Accuracy of sun localization in the second step of sky-polarimetric Viking navigation for north determination: a planetarium experiment.

It is a widely discussed hypothesis that Viking seafarers might have been able to locate the position of the occluded sun by means of dichroic or birefringent crystals, the mysterious sunstones, with which they could analyze skylight polarization. Although the atmospheric optical prerequisites and certain aspects of the efficiency of this sky-polarimetric Viking navigation have been investigated, the accuracy of the main steps of this method has not been quantitatively examined. To fill in this gap, we present here the results of a planetarium experiment in which we measured the azimuth and elevation errors of localization of the invisible sun. In the planetarium sun localization was performed in two selected celestial points on the basis of the alignments of two small sections of two celestial great circles passing through the sun. In the second step of sky-polarimetric Viking navigation the navigator needed to determine the intersection of two such celestial circles. We found that the position of the sun (solar elevation θ(S), solar azimuth φ(S)) was estimated with an average error of +0.6°≤Δθ≤+8.8° and -3.9°≤Δφ≤+2.0°. We also calculated the compass direction error when the estimated sun position is used for orienting with a Viking sun-compass. The northern direction (ω(North)) was determined with an error of -3.34°≤Δω(North)≤+6.29°. The inaccuracy of the second step of this navigation method was high (Δω(North)=-16.3°) when the solar elevation was 5°≤θ(S)≤25°, and the two selected celestial points were far from the sun (at angular distances 95°≤γ(1), γ(2)≤115°) and each other (125°≤δ≤145°). Considering only this second step, the sky-polarimetric navigation could be more accurate in the mid-summer period (June and July), when in the daytime the sun is high above the horizon for long periods. In the spring (and autumn) equinoctial period, alternative methods (using a twilight board, for example) might be more appropriate. Since Viking navigators surely also committed further errors in the first and third steps, the orientation errors presented here underestimate the net error of the whole sky-polarimetric navigation.