An Astronomical Interpretation of the Nebra Sky Disc

Bernd Fiedler

REVIEW 3 major objections 5 minor 40 references

An Astronomical Interpretation of the Nebra Sky Disc

T0 review · 3 major / 5 minor · reviewed 2026-08-12 · deepseek-v4-flash

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Pith's one-line read This paper argues that the Nebra Sky Disc contains a second, scaled drawing of the Auriga star line whose distance ratios match the sky, so its Bronze Age makers must have measured angular distances.

desk verdict A careful, reproducible archaeoastronomical study whose central claim — that the Nebra disc contains a scaled star map proving distance measurement — fails for want of a chance-alignment null model, though the beta-day astronomy and measurement appendices deserve serious referee attention. read the letter →

arxiv 2411.17307 v1 pith:OAVZ76GC submitted 2024-11-26 physics.hist-ph

Bernd Fiedler This is my paper · ORCID

classification physics.hist-ph MSC 01A1585-0385-04

keywords NebraSkyDiscBronzeAgeastronomyAurigalinebetadayPleiadesheliacalsettinglunisolarcalendararchaeoastronomy

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper argues that the Nebra Sky Disc, a Bronze Age bronze-and-gold artifact, encodes two star patterns in addition to the sun, moon, and horizon arcs identified by earlier interpreters. The first is a Taurus-and-Gemini shape resembling a Bronze Age plough. The second is a chain of four stars from Auriga and Gemini—epsilon Gem, theta Aur, beta Aur, alpha Aur—shown once in the main field and again in a smaller rotated group where the Pleiades sit vertically below beta Aur. The paper claims that the distance ratios and angles in that second group match the celestial Auriga line closely enough that the disc's makers must have measured star separations in the sky and transferred them as a scale drawing. If that is right, the disc becomes direct evidence of quantitative astronomical measurement in Bronze Age central Europe, tied to a "beta day" that could set the sowing date.

What carries the argument

The load-bearing object is the Auriga line, the four-star chain epsilon Gem, theta Aur, beta Aur, alpha Aur that forms a characteristic bent line in the sky. The paper's second representation of this line on the disc is the mechanism: its pixel-measured relative distances and the angle between the alpha Aur–epsilon Gem direction and the beta Aur–Pleiades direction are compared with the same quantities computed on the celestial sphere, and the small differences are read as evidence of intentional scaled transfer. Around this sit the beta day (the day the Pleiades appear vertically below beta Aur at nautical twilight) and the beta point (the corresponding point on the ecliptic), whose slow drift relative to the vernal equinox makes the day a stable agricultural anchor.

What would settle it

Re-measure the second Auriga line on a photogrammetrically corrected 3D scan of the disc, keeping the star identifications fixed in advance; if the relative lengths epsilon Gem–theta Aur and theta Aur–beta Aur then differ from the celestial-sphere values by more than the paper's tolerances, the scale-drawing claim is refuted.

Watch

Extended reading notes

Core claim

The central discovery the paper claims is a second occurrence of the Auriga line on the disc. When the disc is rotated so the middle star of the Pleiades rosette is vertically below the plate read as beta Aur, the chain epsilon Gem, theta Aur, beta Aur, alpha Aur reproduces the same bent line these stars form in the Bronze Age sky, and measurements on photographs give relative lengths and an inclination angle close to the celestial-sphere values. On that basis the paper says the distance agreement proves the Nebra people measured star distances and transferred them to scale; the detailed section labels this Conjecture 5.9 and then uses circle fitting and confidence intervals to make the to-scale conclusion (Corollary 5.10) very likely. The same beta-day geometry is used to propose a sowing rule: start sowing on the second round lunar phase after the day the Pleiades hang below beta Aur at dusk.

Load-bearing premise

The load-bearing premise is that the specific gold plates identified as epsilon Gem, theta Aur, beta Aur, alpha Aur, and the Pleiades are deliberate star markers rather than decorative dots; if that identification is arbitrary or chosen after the fact, matching distance ratios would be expected and would not prove measurement.

Editorial extensions

If this is right

If the second Auriga line is a true scale drawing, the Nebra people performed naked-eye angular measurement and similarity scaling in the Bronze Age, without writing or numerals.
The beta day gives a repeatable February warning date 24 to 28 days before the heliacal setting of the Pleiades, so farmers could sow on the second round lunar phase after it.
Because the beta point drifts only about 21 to 25 arcseconds per year relative to the vernal equinox, starting lunar years on the first new moon after the beta day would automatically insert leap months, reproducing a lunisolar calendar locally.
The beta event is now absent on the Mittelberg but still visible at more southern latitudes, which explains why the method is not evident to modern observers at the site.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

An extension the paper does not attempt: run the same ratio-matching test on the Taurus-'plough' group, which the paper treats only qualitatively; an independent distance match there would strengthen the measurement conclusion.
The strength of the claim depends on how many dot subsets on the disc could plausibly be matched to the sky; a formal chance-match analysis over all star plates is the natural next calculation.
If the claim holds, the disc would push quantitative angular measurement in Europe back by more than a millennium and suggest that scale mapping can arise without writing or formal arithmetic.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

Two things to know. First, this is a careful and mostly transparent paper: the Stellarium procedures in Appendix D, the two-photo image measurements, and the circle-fitting with confidence intervals are all checkable, and the author even labels the scale-drawing claim a conjecture (5.9) before the abstract overrides that caution. Second, the central proof claim does not survive its own method. The star-to-plate mapping is selected after the sky pattern is known, no chance-alignment baseline is computed, and Section 7's 'with probability 1' is not a probability over hypotheses — it silently assumes the identification at issue.

What is genuinely new: the specific Auriga-line reading (epsilon Gem, theta Aur, beta Aur, alpha Aur), the second scaled representation, the beta day, and the sowing-week rule. These extend Schlosser's program, and the beta-day astronomy is internally consistent. The author engages honestly with Lorenzen's Brocken objection, and the appendices are reproducible enough that a motivated reader could rerun the measurements.

The soft spots are load-bearing. The abstract says the agreement 'proves' the Nebra people measured distances, but Table 33 shows the agreement is not that tight: one relative length (beta Aur–theta Aur) deviates by 0.136, about 10–14%, and the angle by 1.5–3.7 degrees depending on the photo. Three of the four length ratios match within a couple of percent, which is suggestive — but the paper never quantifies how often a random four-plate subset of the disc would match a 1:2:3.5 pattern to that tolerance. Section 2.2 shows the identification style: missing stars and equidistant spacing are explained away as deliberate choices, so a reader cannot tell whether the second Auriga line was selected neutrally or picked because it fit. The first Auriga line is identified with distances explicitly allowed to differ, while the second line demands precision; the paper never addresses that asymmetry. To be fair, the solar depth h0 and arcus visionis sigma are anchored in the author's own twilight observations and in the standard literature; the genuinely free parameter is the star-to-plate mapping.

There is also an internal tension in the statistical framing: the confidence intervals in Appendix B quantify pixel-center measurement error only after the mapping is assumed, and the 13-digit precision claim in Remark B.4 outruns the pixel-picking input.

Who gets value: archaeoastronomers and Nebra specialists will want the beta-day tables and the measurement appendix, while anyone weighing the 'oldest quantitative star map' claim needs the null model first. I would send it to peer review rather than desk-reject it, but ask for a Monte Carlo chance-alignment analysis and a rewrite that demotes the 'proves' language to conjecture before publication.

Referee Report

3 major / 5 minor

Summary. The paper argues that the Nebra Sky Disc encodes a Bronze Age method for fixing agricultural dates: the identification of the Taurus/Plough pattern, an 'Auriga line' (ϵ Gem, θ Aur, β Aur, α Aur), a 'beta day' when the Pleiades are vertically below β Aur at dusk, and a second, scaled representation of the Auriga line on the Disc. The author claims that the close agreement of measured distances and angles on the second representation with celestial-sphere values proves that the Nebra people measured star distances, and then proposes that the beta day anchored either a lunisolar calendar or a sowing date tied to lunar phases.

Significance. If the scaled-map claim were established, it would be a significant result for European archaeoastronomy, implying quantitative angular and distance measurement and scale transfer in the Early Bronze Age. The paper is admirably transparent about its methods: it uses two photographs, reports repeated measurements, constructs confidence intervals for some angles, provides detailed Stellarium procedures, and explicitly labels the distance-measurement claim as a conjecture in Section 5.2.4. However, the evidence does not establish the central claim: the star-to-plate identification is made after the sky pattern is known, no chance-alignment baseline is provided, and the 'probability 1' statement in Section 7 is not a legitimate statistical conclusion. The significance of the paper is therefore conditional on a substantially stronger analysis than the manuscript currently provides.

major comments (3)

[§2.3, §5.2.4, Appendix B, §7] The load-bearing star-to-plate identification is made after the sky pattern is known, and no chance-alignment baseline is provided. Section 2.3 identifies the first Auriga line from pattern and star count alone, explicitly allowing distances to differ; Section 5.2.4 then selects a second set of plates whose distances happen to resemble the sky. The paper never specifies how the four plates assigned to ϵ Gem, θ Aur, β Aur, and α Aur were chosen from the many gold plates on the disc, nor does it compute the probability that some four-plate subset would approximate the sky configuration under a similarity transform. The confidence intervals in Appendix B (e.g., Propositions B.2 and B.3) quantify repeated manual measurement error conditional on the assumed mapping; they do not quantify uncertainty about the identification. Consequently, the statement in Section 7 that 'with probability 1 the Disc image Figure 20 is a scaled representation of the Auriga line' is not a probability over hypotheses and cannot support the abstract's claim that the disc 'proves' that the Nebra people measured distances.
[Tables 24, 29, 32, 33; Proposition B.3] The quantitative agreement is weaker than claimed and is internally inconsistent across the two photos. Table 33 lists relative-length deviations of −0.100 and −0.136 for β Aur–θ Aur and angle deviations of −3.65° and −1.54° relative to the celestial sphere; no null distribution is given, so these values cannot be judged as 'amazingly well' agreeing. Moreover, the two methods applied to Lipták's photo yield incompatible estimates of the same angle: Table 29 gives γ = 101.2184°, while Proposition B.3 reports a 95% confidence interval of 103.489°–103.589° for γ, a discrepancy of about 2.3° that the paper does not acknowledge. At minimum, the claimed precision needs to be reconciled and compared with the scatter expected from random plate selection.
[§5.2.4, Conjecture 5.9, Corollary 5.10, §7] The manuscript is internally inconsistent about the epistemic status of its main result. Section 5.2.4 states that the distance-measurement claim is 'deliberately formulated as a conjecture because there are still uncertainties,' and lists unresolved issues including single quick measurements and possible image distortion. Corollary 5.10 and Section 7 nevertheless assert that Figure 20 is a scaled representation 'with probability 1' and that the hypothesis is proved. The later sections do not remove the listed uncertainties, so the claims of proof are not supported by the manuscript's own evidence.

minor comments (5)

[Throughout] Stellarium is misspelled as 'Stelarium' in several places, and 'arthmetic' appears in Section B.1; 'Torn on' in Appendix D.3, step 5 should be 'Turn on'.
[Appendix E.1] The coordinate 'N 51°16′60.00″' is not a valid sexagesimal value; it should be written as 51°17′0″.
[§B.1.2 and Figure 34] The text says Lipták's photo was rotated by −3.47°, while the caption of Figure 34b says '+3.47°'; the sign should be reconciled.
[Table 17] The star name is given as 'Arctur' in the table but as 'Arcturus' elsewhere; the spelling should be made consistent.
[§B.1.2] The phrase 'from leftfa to ϵ Tau' appears to be a fragment; it should read 'from left to ϵ Tau' or similar.

Circularity Check

2 steps flagged · score 6.0 of 10

Post-hoc plate selection plus a rotation-imposed alignment make the 'proof' of scaled star-distance measurement circular at the key step.

fitted input called prediction [Section 5.2.4 / Appendix B / Section 7]
"There is a hint on the Sky Disc that the purpose of the Disc is actually to determine beta days. It appears that the Auriga line is shown a second time on the disc (see Fig. 20). ... From our investigations in Appendix B it follows that with probability 1 the Disc image Figure 20 is a scaled representation of the Auriga line."

The load-bearing input is the mapping of specific gold plates to ϵ Gem, θ Aur, β Aur, α Aur, and the Pleiades. The paper gives no rule for choosing these plates among the disc's many dots; the only stated basis is that a second Auriga line 'appears' and that the chosen distances 'correspond more closely to reality.' Appendix B then measures exactly those pre-selected plates, and Section 7 elevates the resulting agreement to 'with probability 1.' Since the same post-hoc identification defines the target and is then used as confirmation, and no chance-alignment or alternative-mapping baseline is computed, the agreement is not an independent test of the hypothesis.
self definitional [Section 5.2.4 and Corollary 5.10]
"If we now rotate the Sky Disc so that the middle star of the Pleiades object on the Disc is perpendicular under the star β Aur, we get an inclination of this Auriga line which is very similar to that which occurs when the Pleiades are perpendicular under β Aur in the Bronze Age on the Mittelberg (see Fig. 21). ... Corollary 5.10. Figure 20 shows an image of the Pleiades at the moment when they are vertically below β Aur."

The perpendicularity of the Pleiades center below β Aur in Figure 20 is imposed by the rotation described in the quoted sentence: the disc is rotated until the middle Pleiades star lies vertically under β Aur. Corollary 5.10 then presents this same imposed alignment as a property that the disc 'shows,' i.e., as confirmation of the beta-day scenario. Any planar image can be rotated to make an arbitrary point vertically below another, so this clause of the corollary is true by construction rather than by measuring the disc. The residual comparison of the inclination angle is a separate, non-imposed check, but the corollary's first assertion and the 'with probability 1' framing inherit the imposed alignment.

full rationale

The paper's celestial-sphere calculations in Appendix B.2 are external and reproducible, and the deviations in Table 33 are genuine quantitative comparisons; if the plate mapping had been fixed a priori, the agreement would be non-circular evidence. The circularity is in the identification step: the second Auriga line is asserted from the same visual similarity that it is then used to prove, and no objective rule identifies the four star plates or the Pleiades center among the disc's many candidate dots. The rotation in Fig. 20 enforces the very vertical alignment that Corollary 5.10 reports as a finding. These are not self-citation issues; they are input-selection and definitional issues. Score 6 reflects partial circularity: the distance-ratio comparison has independent external content, but the claim that the agreement 'proves' the Nebra people measured distances depends on a mapping chosen after the fact and on an alignment imposed by rotation.

Assumptions & free parameters 3 free parameters · 4 assumptions · 2 invented entities

The proof chain rests on (1) the assumption that the gold plates are stars, (2) the choice of which plates count, (3) modern visibility thresholds applied to the Bronze Age, and (4) Stellarium's long-term astronomical accuracy. The first two are the largest burdens: the second Auriga line is identified by the same pattern match used to confirm it, so the measurement claim is not tested against a chance-alignment null model.

free parameters (3)

Solar depth h0 for beta-day visibility = -9 degrees primary, -12 degrees alternative
The beta-day dates in Tables 7-9 shift by several days between h0 = -9 and h0 = -12. The paper selects -9 based on the author's own observations in Appendix E.3, not on an independently established Bronze Age visibility threshold.
Arcus visionis sigma for the Pleiades = 16 degrees and 20 degrees
The choice between good and poor atmospheric transparency changes the computed heliacal-setting date and therefore the 24-28 day gap after the beta day. The paper uses both values without establishing which applied in the Bronze Age.
Star-to-plate identification mapping = specific plates assigned to epsilon Gem, theta Aur, beta Aur, alpha Aur, eta Tau, and Taurus stars
Which gold plates count as stars is determined post hoc to match sky patterns, with no independent rule excluding other assignments. This selection is the load-bearing input to the distance comparison.

assumptions (4)

standard math Stellarium's long-term models of precession, nutation, proper motion, and refraction are accurate for the years -2101 to -1601.
All heliacal settings, beta days, and celestial-sphere distances are computed with Stellarium 0.21.0 following Appendix D, but no independent verification of the software's Bronze Age accuracy is provided.
domain assumption The Nebra Sky Disc's gold objects are intentional depictions of celestial phenomena, with the seven-star rosette representing the Pleiades.
Inherited from Schlosser's interpretation. Section 2.1 argues that a round disc must depict constellations, but that is presented as a plausibility argument, not a proof against null models.
domain assumption Bronze Age observers could see stars down to about magnitude 5 or 6 and could estimate vertical alignment within about 1.6 to 2 degrees.
Based on literature (Brandt) and the author's own 2020 naked-eye observations used in Proposition 5.11. Modern eye thresholds are applied to the Bronze Age without independent evidence.
ad hoc to paper The second Auriga line is a scaled map, with omitted stars, equidistant spacings, and the shifted beta Aur explained as deliberate artistic choices.
Section 2.2 items (i)-(iii) give a different bespoke explanation for each mismatch, such as faint stars being deliberately left out or artists preferring equidistant spacing. No falsifiable rule is stated.

invented entities (2)

Auriga line on the Sky Disc, second representation
purpose: Provides the scale-distance match that is claimed to prove star-distance measurement.
The four stars exist in the sky, but their presence as a distinct intentional line on the disc is inferred from the same pattern match it is used to prove. No independent prediction is made that could have failed.
Beta day and beta point
purpose: Marker day used to predict the Pleiades heliacal setting, start a lunisolar calendar, or set a sowing date.
Defined by the paper in Definitions 5.1 and 5.2 and calculated with a chosen solar depth h0. There is no independent Bronze Age record of the beta day against which the reconstruction could be checked.

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Cite this review

Pith. "Pith review of An Astronomical Interpretation of the Nebra Sky Disc." pith.science (2026). https://pith.science/paper/OAVZ76GC

@misc{pith2026241117307,
  author       = {Pith},
  title        = {Pith review of: An Astronomical Interpretation of the Nebra Sky Disc},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/OAVZ76GC}},
  note         = {Machine review of arXiv:2411.17307}
}

read the original abstract

We agree with the interpretation of W. Schlosser, that the Nebra Sky Disc is a reminder of a method of determining a start date (and possibly also an end date) of the farming year. We extend this interpretation. We think that we found the constellation Taurus on the Disc, which forms by addition of three stars from the constellation Gemini the pattern of a plough of Bronze Age. Moreover we found a line on the disc consisting of the stars epsilon Gem, theta Aur, beta Aur and alpha Aur, which we called the Auriga line. We think that the Nebra people used the Auriga line to determine the day (which we call beta day) on which the Pleiades are vertically below beta Aur at dusk in February. We found a second representation of the Auriga line on the Disc where the distance ratios between the stars are very precisely equal to the distance ratios in the sky, and where the Pleiades are vertically below beta Aur. This proves that the Nebra people must have measured the distances, and that our hypothesis is correct. The beta day could have been used to harmonize a lunisolar calendar with the solar year. However, the most likely possibility seems to us that a good sowing date could be determined by setting the sowing on the second round lunar phase after the beta day. (By round lunar phases we mean the full moon and the new moon.) Such a sowing date makes it possible to start a week count based on the lunar phases with the sowing in order to determine other agricultural dates. The astronomical knowledge for this procedure can be gained by astronomical observations only. No mathematical calculations and import of knowledge from a Mediterranean culture are necessary.

Figures

Figures reproduced from arXiv: 2411.17307 by the authors.

**Figure 1.** The big objects on the Sky Disc • Our ideas about the use of the Auriga line presented in this paper are probably correct. Our investigations are based, among other things, on own astronomical observations from March to May 2020 and October 2022 and on calculations with the Stellarium software 0.21.0 [38, 39], with Mathematica [37] and Peakfinder [29, 33] and on measurements on photos using Gimp [30]. 2. Star Const… view at source ↗

**Figure 2.** The constellation Great Bear is not a cluster of stars but a pattern in a large area. If one has recognized a constellation, one can also identify and use the individual stars in it, for example to navigate a ship. The absence of clusters or a dot placement that does not reveal any connections does not mean that an arrangement of dots does not contain a constellation [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗

**Figure 3.** The constellations Taurus and ”Plough”. The abbreviations tau and gem denote the affiliation of the stars to the constellations Taurus or Gemini. running over the stars 37 Tau and ω Tau. The same image can be found on the Sky Disc (see [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗

Figures from the paper (40 more)

**Figure 4.** Figure 4: The constellations Taurus and ”Plough” on the Sky Disc the left above µ. The resulting constellation is very similar to a plough from the Bronze Age (see [PITH_FULL_IMAGE:figures/full_fig_p006_4.png]

**Figure 5.** Figure 5: Silhouette of the Plough of Walle There are also some problems with the mapping we made between the stars on the Disc and the stars in the sky. (i) The stars ω Tau and 37 Tau, which connect the Pleiades with the constellation Taurus, are faint. They have magnitudes of …

**Figure 6.** Figure 6: The star constellation Taurus on the Sky Tablet of TalQadi: 1=beta, 2=epsilon, 3=delta1, 4=gamma, 5=theta2, 6=alpha, 7=zeta. P. Kurzmann [9, 10] has assigned real constellations to all star arrangements on the Tablet. The second segment from the left shows the constel…

**Figure 7.** Figure 7: On the day of the heliacal setting of the Pleiades, the Plough is steep. If the beginning of this line is marked by two stars that are close together, it is easier to see that one is on the right line. If we accept the explanations given here for the above critical poi…

**Figure 8.** Figure 8: The constellation ”Plough” and the ”Auriga line” on the Sky Disc peak. Only the pattern and the number of stars matter. The distances between the stars on the disc or in the sky can differ as in Subsection 2.2. We call the pattern from the stars considered here ”Auriga…

**Figure 9.** Figure 9: The constellation ”Plough” and the ”Auriga line” • The time that the sun needs to travel from its transit across the local meridian of P back to the local meridian of P after 1 rotation of the Earth is called solar day. • The time that the vernal equinox needs to trave…

**Figure 10.** Figure 10: Solar day and sidereal day. From (3.4) and (3.2) we obtain 1 stellar day − 1 sidereal day = 0, 00837285812 seconds(3.5) 4. Heliacal settings According to the interpretation of W. Schlosser, the Nebra people of the Bronze Age chose the heliacal setting of the Pleiades …

**Figure 11.** Figure 11: shows the arcus visionis of the Pleiades in the year -1601. On the [PITH_FULL_IMAGE:figures/full_fig_p015_11.png]

**Figure 12.** Figure 12: The line from Aldebaran (α Tau) to the Pleiades (η Tau) at -1601-1-1 above the Mittelberg when the Pleiades are 10◦ high in the evening. 5.2. A sign that the heliacal setting of the Pleiades is imminent. 5.2.1. A possible use of the ”Auriga Line”. The stars of the ”Au…

**Figure 13.** Figure 13: 1601-02-01 Julian. Pleiades to the right of α Aur (Capella). Sun height h = −9 ◦ . This movement of the Pleiades under the stars of the Auriga Line is only an apparent movement. In reality, the stars do not move against each other in such a short time. But using α Aur…

**Figure 14.** Figure 14: 1601-02-21 Julian. Pleiades between β Aur and α Aur (Capella). Sun height h = −9 ◦ . Definition 5.1. Let P be a given astronomical observing site. We call a day beta day at P to solar depth h0 if (1) on that day the Pleiades appear from P vertically below β Aur when t…

**Figure 15.** Figure 15: 1601-03-28 Julian. Heliacal setting of the Pleiades at σ = 16◦ . Pleiades to the left of beta Aur. Sun height h = −9 ◦ . If Azη = Azα or Azη = Azβ holds, the Pleiades are perpendicular under α Aur (Capella) or β Aur. ”Hardly any relative movement to β Aur” means Azη −…

**Figure 16.** Figure 16: Determination of the beta point. All events listed in [PITH_FULL_IMAGE:figures/full_fig_p023_16.png]

**Figure 17.** Figure 17: Positions of the Pleiades from [PITH_FULL_IMAGE:figures/full_fig_p025_17.png]

**Figure 18.** Figure 18: Regarding the zenith criterion in Prop. 5.5. All previous considerations of this section were made only for P = Mittelberg and the pair of stars β Aur and η Tau (Pleiades). We now clarify to what extent similar phenomena exist for arbitrary observing sites P and arbit…

**Figure 19.** Figure 19: Proposition 5.8. Let P be a point on the Earth’s equator and S1 and S2 be any two fixed stars. Then S1 and S2 appear either twice or always vertically one above the other from P. Proof. If P lies on the Earth’s equator, then during one revolution of the Earth its zeni…

**Figure 20.** Figure 20: The second Auriga line on the Sky Disc We made length and angle measurements in the Figures 20 and 21 using GIMP [30]. Tables 10 and 11 show the results. Furthermore, by drawing a test line, from ϵ Gem to α Aur, one can determine that θ Aur lies on the line ϵ Gem – α …

**Figure 21.** Figure 21: The skewness of the Auriga line when the Pleiades are perpendicular to β Aur in the Bronze Age on the Mittelberg. line length (pixels) relative length β Aur – α Aur 198,0 1,0 β Aur – θ Aur 177,0 0,89393939 ϵ Gem – θ Aur 396,0 2,0 ϵ Gem – α Aur 691,0 3,4898989 ∢(α Aur …

**Figure 22.** Figure 22: The fit (5.1) (left) and its residuals (right). We can find even more precise functional relationships between the data from [PITH_FULL_IMAGE:figures/full_fig_p038_22.png]

**Figure 23.** Figure 23: The fit (5.2) (left) and its residuals (right) [PITH_FULL_IMAGE:figures/full_fig_p039_23.png]

**Figure 24.** Figure 24: The fit (5.3) (left) and its residuals (right). For a functional relationship between the year y and the ecliptic length λ of the beta point B, we first form the set data of points (yi , λi), where yi is the year in the ith row and λi is the λ-value in the ith row of …

**Figure 25.** Figure 25: The stellar time of the beta event between -2101 and -1601. The fit (5.10) (left) and its residuals (right) [PITH_FULL_IMAGE:figures/full_fig_p043_25.png]

**Figure 26.** Figure 26: The stellar time of the beta event between -2101 and -1601. The fit (5.11) (left) and its residuals (right) [PITH_FULL_IMAGE:figures/full_fig_p043_26.png]

**Figure 27.** Figure 27: The stellar time of the beta event between -2101 and -1601. The fit (5.12) (left) and its residuals (right). t ∗ (5.12) = 34046.437165024734 + 1.3758109207196094 · y + 0.00033832925555652007 · y 2 + 3.524489749962895 · 10−9 · y 3 [PITH_FULL_IMAGE:figures/full_fig_p04…

**Figure 28.** Figure 28: The angle spanned by the horizon arcs. 82◦ -83◦ is the value of W. Schlosser. (B.1) ¯a = 1 n Xn i=1 ai , s = vuut 1 (n − 1) Xn i=1 (ai − a¯) 2 , sa¯ = s √ n Now we apply Sachs’ method. We choose a confidence level 1 − p = 0.95 and determine a constant c from Student’s…

**Figure 29.** Figure 29: The partial angles for the horizon arcs. The c value was calculated using Solve[CDF[StudentTDistribution[30],cc] == 0.975,cc][[1]] with Mathematica [37]. If one calculates (B.5) k = c · sa¯ k = 0.07945◦ (B.6) then ¯a − k ≤ α¯ ≤ a¯ + k is the confidence interval we are…

**Figure 30.** Figure 30: The best-fitting circle for α Aur. We denote the midpoints m given in [PITH_FULL_IMAGE:figures/full_fig_p058_30.png]

**Figure 31.** Figure 31: The best-fitting circles around the central star of the Pleiades and the 4 stars of the Auriga line. We then calculate the length of a line between two points mu = (u1, u2) and mv = (v1, v2) using the elementary formula (B.9) d(mu, mv) = p (v1 − u1) 2 + (v2 − u2) 2 …

**Figure 32.** Figure 32: For the second determination of the direction from β Aur to the center of the Pleiades Rosette. coordinates (in pixel) mβ = (790.6052, 1425.4896) for this center (see [PITH_FULL_IMAGE:figures/full_fig_p061_32.png]

**Figure 33.** Figure 33: The center of the star β Aur. We now draw the tangents f1, f2 and use GIMP to determine the angles δ1, δ2 of these tangents to the image vertical h. We calculate from δ1, δ2 δ = δ1 + δ2 2 (B.21) . δ is also a good value for the angle of direction from β Aur to the cen…

**Figure 34.** Figure 34: The slope of the line ϵ Tau → central star of the Pleiades a) in Nebra Scheibe white.jpg and b) in the photo by Lipt´ak, represented here by the image Nebra Scheibe white rotated by +3.47◦ . central star of the Pleiades touch a vertical line, while in Lipt´ak’s pictu…

**Figure 35.** Figure 35: Sketches for the calculations in Section B.2. As a starting point, Stelarium provides us with the azimuthal coordinates of the stars α Aur, β Aur, θ Aur, ϵ Gem and η Tau on -1601-2-28Julian, 18:10:57 (see [PITH_FULL_IMAGE:figures/full_fig_p069_35.png]

**Figure 36.** Figure 36: Sunset at the summer solstice -1601 between Wurmberg and K¨onigsberg seen from Mittelberg. We checked this using PeakFinder and Stellarium. We simply determined the horizon line using PeakFinder and imported it into Stellarium. We then calculated the sunset on the sum…

**Figure 37.** Figure 37: ). To do this, one sets up a gnomon and marks the end of the shadow at sunset in a period around the summer solstice. In the days near the summer solstice, the direction of the shadow at sunset no longer appears to change to someone observing only with the naked eye […

**Figure 38.** Figure 38: The function (C.12) over 0◦ ≤ A0 ≤ 180◦ . We solve (C.11) with the tool Solve from Mathematica [37] and obtain (C.13) A0 = 48.7059◦ . If we insert (C.13) into (C.7), we get (C.14) 0.404853 = 0.659924 cos φ ⇒ φ = 52.1581◦ . Thus we have found the lower limit of the int…

**Figure 1.** Figure 1: Starting point [source 1]. Conversion to black and white. Inserting labels [PITH_FULL_IMAGE:figures/full_fig_p084_1.png]

**Figure 3.** Figure 3: Own work. Stellarium screenshot. Inserting lines and labels [PITH_FULL_IMAGE:figures/full_fig_p085_3.png]

**Figure 21.** Figure 21: Own work. Stellarium screenshot. Inserting lines and labels [PITH_FULL_IMAGE:figures/full_fig_p086_21.png]

**Figure 35.** Figure 35 [PITH_FULL_IMAGE:figures/full_fig_p086_35.png]

**Figure 36.** Figure 36: Own work. Stellarium screenshot using a horizon line generated with Peakfinder. Inserting lines and labels [PITH_FULL_IMAGE:figures/full_fig_p087_36.png]

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Reference graph

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[1] [1]

P. Ahnert. Kleine praktische Astronomie . Johann Ambrosius Barth, Leipzig, 1974

work page 1974

[2] [2]

R. Brandt. Himmelsbeobachtungen mit dem Feldstecher . Johann Ambrosius Bart, Leipzig, 1972

work page 1972

[3] [3]

Gebhard and R

R. Gebhard and R. Krause. Kritische Anmerkungen zum Fundkomplex der sog. Himmelss- cheibe von Nebra. Arch¨ aologische Informationen, 43:1–22, 2020. Early View, published online

work page 2020

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G¨ unther.Astronomische Geographie, volume 92 of Sammlung G¨ oschen

S. G¨ unther.Astronomische Geographie, volume 92 of Sammlung G¨ oschen. G. J. G¨ oschen’sche Verlagshandlung, Leipzig, 1905

work page 1905

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R. Hansen. Die Himmelsscheibe von Nebra - neu interpretiert: Sonne oder Mond? Wie der Mensch der Bronzezeit mit Hilfe der Himmelsscheibe Sonnen- und Mondkalender ausgleichen konnte. Arch¨ aologie in Sachsen-Anhalt, 4/2/2006:289–304, 2007

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R. Hansen. Sonne oder Mond? Verewigtes Wissen aus der Ferne. In H. Meller and F. Bertemes, editors, Der Griff nach den Sternen: Wie Europas Eliten zu Macht und Reich- tum kamen. Internationales Symposium in Halle (Saale), 16. - 21. Februar 2005 , volume 5 of Tagungen des Landesmuseums f¨ ur Vorgeschichte Halle, pages 953–962, Halle (Saale), 2010

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