First part of this article deals with the basic concepts regarding to the four cardinal or royal stars; Aldebaran, Regulus, Antares, and Fomalhaut. Then, examines the possibility of a combination fitting to the assessment, in our present time. This second part is about the search of a fitting configuration throughout a large scale time interval, since the four cardinal stars are not exactly marking the four corners, as it is suggested, in present time.

Although the stars are mostly regarded as fixed and remote objects in the sky, due to their secular motions, the angular distances between them do change in time, which causes even a considerable displacement after long time intervals. In this case, the ideal configuration that is wanted is the 180° separation between Aldebaran & Antares, and Regulus & Fomalhaut, where the two opposing couples are also forming a rectangular cross.

Independent of the motion of the reference systems, we can calculate the angular distances between the objects, and then examine the deviations from the wanted configuration, by demonstrating the excesses of perpendicularities. The graphical presentation below is based on this qualification, where the ordinate is showing the excess in degrees of arc, and the abscissa is for the time scale in Julian years. The color legend for the curves is given on the left, which is valid for all graphics in the article, unless defined otherwise.

During an interval of 200,000 years, the true angular distances for the epoch are showing that a minimal value can be reach at round 90,000 BC, but only down to 14° deviation from the exact placement, for Regulus and Fomalhaut.

But, if Fomalhaut would be ignored,

the configuration based on three remaining stars (Aldebaran-Regulus-Antares) was forming a very close sample at round 120,000 BC, with a maximum excess of 2°, and an exact rectangular Aldebaran-Regulus placement. Yet, in that case, another star is wanted to be placed in the fourth corner. But, to my knowledge, there is not a single star in that region to substitute Fomalhaut, as far as the apparent magnitudes at the epoch are concerned. If the present proper motion catalogues are not missing a fundamental one, the other stars in the region with wanted qualifications are not that bright for the naked eye to substitute Fomalhaut. Because, what we want is a star at least with 1.5 apparent magnitude, right at the opposite of Regulus.

Above is the part of the sky as it appears at 120,000 BC. Note that the brightest one close to the midpoint of Aldebaran and Antares is no other but Fomalhaut. Magnitudes down to 1.0 are labeled, and the dark purple line is representing the ecliptic of the epoch 2000.

As a conclusion, regarding the spherical angular distances, it seems hardly possible to place these stars at the four corners of any rectangular cross.

Right is the graphic presentation of apparent magnitudes of four stars. 

Aldebaran seems to reach its peak round 300,000 years ago, with a -1.5 magnitude, which gives quite a high brilliance.

Fomalhaut was 1.0,  round 200,000 years ago.

Regulus was 1.3, about 150,000 years ago. Apparent magnitude of Antares (about 1.0) remains almost the same, because it is a very distant star relative to the others, and the double curve is for the upper and lower limits.

Since the true angular distances are not assisting to develop a suitable model consistent with the hypothesis, we may then examine the angular separations between these stars throughout the time, based either on the equator or the ecliptic. Angular separations do not reflect the actual distances, for they are measured on the base plane of the selected reference frame. But, if the reference frame has a substance, like being originated from the rotation or revolution of the celestial body, then these separations gain importance relevant to the present hypothesis. Namely, not any but certain points of the celestial equator or the ecliptic, which are forming a rectangular cross, can be the reference of the hypothesis.

The obliquity of the ecliptic varies slightly with a period of about 41,000 years, around 23.3°±1.3°, and subsequently the latitude of a star changes in due time. Also, because of the precession of the equinoxes, the longitude of a star advances about one degree in round 72 years. But, apart from these positional changes caused by the movement of the reference system, the star itself moves in space, which is named as the peculiar motion of the star.[N1] 

The peculiar motions of the four stars are shown on the left. Since effect of the precession is uniform on the ecliptic plane, the longitudinal difference caused by the precession is ignored here, in order to explicit the amount of secular motions. Undulations are due to the variation of the obliquity. The horizontal light cyan bars are showing the longitudinal displacement of the star in 400,000 years. Ordinate is showing the latitudes.

As the above graph shows, the longitudinal displacements of Antares and relatively of Aldebaran are not big as of the two other stars, which are constituting one axis of the cross. Within the given time interval, positions of Fomalhaut and Antares are not reaching to the ecliptic circle. But, Aldebaran appears to be in the solar occultation limits between circa -88216 (l=251°) and -65405 (l=211°), which is a very long time indeed. Regulus also enters into this zone between -6034 (40°) and -4794 (57°), and twice more in the remote future; 19289 (35°) to 25531 (122°), and 46058 (43°) to 54283 (160°). All in Julian years, and the computation method is approximation.

Here, we notice that there is a possibility of an exact cross based on the ecliptic plane. The next graph below is showing the separations based on the ecliptic of the epoch. But, the coincidence of the exact rectangularity is not occurring simultaneously.

The minimum total excess was reached at about 30,000 BC, but the amount 8° for two angles and 7.5° for two other angles are beyond acceptable limits.

Simultaneously, the opposing stars are forming almost a 180° separation, but the angle between two axes is far

from being 90°. Namely, the axial deviation is around 7.5°-8°, and this is the only possible minimal one in more than 400,000 years. But, even with this minimal shift of the Regulus-Fomalhaut axis, the configuration becomes hardly acceptable to confirm the hypothesis. Undulations are due to the variation of the obliquity.

If Fomalhaut is ignored, then the other three stars (Aldebaran-Regulus-Antares) are presenting almost an exact mach at round 120,000 BC, just like in the case with true angular distances, with an acceptable excess of 2°. Yet, as seen above, there is no possibility to substitute Fomalhaut for the given time, with a star in the region, due to deficiency of brightness. In addition, in case of an omitted Regulus, at about 85,000 AD, there is a possibility of a matching triplet. But this case is not supported by the true angular distances. Also logically, the sequential part of the hypothesis would be confusing if the supporting evidence of it were to be placed in the remote future.

The search based on the equatorial reference system is not easy as the former one. Because, since the precession of the equinoxes is causing a drift in all astrometric positions along the path of the ecliptic, throughout the time, the equatorial parameters are not changing uniformly for all celestial objects. As a sample for this inconsistency, let us first examine the possibility of a minimal excess epoch in separations based on the fixed equator. The search is done for 400,000 years like the previous ones, but the equator is fixed to J2000 epoch, and the graphic result is shown below:

The white line is demonstrating the total excess quantity, and the minimal value is at J-66359.1, with an amazing small value of 02°02', where the single maximal shift is only 33'.

For an interval of about 9,000 years, rectangular exactness of the cross seems well preserved, with a

total excess below 3°. But, in reality, such a fitting combination can occur only with a fixed reference frame. On the other hand, a fixed equator is a very misleading reference, if the cardinal points are sought for a remote epoch [N2]. But, it can be used to determine the period and the amplitude for an oscillator model, which will be described in the forthcoming part of this article. Now, with the mean equator of the epoch, we will examine the same possibility for a span of 400,000 years. [N3]

The graph on the right is indicating that not at the time as predicted by the fixed epoch computation, but some other time,  there is a possibility of such a configuration supporting the hypothesis.

Ordinate scale is for the excess amount in

degrees. The white curve is representing the total excess in angular separations based on the mean equator of the epoch, as the sum of six curves. The legend for the other curves is the same above. The white dots seen at the bottom, under the abscissa line, are indicating the epochs where the wanted possibility is likely to be found.

Our next step will be a detailed examination of the intervals pointed out in the main search regarding the mobile equator. For this purpose, we may examine the indicated spots in detailed graphics, as depicted below. The legend is the same, and the white curves are representing the total excess for the epoch. The white dots under the abscissa line, are not coinciding with the minimal points of total excesses, just because they are for marking the possible nearest date to the minimal total excess, where the four stars are maximum 5° apart from one of the cardinal points of the equator, namely the points with 0°, 90°, 180°, and 270° right ascension of the equator of the epoch. Dates are in Julian years:

Minimum total excess in angular separations is 19.1° at the epoch -100630.

Minimum total deviation from cardinal points is 9.3° at the epoch -99801.

Minimum total excess in angular separations is 5.3° at the epoch -75288, and 4.4° at -52119.

Minimum total deviation from cardinal points is 7.4° at the epoch -73822, and 7.1° at -48240.

Minimum total excess in angular separations is 16.0° at the epoch -26526.

Minimum total deviation from cardinal points is 15.1° at the epoch -28595, and 13.1° at        -22460.

Here we have five dates to examine in detail to find a possible fitting configuration supporting the hypothesis. The following table is a summary of the positions and angular excesses, as well as the deviations from cardinal points, for four stars. At the moment, positions for remote dates can be calculated only by approximation. Error limits are not computed, for this is just an overview, but the figures are truncated on purpose.

A quick examination of the table at left, reveals that positions at the Julian date -73822 can be the only supporting material for the hypothesis of cardinality of these stars, in regard to equatorial placements. The next date to consider may be -48240, but with a suspicious positioning of Regulus. The other three dates are presenting configurations beyond the acceptable limits, even the error factors would be considered.

Yet, with the both epochs, which may be acceptable form an astronomical point of view, there is an anthropological problem pending to be solved. Namely, the possibility of an existing culture at the epoch, which is expected to be capable of observing these celestial objects, and then determining their coincidence with the cardinal points.

Our knowledge about the historical human societies concerning such remote dates is not sufficient to estimate the possibility of a likelihood. But, if we rely on the archeological evidences, the probability of such a developed human society is not very high.

The only remaining possibility, which may support the hypothesis that some 76,000 years ago, a well developed human society did noticed the exceptional positions of these stars, can be traced in the unverified archeological myths, such as Atlantis or Lemuria!

Yet,  if  we  begin  to tangle  with  the

mythological legends, the importance of an astronomical support becomes unnecessary, for the legends do not need any scientific material supporting their reliability, since they are already part of a human lore. But, if we need them to support our hypotheses, then we must wait until an archeological evidence appears to verify the reliability of that legend. As a matter of fact, there has not been any evidence supporting the historical validity of legends about Atlantis or Mu, or any similar one claiming a high civilization during the age of anthropologist's cavemen.[N4]

For a moment, we may assume that the supporting configuration was detected by an unknown civilization, and their assessment reached up to us by oral tradition throughout a huge span of 76,000 years. Then it will be wise to query the impact of this observation on that unveiled civilization. If this configuration did happen only once and for a relative short duration, which is very likely according to the computations (from -73935 to -73709, about 226 years, when the limit for all cases is 5.0°), then why it has been considered so important if there was not a similar occurrence through all these millenniums while the definition was considered important to keep vital?