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

Alexandra Farkas, Dénes Száz, Ádám Egri, Miklós Blahó, András Barta, Dóra Nehéz, B. Bernáth, Gábor Horváth

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Abstract

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 θS, solar azimuth πS) was estimated with an average error of +0.6° ≤ Δθ ≤ +8.8° and -3.9° ≤ Δπ ≤ +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 (ωNorth) was determined with an error of -3.34° ≤ ΔωNorth ≤ +6.29°. The inaccuracy of the second step of this navigation method was high (ΔωNorth = -16.3°) when the solar elevation was 5° ≤ θS ≤ 25°, and the two selected celestial points were far from the sun (at angular distances 95° ≤ γ1, γ2 ≤ 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.

Original languageEnglish
Pages (from-to)1645-1656
Number of pages12
JournalJournal of the Optical Society of America A: Optics and Image Science, and Vision
Volume31
Issue number7
DOIs
Publication statusPublished - Jul 1 2014

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Solar System
navigation
Sun
sky
sun
Navigation
Experiments
navigators
solar azimuth
great circles
autumn
daytime
azimuth
intersections
summer
horizon
alignment
Polarization
Crystals
Direction compound

ASJC Scopus subject areas

  • Atomic and Molecular Physics, and Optics
  • Electronic, Optical and Magnetic Materials
  • Computer Vision and Pattern Recognition
  • Medicine(all)

Cite this

Accuracy of sun localization in the second step of sky-polarimetric Viking navigation for north determination : A planetarium experiment. / Farkas, Alexandra; Száz, Dénes; Egri, Ádám; Blahó, Miklós; Barta, András; Nehéz, Dóra; Bernáth, B.; Horváth, Gábor.

In: Journal of the Optical Society of America A: Optics and Image Science, and Vision, Vol. 31, No. 7, 01.07.2014, p. 1645-1656.

Research output: Contribution to journalArticle

Farkas, Alexandra ; Száz, Dénes ; Egri, Ádám ; Blahó, Miklós ; Barta, András ; Nehéz, Dóra ; Bernáth, B. ; Horváth, Gábor. / Accuracy of sun localization in the second step of sky-polarimetric Viking navigation for north determination : A planetarium experiment. In: Journal of the Optical Society of America A: Optics and Image Science, and Vision. 2014 ; Vol. 31, No. 7. pp. 1645-1656.
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