Tag: Hipparchus

5.3.3 Measuring of Precession

AbbreviATIONS
EXPLANATIONS

The most suitable stars for measuring the coordinates of the precession of the AEQ/VEQ points are those that are visible near the Ecliptic.

Spica is next to the Ecliptic, in the constellation of Virgo.

(In the middle of the goblet held in the left hand of the virgin sign, as shown in the photo above.)

Spica is easy to observe today on AEQ days because it appeared above the horizon when the Sun dipped below, and the sky darkened. This was not the case in ancient times. It is known that the coordinates of Spica in antiquity were measured primarily indirectly through the coordinates of the moon. The reason for this is as follows:

In the centuries of Timocharis, Hipparchus and Ptolemy, the celestial point of the autumn equinox, the AEQ point, was virtually very close to Spica. Today, the AEQ point is further away from Spica, as the photo above shows. Around the AEQ day, the Sun is also close to the AEQ point in the sky. This means that Spica also appears close to the Sun around the date of the AEQ. Therefore, in the centuries above, around the AEQ day, Spica was not visible to the naked eye because the Sun blinded the observer, as shown in the figure below.

Spica went under the horizon just before sunset and rose above the horizon just before sunrise. The following photo is darkened to show Spica just above the green line of the horizon and the Sun just on the horizon. (Of course, you can’t look below the horizon, only Stellarium allows you to do that.)

Both photos above were shot by the blogger with Stellarium at Sunrise on AEQ day of 128BC, in Alexandria, Egypt.

Fortunately, the full moon is just opposite the Sun. So, the coordinates of the Sun can be determined easily by measuring the coordinates of the moon. This was a usual procedure in antique astronomy.

Consequently, the simultaneity of the AEQ day and the full moon day could play an essential role in measuring the celestial position of the Spica. Note: Of course, the relative coordinates of Spica and the other stationary observable stars near the ecliptic plane (Alpha LEO; Alpha CMi, etc.) also supported the determination of the coordinates of Spica.

Let us look at the years of measurement from this point of view.

It can be observed that in two of the measurement years mentioned (278BC (-279); 128BC (-127)), AEQ and the full moon coincided. But the currently hypothetical year AD138 was not such an AEQ & full moon year.

It looks likely that all three years of measurement had to be coincident AEQ & full moon years.

However, instead of the uncertain AD138, 
the year AD131 would have been more appropriate, 
as this is the closest AEQ & full moon year.

AD150 could also fit but is out of the question because it is already the year of publication of Ptolemy’s very long and earlier written work.

The photo below was taken on 24 September AD131, on the day of the AEQ, about 1 hour before sunrise, and shows the sky from Alexandria. The Sun is still below the horizon, marked by the horizontal green line, near the AEQ point, the intersection of the Ecliptic and the celestial equator. Spica is to see in the circular frame next to both the AEQ point and the Sun. The coordinates of Spica are shown in the list on the left of the photo. It can also be seen that Spica is just above the Sun, and it will rise slightly before the Sun but will not be directly observable due to the Sun’s blinding proximity. (Stellarium photo by the blogger.)

The following photo is a wide-angle view of the East-West sky on AD131 on 24 September, on the day of AEQ, at the same time as the photo above. The full moon is well visible above the horizon, near the symbol for the VEQ celestial point, the other intersection of the Ecliptic and the celestial equator. The full moon is positioned opposite the Sun but will soon dip below the horizon. The coordinates of Spica can be calculated indirectly from the coordinates of the full moon. (Stellarium photo by the author.)

Let us have a look at the Ecl. long. coordinates of Spica on the dates of measurings as we see it, on the possible dates of AEQ and full Moon coincidence:

Table 4.

The above Table 4. is based on the data of Stellarium. It shows the changing of the ecliptical longitudinal (Ecl. long.) coordinates of Spica. The ecliptical longitudinal coordinates are traditionally measured from the VEQ point’s longitude zero. That is why the coordinates of Spica (and not those of the AEQ point) are changing.

Table 4. tells us, too, that the Ecl. long. of Spica gradually “approached” the AEQ point, which is at 180° Ecl. long. This table plays an essential role in the following.

5.3.1 Ptolemy, Almagest

AbbreviATIONS
EXPLANATIONS

Claudius Ptolemy was a Greek staff member of the “Great Library of Alexandria” (Musaeum or Mouseion), the knowledge centre of antiquity. Ptolemy was neither an innovator, researcher, or practical scientist but rather a “systematic mind”, an “integrator”.

As a diligent reader and scholar of the scientific achievements of his time, he collected and integrated the accepted teachings of mathematics and astronomy in his magnum opus, “Syntaxis Mathematica“. The “Magna Syntaxis” was later called “Almagest” from the Arabic word for “greatest”.

Hipparchus’ ideas and calculation data on precession are known from Ptolemy’s Almagest, which the author completed around 150 AD, as we know it today.

Unfortunately, Hipparchus’ works have been lost. (Except the so-called “Phaenomena” commentaries).

Furthermore, “the source of the source”, Almagest, has been lost, too.

Ptolemy’s work was written in Egyptian Greek and first only translated into Latin in the 12th century on the basis of an earlier Arabic translation. Earlier fragments of ancient Greek copies also surfaced in the 15th century.

The Almagest had defined astronomers’ “geocentric world view” for over a thousand years. Unfortunately, it has displaced and almost forced into oblivion all other ideas such as the “heliocentric theory”, previously known in Mesopotamia.

It is particularly noteworthy that despite the absence of the original work, Almagest’s astronomical claims were for many centuries regarded by the Roman Church and scholars alike as indisputable astronomical truth. Despite (or perhaps because of?) Almagest (following Hipparchus’ worldview) held to the geocentric theory; it became a long-living paradigm of astronomy.

An essential “annexe” of the Almagest is the so-called “star catalogue“, which gives the celestial positions of hundreds of stars in tabular form based on data from Hipparchus. (Almagest’s “Star Catalogue”: coordinates of 1022 stars, the vast majority of which are derived from Hipparchus, as we know it today.)

Of course, from the voluminous Almagest, we highlight and examine only the issues of interest to us.

The change in stellar coordinates relative to AEQ and VEQ due to precession is most apparent and measurable in the case of fixed stars along the ecliptic (e.g. SPICA, REGULUS).In antiquity, due to the slow rate of precession change, this observation could only be made by comparing the data from old and new measurements repeated centuries later. Hipparchus also compared his own data with the old data of his predecessors. And Ptolemy compared the measured data of his own time with those of Hipparchus.

Ptolemy did not mention any historically identifiable date for Hipparchus’ years of life (190BC-120BC), these years being derived from a posterior astronomical countdown.

It is now reckoned that Hipparchus compared the data of his astronomer predecessor Timocharis and of earlier astronomers in New Babylonia (Chaldee, registered around 280BC) with his own data (measured around 128BC).

It is also assumed that the astronomical data of Ptolemy’s own time were taken from measurements made in or around AD138. Probably, they were not Ptolemy’s own measurements but the somewhat earlier results of a more practical contemporary.

5.3 The Precession Objection

AbbreviATIONS
EXPLANATIONS

The precession objection is the most compelling of the above astronomical refutations to the possibility of a historical time insertion. So I will devote some posts to its examination. 

The objection is essential, so I will repeat it:

“If history were about 2.5 centuries shorter, there would have been about 3 degrees less angular rotation because the angular velocity of precession is constant to an excellent approximation. Three degrees would be too much of an error even for old historical measurements, ”

As told, it is almost a paradox!

Namely, we must assume that only the years of the Roman era are shifted back in time, while the AD years of Hipparchus’ lifetime should be considered correct. In other words, we should find an astronomical solution to solve this contradictory situation.

Familiarity with some elements of astronomy is essential in this part, so I am serving the description in several smaller “portions” in the hope that it will be more “digestible”.

First, I will briefly explain the essence of precession because, in my experience, relatively few people are well informed on the subject.

Since ancient times, astronomers have been able to determine the time and celestial position of Vernal Equinox (VEQ) and Autumnal Equinox (AEQ), the astronomical date and celestial points in the sky with sufficient accuracy.

The VEQ and AEQ points are the intersections of two well-known “virtual orbital curves”. They are the intersection points of the Sun’s elliptic orbit (as seen from the Earth in the ecliptic plane) and the celestial equator (the projection of the Earth’s equator onto the sky in the Earth’s equatorial plane).

Ancient astronomers considered these points of intersection, which are almost opposite each other in the sky, as fixed. They usually determined the position of planets, stars and constellations, the celestial coordinates of the latter, relative to the AEQ or VEQ point.

Hipparchus (Greek: Hipparchcos; BC190-BC120), the great ancient Greek mathematician-geographer-astronomer, is credited with the first description of the astronomical fact that the position of AEQ and VEQ in the sky relative to the fixed stars is not constant. According to many researchers, this phenomenon had been known before, for example, in Babylonia, but was generally neglected.

Hipparchus recognised that (according to the geocentric model) it is not only the Sun and the stars that orbit the Earth. For the observer on Earth, the celestial coordinates of the VEQ and AEQ points change relative to the virtually stable position of the fixed stars.

Both points wander around the ecliptic over a very long period, roughly 25.920 years. It is a motion alongside the constellations observable near the ecliptic plane but in the opposite direction to the celestial motion of the Sun. (The round 25.920 years cycle time is usually used, but the calculations and measurements differ slightly from this rounded value)

This phenomenon is called the precession of equinoxes, short precession.

Precession is the third form of Earth’s movement, besides the rotation of the Earth around its own axis and its orbit around the Sun.

We can say that the Earth’s axis, seen from the north but from a very great distance, rotates (like the axis of a spinning top) from east to west around the north pole of the ecliptic in about 25.920 years. During this time, the Earth’s axis of rotation slowly aligns with different stars. Currently, we see the North Pole Star (Polaris) near the extension of the Earth’s axis of rotation. This was not the case in the past and will not be the case in the distant future. So, in about 13 000 years, Earth’s axis of rotation will be aligned with the brightest star in the constellation Lyra, the fixed star Vega.

CTRL+click here to watch this highly accelerated video!

The phenomenon of precession is also one of the foundations of astrology, as the zodiac signs are the “wandering constellations” visible close to the ecliptic plane. The average time between adjacent zodiacal constellations is 25.920/12 = 2.160 years. The boundaries of the signs are not clearly defined. These years we are moving from the constellation of Pisces to Aquarius.

The above diagram clearly shows the ancient symbol of VEQ, ♈︎. In celestial coordinate systems, the VEQ point has been used as a reference point for a very long time, for as long ago as the VEQ point yet coincided with the starting point of the constellation Aries. In fact, the symbol ♈︎ is a simplified drawing of the “horns of Aries”. And, as I see, it resembles a renewal, an unfolding flower, a branching shoot, too. Because of a similar reason, the symbol of the AEQ point, opposite to the VEQ point resembles a balance ( Ω, underlined Greek omega) and symbolizes the constellation Libra. Both ancient symbols reveal the symmetry of duality.

On both, the VEQ day and the AEQ day of the year, the 24-hour solar day is divided into two equal parts, a 12-hour light day and a 12-hour dark night.

1.3 Astro-Refutations of Phantom Time

AbbreviATIONS
EXPLANATIONS

The official historiography classified Illig’s work as a “conspiracy theory” and did not go into a detailed refutation of the individual claims. Some astronomers have found “astronomical counterarguments“, and these are briefly summarised below.

An essential astronomical counterargument to the year-shifting of 200-300 years is that only the insertion of a Great Easter Cycle, 532 years, would have been possible because only this interval would have been difficult to detect. The reason for this is that in the Julian calendar months, days of the week and the corresponding phases of the moon repeat themselves in the same way only after 532 years. For astronomical and calendrical reasons, in mathematical terms, this means that the number of inserted fictitious years should be divisible by 19 and 28 (19*28 = 532). The 19 years is the length of the “Metonic cycle” (See Explanations). The 28 (7*4) years are the “solar cycle“, the number of years required in the Julian calendar for the leap years to repeat in the same way. The 7 is the “weekly cycle”, the number of the days of the week, and the 4 is the “leap year cycle“. (All this seems correct but is wrong because it is inaccurate, as we will show later).

The strongest counterargument of the astronomers is the “precession objection”, based on the approximately 25,920-year precession cycle of the Earth’s rotation axis.

The great ancient Greek astronomer Hipparchus is considered the first describer and measurer of precession. Hipparchus determined the celestial position of many fixed stars, e.g., Spica. Since the year of Hipparchus measurement (128BC), 2144 years have passed until AD2017, corresponding to a precession angle difference of 29.8 degrees. (See later)

"If history were about 2.5 centuries shorter, 
there would have been about 
three degrees less angular rotation, 
since the angular velocity of precession 
is constant to a good approximation. 
Three degrees would be too large an error 
even for ancient (astronomical) measurements."

According to experts, the above relationships and astronomical cycles were already well known to ancient astronomers. Eventual forgers or those who accepted an error afterwards would undoubtedly have considered them.

Of course, these cycles exist and were well-known also in ancient times. Despite these facts, the refutations based on them are not acceptable.

We will show later that 
these cycles cannot exclude the possibility 
of the insertion of an era into the AD time.