Navigation by sky when nearing polar opening, an analysis of Nansen in 1895 at 86° latitude

Nansen mentions in Farthest North, Vol II, on page 164, when he is further north than anyone has ever been (he was also the first to cross the interior of Greenland and did so 7 years before that), that he seemed to not be making progress forwards,

"It became more and more of a riddle to me that we did not make greater progress northward. I kept on calculating and adding up our marches as we went along, but always with the same result; that is to say, provided only the ice were still, we must be far above the eighty-sixth parallel. It was becoming only too clear to me, however, that the ice was moving southward, and that in its capricious drift, at the mercy of wind and current, we had our worst enemy to combat. "

On a hollow planet with polar holes, if the crust had begun to bend inwards by 86°, the slope would shift the position of objects in the sky, and distort navigational measurements (Nansen was using theodolite and sextant to navigate by sky), the observer will be looking at the sky from a different angle than what they assume. For example, visualize when the slope is equivalent to being on the other side of the planet, they positions of stars will be completely wrong. As another example, when you are halfway through the hole, the pole star will be at 90° angle to you, and navigating towards the pole star will move you towards the outside surface.

Perhaps an explanation could be that he navigated in the right direction, but his measurements fooled him into thinking he made less progress, because the slope of the Earth changed along the way, and along with that the angle to the stars and the pole star. On page 153 of Farthest North, Vol II,

"That day I took a meridian observation, which, however, did not make us farther north than 85° 30′. I could not understand this; thought that we must be in latitude 86°, and, therefore, supposed there must be something wrong with the observation. "

and page 163,

“I turned out at midday and took a meridian observation, which makes us in 85° 59′ N. It is astonishing that we have not got farther; we seem to toil all we can, but without much progress. Beginning to doubt seriously of the advisability of continuing northward much longer. "