station was determined by a series of bearings of the sun. This gives us the absolute direction of the last day’s line of route. The length of this line was measured as five and a half geographical miles. With the help of this we are able to construct for Polheim a field of the same form and extent as that within which the first Polar station must lie.

At Polheim, during a period of twenty-four hours (December 16 — 17), observations were taken every hour with one of the sextants. The observations show an upper culmination altitude of 28° 19.2’, and a resulting lower culmination altitude of 23° 174’. These combining the above two altitudes, an equal error on the same side in each will have no influence on the result. The combination gives a latitude of 89° 58.6’. That this result must be nearly correct is confirmed by the considerable displacement of the periods of culmination which is indicated by the series of observations, and which in the immediate neighbourhood of the Pole is caused by the change in the sun’s declination. On the day of the observations this displacement amounted to thirty minutes in 89° 57’, forty-six minutes in 89° 58’, and over an hour and a half in 89° 59’. The upper culmination occurred so much too late, and the lower culmination so much too early. The interval between these two periods was thus diminished by double the amount of the displacements given. Now the series of observations shows that the interval between the upper and the lower culmination amounted at the most to eleven hours; the displacement of the periods of culmination was thus at least half an hour. It results that Polheim must lie south of 89° 57’, while at the same time we may assume that it cannot lie south of 89° 59’. The moments of culmination could, of course, only be determined very approximately, and in the same way the observations as a whole are unserviceable for the determination of longitude. It may, however, be stated with some certainty that the longitude must be between 30° and 75° E. The latitude, as already mentioned, is between 89° 57’ and 89° 59’, and the probable position of Polheim may be given roughly as lat. 89° 58.5’ S., and long. 60° E.

On the accompanying sketch-chart the letters abcd indicate the field within which the first Polar station must lie; ABCD is the field which is thereby assigned to Polheim; EFGH the field within which Polheim must lie according to the observations taken on the spot itself; P the probable position of Polheim, and L the resulting position of the first Polar station. The position thus assigned to the latter agrees as well as could be expected with the average result of the observations of December 15. According to this, Polheim would be assumed to lie one and a half geographical miles, or barely three kilometres, from the South Pole, and certainly not so much as six kilometres from it.

From your verbal statement I learn that Helmer Hanssen and Bjaaland walked four geographical miles from Polheim in the direction taken to be south on the basis of the observations. On the chart the letters efgh give the field within which the termination of their line of route must lie. It will be seen from this that they passed the South Pole at a distance which, on the one hand, can hardly have been so great as two and a half kilometres, and on the other, hardly so great as two kilometres; that, if the assumed position of Polheim be correct, they passed the actual Pole at a distance of between 400 and 600 metres; and that it is very probable that they passed the actual Pole at a distance of a few hundred metres, perhaps even less.

I am, etc.,

(Signed) Anton Alexander.

Christiania,

September 22, 1912.

Here is Amundsen’s account:

The first thing we did — Hanssen and I — was to set about arranging a lot of trifling matters; there was something to be done here, something there, and above all we had to be ready for the series of observations we were to carry out together, so as to get as accurate a determination of our position as possible. The first observation told us at once how necessary this was. For it turned out that this, instead of giving us a greater altitude than the midnight observation, gave us a smaller one, and it was then clear that we had gone out of the meridian we thought we were following. Now the first thing to be done was to get our north and south line and latitude determined, so that we could find our position once more. Luckily for us, the weather looked as if it would hold. We measured the sun’s altitude at every hour from 6 a.m. to 7 p.m., and from these observations found, with some degree of certainty, our latitude and the direction of the meridian.

By nine in the morning we began to expect the return of our comrades; according to our calculation they should then have covered the distance — twenty-five miles. It was not till ten o’clock that Hanssen made out the first black dot on the horizon, and not long after the second and third appeared. We both gave a sigh of relief as they came on; almost simultaneously the three arrived at the tent. We told them the result of our observations up to that time; it looked as if our camp was in about 89° 54’ 30’’ S., and that with our encircling we had therefore included the actual Pole. With this result we might very well have been content, but as the weather was so good and gave the impression that it would continue so, and our store of provisions proved on examination to be very ample, we decided to go on for the remaining ten kilometres (five and a half geographical miles), and get our position determined as near to the Pole as possible. Meanwhile the three wanderers turned in — not so much because they were tired, as because it was the right thing to do — and Hanssen and I continued the series of observations.

In the afternoon we again went very carefully through our provision supply before discussing the future. The result was that we had food enough for ourselves and the dogs for eighteen days. The surviving sixteen dogs were divided into two teams of eight each, and the contents of Bjaaland’s sledge were shared between Hanssen’s and Wisting’s. The abandoned sledge was set upright in the snow, and proved to be a splendid mark. The sledge-meter was screwed to the sledge, and we left it there; our other two were quite sufficient for the return journey; they had all shown themselves very accurate. A couple of empty provision cases were also left behind. I wrote in pencil on a piece of case the information that our tent — “Polheim” — would be found five and a half geographical miles north-west quarter west by compass from the sledge. Having put all these things in order the same day, we turned in, very well satisfied.

Early next morning, December 16, we were on our feet again. Bjaaland, who had now left the company of the drivers and been received with jubilation into that of the forerunners, was immediately entrusted with the honourable task of leading the expedition forward to the Pole itself. I assigned this duty, which we all regarded as a distinction, to him as a mark of gratitude to the gallant Telemarkers for their pre-eminent work in the advancement of ski spot. The leader that day had to keep as straight as a line, and if possible to follow the direction of our meridian. A little way after Bjaaland came Hassel, then Hanssen, then Wisting, and I followed a good way behind. I could thus check the direction of the march very accurately, and see that no great deviation was made. Bjaaland on this occasion showed himself a matchless forerunner; he went perfectly straight the whole time. Not once did he incline to one side or the other, and when we arrived at the end of the distance, we could still clearly see the sledge we had set up and take its bearing. This showed it to be absolutely in the right direction.

It was 11 a.m. when we reached our destination. While some of us were putting up the tent, others began to get everything ready for the coming observations. A solid snow pedestal was put up, on which the artificial horizon was to be placed, and a smaller one to rest the sextant on when it was not in use. At 11.30 a.m. the first observation was taken. We divided ourselves into two parties — Hanssen and I in one, Hassel and Wisting in the other. While one party slept, the other took the observations, and the watches were of six hours each. The weather was altogether grand, though the sky was not perfectly bright the whole time. A very light, fine, vaporous curtain would spread across the sky from time to time, and then quickly disappear again. This film of cloud was not thick enough to hide the sun, which we could see the whole time, but the atmosphere seemed to be disturbed. The effect of this was that the sun appeared not to change its altitude for several hours, until it suddenly made a jump.

Observations were now taken every hour through the whole twenty-four. It was very strange to turn in at 6 p.m., and then on turning out again at midnight to find the sun apparently still at the same altitude, and then once more at 6 a.m. to see it still no higher. The altitude had changed, of course, but so slightly that it was imperceptible with the naked eye. To us it appeared as though the sun made the circuit of the heavens at exactly the same altitude. The times of day that I have given here are calculated according to the meridian of Framheim; we continued to reckon our time from this. The observations soon told us that we were not on the absolute Pole, but as close to it as we could hope to get with our instruments. The observations, which have been submitted to Mr. Anton Alexander, will be published, and the result given later in this book.

On December 17 at noon we had completed our observations, and it is certain that we had done all that could be done. In order if possible to come a few inches nearer to the actual Pole, Hanssen and Bjaaland went out four geographical miles (seven kilometres) in the direction of the newly found meridian.

[DPRK]

So, near the pole the altitude of the sun changes pretty slowly, and they took 24 hours to make a set of observations. Also, the mist in the air caused the image of the sun to jump around, which has to be averaged out. Note that they knew they were a couple of miles north; they theoretically could have repeated the process. The declination of the sun was changing by a couple of minutes per day; on the other hand they had all the noise to contend with, and who knows how much mathematical sophistication they were willing to put into it. Note that they were already getting a mean error of 2’ at 89° 54’; maybe they figured they could not do any better.

@Dr.Strangelove

A shadow at noon always points south

…which is super useful if you can figure out the moment of noon

[Chronos]

@Dr.Strangelove

Walking west or any other direction is easy. A shadow at noon always points south.

OK, but determining noon requires knowing your latitude, and knowing your latitude requires knowing your position relative to the pole.

[Dr.Strangelove]

@DPRK

which is super useful if you can figure out the moment of noon

Sure. But the closer you get to the pole, the less accurate the heading needs to be.

I don’t see how the altitude changing slowly really changes things. There will be a high and a low point, and your latitude relative to the pole will be half the difference. Repeat as many times as needed.

The aberrations sound like a bigger deal, if they were causing an error of 2’. I suppose that gets worse when all readings are only ~23° from the horizon. It’s going through a lot of atmosphere at that point.

Bringing a clock along would have made some things easier, but I suppose that wasn’t in the cards given the environmental conditions.

@Chronos

OK, but determining noon requires knowing your latitude

Noon is just the point when the sun is highest in the sky. Of course, that breaks down at the pole, and gets less accurate as you get closer. But you could perform readings farther away and determine a heading based on distant landmarks.

[Hari_Seldon]

@Dr.Strangelove

Walking west or any other direction is easy. A shadow at noon always points south.

And how do you know it’s noon? The sun just goes around in a circle, height changing only with the season. How do you know what time zone you are in (assuming they had time zones then). In fact, noon would be defined by the time your shadow points due south.

[Dr.Strangelove]

The time zone matters if you want to know when it’s 12:00. But noon (and in case it’s not clear, I’m talking solar noon) is just when the sun is at its highest point.

As I mentioned, that breaks down when you’re exactly at the pole, and your ability to discern the time of the highest point gets worse as you get closer, but there is nevertheless still a highest point if you’re any finite distance from the pole.

[DPRK]

They did stay in one spot for 24 hours and observe the (very slowly changing) altitude of the sun; I understood from the quoted paragraphs that the data was noisy enough that they determined they were at the limit of their precision, at the same time there was no doubt they were not exactly at the pole. They decided just to walk in a circle around where the pole was sure to be.

[Slithy_Tove]

Putting up a tent and a foucault pendulum wouldn’t have worked. The staff down there did that in 2001 and they had to keep tweaking it over and over.

[Dr.Strangelove]

If they had a clock of modest accuracy (could keep decent time over a 1-day period), using the phase of the sun might have better results. That is, determine the high and low points, then determine the time that the sun passes through the halfway mark (both rising and falling). Noon (or midnight) is halfway between those points.

[DPRK]

But greatest altitude will not coincide with the moment of transit, even pretty close but not exactly on the pole. Of course, they had enough observations to work everything out, which is exactly what Anton Alexander did if you read what he wrote, but he says that “The moments of culmination could, of course, only be determined very approximately” and does not presume any more precision than that the tent was “between 89° 57’ and 89° 59’”. On or very near the pole itself, of course the altitude would just gradually keep increasing so you would not try to observe any up and down oscillations.

Perhaps that is one reason why they did not try to repeat 24 hours of observation nearer the pole; they just walked south (as best they could determine it) from the tent and called it good enough.

[Dr.Strangelove]

Sorry, haven’t had a chance to more than skim the passages yet. I agree that there are some other factors they’d have to correct for, though I’m not sure why you’d stop observing oscillations except when right at the pole. Even tiny deviations should be easily measurable; in fact they’d get more accurate as they got closer since the amount of atmosphere being passed through would vary less.

Since they arrived at the pole on Dec 11, the sun wouldn’t be quite at 23.5°, though I don’t have a table handy to tell me what it would have been. Wouldn’t be much different, though that close to the pole it might have been significant. At any rate, all easily determined via table.

Regardless, if their mean error was 2’, then they aren’t going to get too much closer than that unless they average over a very long period. Too bad they didn’t have the (not Sun) stars available, but I guess it gets pretty chilly down there in June…

[Napier]

At the south pole, shadows all point north all the time, don’t they?

[Richard_Pearse]

Yep so you could wait for your shadow to point north then you’d know you were at the pole.

[DPRK]

@Dr.Strangelove

Sorry, haven’t had a chance to more than skim the passages yet. I agree that there are some other factors they’d have to correct for, though I’m not sure why you’d stop observing oscillations except when right at the pole. Even tiny deviations should be easily measurable; in fact they’d get more accurate as they got closer since the amount of atmosphere being passed through would vary less.

The trigonometry to figure out exactly how close you can get to the pole is not too bad, but let’s run some numbers through the computer first. Ignoring refraction and other issues, let’s print out the apparent altitude of the Sun every hour at the pole:

Summary

Target body name: Sun (10)                        {source: DE441}
Center body name: Earth (399)                     {source: DE441}
Center-site name: (user defined site below)
*******************************************************************************
Start time      : A.D. 1911-Dec-15 00:00:00.0000 UT      
Stop  time      : A.D. 1911-Dec-16 00:00:00.0000 UT      
Step-size       : 60 minutes
*******************************************************************************
Target pole/equ : IAU_SUN                         {East-longitude positive}
Target radii    : 696000.0 x 696000.0 x 696000.0 k{Equator, meridian, pole}    
Center geodetic : 60.0000000,-90.000000,3.919E-13 {E-lon(deg),Lat(deg),Alt(km)}
Center cylindric: 60.0000000,3.9186E-13,-6356.752 {E-lon(deg),Dxy(km),Dz(km)}
Center pole/equ : ITRF93                          {East-longitude positive}
Center radii    : 6378.1 x 6378.1 x 6356.8 km     {Equator, meridian, pole}    
Target primary  : Sun
Vis. interferer : MOON (R_eq= 1737.400) km        {source: DE441}
Rel. light bend : Sun, EARTH                      {source: DE441}
Rel. lght bnd GM: 1.3271E+11, 3.9860E+05 km^3/s^2                              
Atmos refraction: NO (AIRLESS)
RA format       : HMS
Time format     : CAL 
EOP file        : eop.220728.p221021                                           
EOP coverage    : DATA-BASED 1962-JAN-20 TO 2022-JUL-28. PREDICTS-> 2022-OCT-20
Units conversion: 1 au= 149597870.700 km, c= 299792.458 km/s, 1 day= 86400.0 s 
Table cut-offs 1: Elevation (-90.0deg=NO ),Airmass (>38.000=NO), Daylight (NO )
Table cut-offs 2: Solar elongation (  0.0,180.0=NO ),Local Hour Angle( 0.0=NO )
Table cut-offs 3: RA/DEC angular rate (     0.0=NO )                           
*********************************************************************************************************
 Date__(UT)__HR:MN     R.A.__(a-apparent)__DEC  Azi____(a-app)___Elev  Sky_motion  Sky_mot_PA  RelVel-ANG
*********************************************************************************************************
$$SOE
 1911-Dec-15 00:00 *m  17 24 43.37 -23 12 09.4  273.384665  23.202617   2.5440417   93.500378   -0.301779
 1911-Dec-15 01:00 *m  17 24 54.43 -23 12 18.7  258.389645  23.205199   2.5440698   93.482237   -0.301202
 1911-Dec-15 02:00 *m  17 25 05.48 -23 12 28.0  243.394627  23.207767   2.5440978   93.464092   -0.300625
 1911-Dec-15 03:00 *m  17 25 16.53 -23 12 37.2  228.399612  23.210322   2.5441256   93.445945   -0.300050
 1911-Dec-15 04:00 *m  17 25 27.58 -23 12 46.3  213.404599  23.212864   2.5441534   93.427795   -0.299476
 1911-Dec-15 05:00 *m  17 25 38.64 -23 12 55.4  198.409588  23.215392   2.5441811   93.409642   -0.298903
 1911-Dec-15 06:00 *m  17 25 49.69 -23 13 04.5  183.414579  23.217907   2.5442088   93.391485   -0.298331
 1911-Dec-15 07:00 *m  17 26 00.75 -23 13 13.5  168.419573  23.220409   2.5442363   93.373326   -0.297760
 1911-Dec-15 08:00 *m  17 26 11.80 -23 13 22.4  153.424569  23.222897   2.5442637   93.355165   -0.297190
 1911-Dec-15 09:00 *m  17 26 22.86 -23 13 31.3  138.429567  23.225372   2.5442911   93.337000   -0.296622
 1911-Dec-15 10:00 *m  17 26 33.91 -23 13 40.2  123.434567  23.227833   2.5443184   93.318832   -0.296054
 1911-Dec-15 11:00 *m  17 26 44.97 -23 13 49.0  108.439569  23.230281   2.5443455   93.300661   -0.295487
 1911-Dec-15 12:00 *m  17 26 56.03 -23 13 57.8   93.444574  23.232715   2.5443726   93.282488   -0.294921
 1911-Dec-15 13:00 *m  17 27 07.09 -23 14 06.5   78.449581  23.235136   2.5443996   93.264312   -0.294356
 1911-Dec-15 14:00 *m  17 27 18.15 -23 14 15.2   63.454590  23.237544   2.5444266   93.246132   -0.293792
 1911-Dec-15 15:00 *m  17 27 29.21 -23 14 23.8   48.459601  23.239938   2.5444534   93.227950   -0.293229
 1911-Dec-15 16:00 *m  17 27 40.26 -23 14 32.3   33.464614  23.242319   2.5444801   93.209766   -0.292667
 1911-Dec-15 17:00 *m  17 27 51.32 -23 14 40.9   18.469629  23.244686   2.5445068   93.191578   -0.292105
 1911-Dec-15 18:00 *m  17 28 02.39 -23 14 49.3    3.474647  23.247040   2.5445334   93.173388   -0.291545
 1911-Dec-15 19:00 *m  17 28 13.45 -23 14 57.8  348.479666  23.249381   2.5445598   93.155194   -0.290986
 1911-Dec-15 20:00 *m  17 28 24.51 -23 15 06.1  333.484688  23.251708   2.5445862   93.136999   -0.290427
 1911-Dec-15 21:00 *m  17 28 35.57 -23 15 14.5  318.489712  23.254022   2.5446126   93.118800   -0.289870
 1911-Dec-15 22:00 *m  17 28 46.63 -23 15 22.8  303.494738  23.256322   2.5446388   93.100599   -0.289313
 1911-Dec-15 23:00 *m  17 28 57.70 -23 15 31.0  288.499766  23.258609   2.5446649   93.082395   -0.288758
 1911-Dec-16 00:00 *m  17 29 08.76 -23 15 39.2  273.504796  23.260882   2.5446910   93.064188   -0.288203
$$EOE
*********************************************************************************************************

As expected, it slowly increases.

Now at 89° 59’:

Summary

 1911-Dec-15 00:00 *m  17 24 43.37 -23 12 09.4  118.757074  23.194599   2.5440474   93.500459   -0.301985
 1911-Dec-15 01:00 *m  17 24 54.43 -23 12 18.7  103.762732  23.201235   2.5440727   93.482331   -0.301430
 1911-Dec-15 02:00 *m  17 25 05.48 -23 12 28.0   88.767919  23.208127   2.5440978   93.464193   -0.300861
 1911-Dec-15 03:00 *m  17 25 16.53 -23 12 37.2   73.772622  23.214981   2.5441227   93.446046   -0.300276
 1911-Dec-15 04:00 *m  17 25 27.58 -23 12 46.3   58.776860  23.221504   2.5441478   93.427889   -0.299678
 1911-Dec-15 05:00 *m  17 25 38.64 -23 12 55.4   43.780683  23.227426   2.5441731   93.409722   -0.299066
 1911-Dec-15 06:00 *m  17 25 49.69 -23 13 04.5   28.784170  23.232515   2.5441989   93.391547   -0.298445
 1911-Dec-15 07:00 *m  17 26 00.75 -23 13 13.5   13.787425  23.236595   2.5442253   93.373365   -0.297817
 1911-Dec-15 08:00 *m  17 26 11.80 -23 13 22.4  358.790565  23.239560   2.5442524   93.355177   -0.297186
 1911-Dec-15 09:00 *m  17 26 22.86 -23 13 31.3  343.793717  23.241376   2.5442801   93.336986   -0.296557
 1911-Dec-15 10:00 *m  17 26 33.91 -23 13 40.2  328.797007  23.242089   2.5443085   93.318792   -0.295933
 1911-Dec-15 11:00 *m  17 26 44.97 -23 13 49.0  313.800551  23.241817   2.5443375   93.300599   -0.295318
 1911-Dec-15 12:00 *m  17 26 56.03 -23 13 57.8  298.804450  23.240746   2.5443670   93.282407   -0.294715
 1911-Dec-15 13:00 *m  17 27 07.09 -23 14 06.5  283.808778  23.239115   2.5443967   93.264217   -0.294128
 1911-Dec-15 14:00 *m  17 27 18.15 -23 14 15.2  268.813581  23.237200   2.5444266   93.246031   -0.293557
 1911-Dec-15 15:00 *m  17 27 29.20 -23 14 23.8  253.818874  23.235294   2.5444563   93.227850   -0.293003
 1911-Dec-15 16:00 *m  17 27 40.26 -23 14 32.3  238.824637  23.233692   2.5444858   93.209672   -0.292465
 1911-Dec-15 17:00 *m  17 27 51.32 -23 14 40.9  223.830819  23.232664   2.5445148   93.191498   -0.291942
 1911-Dec-15 18:00 *m  17 28 02.39 -23 14 49.3  208.837341  23.232441   2.5445432   93.173327   -0.291431
 1911-Dec-15 19:00 *m  17 28 13.45 -23 14 57.8  193.844101  23.233198   2.5445708   93.155157   -0.290928
 1911-Dec-15 20:00 *m  17 28 24.51 -23 15 06.1  178.850979  23.235044   2.5445976   93.136987   -0.290431
 1911-Dec-15 21:00 *m  17 28 35.57 -23 15 14.5  163.857850  23.238012   2.5446235   93.118815   -0.289934
 1911-Dec-15 22:00 *m  17 28 46.63 -23 15 22.8  148.864588  23.242056   2.5446486   93.100639   -0.289434
 1911-Dec-15 23:00 *m  17 28 57.70 -23 15 31.0  133.871076  23.247059   2.5446730   93.082458   -0.288927
 1911-Dec-16 00:00 *m  17 29 08.76 -23 15 39.2  118.877216  23.252834   2.5446966   93.064270   -0.288409

It goes up and down, all right. But let’s be at 89° 59’.5 :

Summary

1911-Dec-15 00:00 *m  17 24 43.37 -23 12 09.4  118.857132  23.198595   2.5440446   93.500418   -0.301882
 1911-Dec-15 01:00 *m  17 24 54.43 -23 12 18.7  103.862452  23.203202   2.5440713   93.482284   -0.301316
 1911-Dec-15 02:00 *m  17 25 05.48 -23 12 28.0   88.867539  23.207932   2.5440978   93.464143   -0.300743
 1911-Dec-15 03:00 *m  17 25 16.53 -23 12 37.2   73.872384  23.212637   2.5441242   93.445995   -0.300163
 1911-Dec-15 04:00 *m  17 25 27.58 -23 12 46.3   58.876998  23.217172   2.5441506   93.427842   -0.299577
 1911-Dec-15 05:00 *m  17 25 38.64 -23 12 55.4   43.881405  23.221399   2.5441771   93.409682   -0.298985
 1911-Dec-15 06:00 *m  17 25 49.69 -23 13 04.5   28.885645  23.225204   2.5442038   93.391516   -0.298388
 1911-Dec-15 07:00 *m  17 26 00.75 -23 13 13.5   13.889770  23.228499   2.5442308   93.373346   -0.297789
 1911-Dec-15 08:00 *m  17 26 11.80 -23 13 22.4  358.893839  23.231229   2.5442581   93.355171   -0.297188
 1911-Dec-15 09:00 *m  17 26 22.86 -23 13 31.3  343.897914  23.233378   2.5442856   93.336993   -0.296589
 1911-Dec-15 10:00 *m  17 26 33.91 -23 13 40.2  328.902058  23.234969   2.5443134   93.318812   -0.295993
 1911-Dec-15 11:00 *m  17 26 44.97 -23 13 49.0  313.906331  23.236060   2.5443415   93.300630   -0.295402
 1911-Dec-15 12:00 *m  17 26 56.03 -23 13 57.8  298.910781  23.236744   2.5443698   93.282447   -0.294818
 1911-Dec-15 13:00 *m  17 27 07.09 -23 14 06.5  283.915446  23.237141   2.5443982   93.264264   -0.294242
 1911-Dec-15 14:00 *m  17 27 18.15 -23 14 15.2  268.920351  23.237387   2.5444266   93.246082   -0.293674
 1911-Dec-15 15:00 *m  17 27 29.21 -23 14 23.8  253.925501  23.237631   2.5444549   93.227900   -0.293116
 1911-Dec-15 16:00 *m  17 27 40.26 -23 14 32.3  238.930887  23.238019   2.5444830   93.209719   -0.292566
 1911-Dec-15 17:00 *m  17 27 51.32 -23 14 40.9  223.936485  23.238686   2.5445108   93.191538   -0.292024
 1911-Dec-15 18:00 *m  17 28 02.39 -23 14 49.3  208.942254  23.239748   2.5445383   93.173357   -0.291488
 1911-Dec-15 19:00 *m  17 28 13.45 -23 14 57.8  193.948143  23.241293   2.5445653   93.155176   -0.290957
 1911-Dec-15 20:00 *m  17 28 24.51 -23 15 06.1  178.954093  23.243376   2.5445919   93.136993   -0.290429
 1911-Dec-15 21:00 *m  17 28 35.57 -23 15 14.5  163.960040  23.246013   2.5446180   93.118807   -0.289902
 1911-Dec-15 22:00 *m  17 28 46.63 -23 15 22.8  148.965923  23.249182   2.5446437   93.100619   -0.289374
 1911-Dec-15 23:00 *m  17 28 57.70 -23 15 31.0  133.971682  23.252823   2.5446689   93.082427   -0.288842
 1911-Dec-16 00:00 *m  17 29 08.76 -23 15 39.2  118.977268  23.256845   2.5446938   93.064229   -0.288306

It looks like it is (barely) monotonically increasing.

Preliminary conclusion: if the sun continuously rises, you must be pretty close to the pole, but maybe not exactly (you could be up to half a mile away). If you observe oscillations, you did not make it within half a mile of the pole. On 15 December 1911, 60°E.

[Saint_Cad]

@Chronos

OK, but determining noon requires knowing your latitude

Latitude or longitude?

[dtilque]

@mixdenny

At the present day South Pole station they remark the exact pole each year.

Note that this is because the ice moves, not an actual movement of the pole. It says so at the link, but they don’t emphasize it. If you missed that point, you might get the idea that the pole is actually moving in a straight line.

[Chronos]

@Saint_Cad

Latitude or longitude?

Longitude. Even when I stop to think about it, I still often get those two mixed up. And I think that when I made that post, I didn’t stop to think about it. Thanks for catching that.