In Celebration of Psalm Nineteen:
God's handiwork in Creation

Signs and Seasons, Days and Years
Comments on Genesis 1:14

And God said, “Let there be lights in the expanse of the heavens to separate the day from the night. And let them be for signs and for seasons, and for days and years."

I  think thy thoughts after thee, O God.
Johannes Kepler

The Silent Speech in Astronomy
as a Prototype for God's Silent Speech
    On Creation Day 4, God commissioned the starry heavens to be timekeepers  for his human creation. This is a prime example of Nature's built-in Silent Speech.  For stars to be timekeepers humans must draw that speech out of a random scatter of heavenly light: order must come out of apparent disorder.
   Timekeeping doesn't come automatically without effort and skill, and so this example is a prototype of how the silent speech of Psalm 19:4 works in practice.
  The silent speech in astronomy declares God's glory and handiwork in greater and greater detail, as skilled craftsmen interpret the starry hosts as timekeepers. This skilled work goes on for centuries and millennia, and even continues today, always providing greater cause for awe and wonder, as each major advance in astronomy leads to further evidence for God's handiwork at timekeeping, and its unfolding shows an unending increase in marvelous and unexpected depth and complexity. [FOOTNOTE: In contrast to this, consider Ernst Haeckel's claim that the explanation of the spontaneous origin of life (another grand theme of God's Silent Speech) is "no more difficult to us than the explanation of the physical properties of inorganic bodies." History of Creation (1876), Vol I. p. 406. See also his Riddle of the Universe and commentary on it by Sir Oliver Lodge, Life and matter : a criticism of Professor Haeckel's "Riddle of the Universe" (1907). Haeckel fell into the trap of assuming that the current understanding of science is final and authoritative.]

The  Beginnings of Astronomy: Constellations and the Zodiac

Since no written records exist from prehistoric times (by definition!), a bit of "just so" storytelling is needed -- but I think the general facts are clear. Since prehistoric times the stars have been used to mark off
"seasons and days and years", and the earliest historical records imply that the major constellations had already been long identified and named back in the mists of antiquity, many thousands of years ago.

    Constellations. Faced with the apparent random sprinkling of stars throughout the heavens, the mind looks for patterns. This is an automatic response: the mind cannot help it (one reason why people see patterns in gambling, the stock market and anything else that appears -- or is in fact -- random)! This leads naturally to the identification and naming of the major constellations.

The Orion Constellation
Orion Constellation

By a remarkable providence there are literally hundreds of beautiful (and very fragile) cave paintings preserved in France and Spain composing what is called the Magdalenian culture, spanning from about 18,000 to 10,000 BP  (Before the Present). In my view the preservation of these paintings is an example of a silent voice lovingly preserved for our benefit by God [FOOTNOTE: Having been preserved for thousands of years, since their first discovery in the early 20th Century, many of the paintings have suffered severe and irreversable damage -- not because of vandalism, but because of carbon dioxide and other contaminents brought into the caves by visitors. For this reason many of the caves -- Altamira (first discovered 1879, dated 18,500 to 14,000 BP) Lascaux (first discovered 1940, dated 20,000 to 10,000 BP) , Chauvet (first discovered 1994, dated 30,000 BP) -- have been closed to visitors, and even to most scientists.]

A cave painting
at Lascaux cave in France, dated to 16,000 BP appears to be the earliest known depiction of a constellation (Figure 1). It is painted on the ceiling of the Hall of Bulls, and is one of many images in a panorama that extends around the hall on the walls and ceiling.   Normally such cave paintings would not be associated with constellations, except that in this case there are a series of black spots which appear by their spacing and orientation to represent the constellations Pleiades, Taurus and Orion's belt (Figure 2)[FOOTNOTE: The panorama -- see Figure 4 -- reminds one of the rim of the sky at night. I would not be surprised to learn that the whole panorama depicts figures in the night sky.]. The eye of Taurus is the red giant star Aldebaran. Even more remarkably, the cave painting is clearly a bull (actually an auroch, the extinct ancestor of domestic cattle), which indicates that the constellation's representation as a bull, may date back to 16,000 BP. The tips of the horns are correctly placed to mark the stars ζ = zeta tauri and β = beta (el nath) shown in  Figure 2a and 6.  Figure 3 shows the actual locations of the constellation stars in the night sky. The paintings have the correct relative geometries but rotate counter-clockwise as one moves from Orion to Taurus to Pleiades -- as if the artist is painting by memory from an awkward position on a scaffold, pivoting his body as he paints (Figure 4).

Lascaux constellations painting
Lascaux Cave Painting from the
Chamber of Bulls, Lascaux Cave (17,000 BC)

Identification of Pleiades, Taurus and Orion's Belt
The insets show the actual star configurations.
The stars to the right of Aldebaran are, in counterclockwise order
theta tauri, gamma tauri, delta tauri and epsilon tauri (all red giants)

The Taurus Constellation
Figure 2a
Star map showing the Taurus Constellation
with Pleiades and Orion's belt

Lascaux constellations painting
Star map showing
Pleiades, Aldeberan and Orion's belt

Lascaux Hall of Bulls Panorama
Figure 4
Lascaux Hall of Bulls Panorama
The bull of Figures 1-3 is on the ceiling partially visible at the upper right
Photograph reproduced by courtesy of Musée de Périgord, Periguex, France

The cave paintings at Lascaux and other sites in France (the  most recent find is the Chauvet Cave, discovered in 1994 and dated to 30,000 BP) do not have obvious religious significance, being mostly scenes of the hunt, of nature and other similar subjects -- despite many references to shamaans, rites and magic by the various "scholars" who comment on the work [FOOTNOTE: Paul Johnson in his book Art: A New History states, "There is nothing in these art works as such to suggest religious purpose." There is a modern prejudice (hubris?) that makes the default assumption that such artwork is based on religion and superstition, but that should be resisted unless there is positive evidence for that interpretation. This modern prejudice goes back to books such as James George Frazer's Golden Bough (1890) which has been called "a model of intriguing specificity wed to speculative imagination."].

Another rich source of early artwork is found in the Egyptian temples, funeral crypts and coffins. In my view these depictions -- some very realistic, some fanciful, some whimsical -- are simply that, although Egyptian culture was rife with gods and godlets -- but that doesn't mean that the painters lack a sense of fantasy and humor. For example, consider the sky goddess Nut and earth god Shu that appear on many ancient Egyptian coffins and paintings (Figure 4). Did the Egyptians believe that these are literal gods, or are the stories and depictions of these gods on the par with Kipling's Just-So stories? That is how I view such artistic work as Figure 5. Certainly the Egyptians did worship nature and had many nature gods, but they also used considerable artistic license in depicting them.

Sky goddess Nut and Earth god Shu
The Egyptian Sky goddess Nut and the Earth god Shu
depicted in many burial chambers and coffins

When the book of Job refers to the constellations Pleiades, Orion and the Bear (great dipper), it does not view them as gods. They are constellation patterns with widely accepted and
imaginative names. The astrological and religious attributions to these constellations are almost certainly late additions layered onto pre-existing mnemonic patterns.

    The Zodiac. Given the year to year return of the same constellations, it is natural to identify the particular constellations along the the sun's path on its annual journey
-- the sun's "house" is the constellation that can be seen in the direction of the sunrise, just before dawn, and at sunset. These constellations form the zodiac (the word means "circle of animals"). Nobody knows precisely how this happened in the first instance, but it does seem to be a logical and fully reasonable process.

Some scientific facts fall out automatically -- over a lifetime of careful observation -- and would have been known in pre-history:

    (1) The Sun's path through the fixed star background is always precisely the same from year to year: this is called the ecliptic. The word literally means "line of eclipses" because lunar and solar eclipses occur when the Sun, Moon and Earth all lie in the Earth's orbital plane. Thus the ecliptic traces out the Earth's orbital plane in the background of fixed stars.
In a sidereal yearthe Sun returns to the same zodiac constellation at the same time each year. In particular the constellation at the spring  equinox is the same from year to year, and marks the beginning of the planting season for spring crops. The constellation that houses the Sun at the spring equinox usually heads the zodiac.
    (3) Most stars are fixed stars; that is, they do not move relative to each other. F
ive planets or "wandering stars" and the Moon move relative to the fixed stars. They do not follow the same paths from year to year, but they do always move within about 8° of the ecliptic.
    (4) The field of stars appears to rotate about a fixed location -- the north pole or south pole.

Today we commonly think of these constellations in terms of the mythical heroes of ancient Egyptian, Greek and Babylonian cosmologies, but their true value is not in the supposed influence over mankind narrated in these myths and in astrology, but in their value to measure time.

Some more subtle facts about the Zodiac have to wait for written records taken over many lifetimes, when detailed star maps are made and observed over many years. But these are enough to make the beginnings of a starry timepiece.

The Babylonian Zodiac

The first organized record of the constellations and zodiac is the Babylonian Three Stars Each clay tablets  dated to around 1200 BC. It can be inferred from this record that the constellations go back at least
a thousand years earlier to the Sumerian Akkadian Empire period, 2270-2083 BC, the era of Sargon and the time of the Hebrew patriarch Abraham, when  Ur was a center of civilization. The inference comes about because many of the constellation names in the Babylonian list are Akkadian words. For example, the word "constellation" or "star" in the Babylonian text is  the Akkadian glyph MUL,MUL=Star.  Many current constellation names also trace back to Sumerian sources: Taurus, Leo, Scorpio, Capricorn, Gemini, Cancer.

It is particularly interesting that the head of the Babylonian star list is Pleiades, the
Akkadian glyph MUL.MUL,MUL.MUL = Star of Stars = Pleiades or "star of stars". The name and head position imply that the Pleiades were the constellation at the vernal equinox -- nominally March 21 -- the beginning of the Spring planting season. This was the case around 2300 BC (see the Figure 6), and lends support to the thought that the entire star list may have originated around that time. Since the time of the later Bablylonian star tables, Pleiades and Orion have not been named as Zodiac signs, having been replaced by Aries, Taurus and Gemini.

The book of Job mentions three constellations: Pleiades, Orion and the Bear (Big dipper). The mention of the Pleiades and Orion may hint at an early date for the book -- when the Pleiades were considered the head of the zodiac, i.e. around 2000-2300 BC [FOOTNOTE: But perhaps not, since Zodiac lists tend to be fixed for long periods of time: witness the fact that the astrological zodiac today still associates March with Aries.This was true around 500 BC, but currently the constellation for March is Pisces and will be Aquarius.]. Orion and the Bear are two of the most easily identified constellations in the winter night sky.

Ecliptic and Orion-Pleiades
Figure 6
The Ecliptic showing Pleiades, Taurus and Orion

Precession of the Equinoxes.

Some of the more subtle facts about astronomy had to wait for written records taken over many lifetimes, when detailed star maps could be compared over centuries. One of these facts is that the location of the Sun at the vernal equinox moves along the ecliptic about one degree in 70 years, returning to its initial position after 26,000 years, called the Great Year or Platonic Year[FOOTNOTE: Technically, the use of the term "Platonic year" is a misnomer but is widely used. The "Platonic year" or "perfect year" as defined by Plato is the time for the planets to return to their original positions. The "Great Year"is the time for the constellations to return. But through history, these terms have been confused. The length of the Platonic year is about 16,000 years (?) compared with 25,600 years for the great year. The internet references are very confused about this distinction.]. This is about five times longer than the entire span of recorded history, but it is long enough  so that star catalogs prepared over hundreds of years will show the change.  

The movement of the equinox through the constellations is called "precession of the equinoxes" and is due to the fact that the Earth's axis precesses (much as a spinning top's axis circles around a  central  axis, only of course much slower -- see the figure). The plane of the Earth's orbit doesn't change (so the Ecliptic and the constellations of the Zodiac are unchanged) but the time of the equinox changes. In addition the north star changes. Currently the earth's axis is aligned quite closely with the North star Polaris, but in ancient times that was not the case, and a few thousand years from now, the North star will change again. Even 500 years ago in the days of Chrstopher Columbus, Polaris was a degree further away from the north pole than it is today.


The earliest estimate of the great year was made by Hipparchus (190-130 BC)), based on the small changes in the position of the vernal equinox as recorded in star catalogs since the times of the Babylonians, around 600 BC.  He estimated that it takes about 30,000 years for the Vernal Equinox to cycle through the 12 signs of the zodiac.   This equates to 2,500 years for a Zodiac sign to move to the position of its neighbor.  The modern value for this parameter  is 25,771 years.

At present, the zodiac sign of the vernal equinox, which marks the beginning of Spring, is now just leaving the zodiac constellation Pisces (entering Aquarius). Figure 7 shows the precession between 4,000 BC and 2,000 AD.

Precession of the Equinoxes
Figure 7
Precession of the Equinoxes
4000 BC to 2000 AD

Are the Fixed Stars Really Fixed?

Almost all of the stars visible to the naked eye belong to our own Milky Way galaxy. In the Northern Hemisphere the only exception is the Andromeda galaxy which is a faint haze of stars in the Adromeda constellation. Perhaps one can also see the Orion Cluster, a proto-galaxy (and the nearest birthplace of new stars) in Orion's sword. In the Southern Hemisphere the Magellenic clouds are also galaxies outside the Milky Way.

background of stars appears fixed because of the vast distances to even the nearest stars. In fact, the stars do move, just as our own Solar System moves, but the distances make the stars -- particularly the constellations -- appear to be virtually immobile over long periods of time -- more than the entire span of recorded history. All of the apparent motion of the sun, moon and planets against this background of fixed stars is due to the motions of the earth, moon and planets, and the earth's spin around its axis. A few of the nearest stars have a parallax -- the apparent change in position when viewed at opposite positions on the earth's orbit -- but it is invisible to the naked eye.

As an example, Figure 8 shows the movements of the stars around the Big Dipper (Ursa Major) over 50,000 years. Clearly over this time the constellation is still recognizable. Over all of recorded history -- even up to 30,000 years ago, if one includes the era of cave paintings, the big dipper has looked nearly the same. So, yes, star positions do change, but the vast majority of visible stars have barely changed their position over the entire extent of human history[FOOTNOTE:
See the Big Dipper animation over 200,000 years at the Ohio State University Website.]

Precession of the Equinoxes
Figure 8
Motion of Stars near the Big Dipper

Early Astronomy and Mathematical Formality

Star catalogs and the Ptolemaic System.
The Greek civilization first introduced mathematical formality to the study of Astronomy.  Hipparchus (c. 190 BC – c. 120 BC) was the first to develop and use constructions from spherical trigonometry, and an effective measurement system to record star positions in space -- similar to the present earth-coordinate system of latitudes and longitudes, which he expressed in degrees and minutes of arc. The origin (0,0) was fixed at the position of ?? at the vernal equinox.

By making extensive use of earlier Babylonian star catalogs (lost today), he constructed a star catalog of some 850 stars visible in the night sky. That catalog is lost, or rather it was merged by Ptolemy (c. 90 AD – c. 168 AD) into his own star catalog of 1025 stars (the Almagest). Ptolemy appears to have incorporated the Hipparchus tables by adding 2°40' to the longitude of Hipparchus (1° per century for the 260 years lapse between the tables -- correct value is 1.4° per century) so there was a systematic error of slightly over 1° in Ptolemy's extrapolation from Hipparchus'  tables. This is absolute position error, not relative position error, which is generally on the order of 1-10 arc-minutes (Ptolemy himself considered his tables to be accurate to 10 arc-minutes[FOOTNOTE: N.M. Swerdlow, "Astronomy in the Renaissance" in Christopher Walker, ed., Astronomy Before the Telescope, p.218]).

Ptolemy's  outstanding contribution was to develop a mathematical model of the Solar System which could be used to calculate planet positions. This involved a system of epicycles (Figure 9). This was a mathematical fit to the star catalog data and a method  of calculating past and future positions of the planets. There is no evidence that Ptolemy believed that the planets followed this system of epicycles -- it was a mathematical construction[FOOTNOTE: See the discussion here. Fourier analysis (harmonic analysis) is a modern mathematical equivalent to this -- this expresses general functions as sums of trig functions (sine waves of various frequencies), without any assertion that the trig approximations have an actual underlying reality. Note that a point moving at constant speed along an offset circle traces out a sine wave. The approximation of elliptic paths by Ptolemy's method of epicycles can, as can Fourier methods, match the actual positional data with remarkable accuracy -- and can be made arbitrarily accurate by adding more epicycles.]. It is likely that later "theologians" and "scholars" prior to Copernicus, who had an inaccurate concept of practical mathematics may have credited the Ptolemaic system with a reality that he didn't claim -- much as many antiquarians today assume that the Egyptians accepted the "reality" of their depictions of cosmology.

The Ptolemaic System
Figure 9
Ptolemaic System of epicycles.
Click on the image for animation.
[FOOTNOTE: If the animation doesn't work note that Java is required. Go to the Wikipedia article on epicycles and click on the  "Java simulation of the Ptolemaic System" under the heading "Animated Simulations" at the bottom of the page. The simulation is from at Paul Stoddard's Animated Virtual Planetarium, Northern Illinois University.]

The Copernican Revolution.
  Nicholas Copernicus (1473-1543) replaced the Ptolemaic representation of the Solar System with one in which a rotating Earth and the planets follow circular orbits centered on the Sun (more precisely -- each planet circled around a position centered near to but not exactly at the position of the Sun) -- see Figure 10[FOOTNOTE This is an oversimplification: a thorough discussion of Copernicus' model is in Swerdlow, op cit.]. Copernicus could not dispense entirely with epicycles -- although he used far fewer than Ptolemy.

Copernicus' Solar System
Figure 10
Copernicus' Solar System
from De Revolutionibus Orbium Coelestium (1543)
First Book, Folio 9 Verso
This diagram does not show the epicycles that
Copernicus used to adjust for the apparent speed change over an orbit.

Ideally any system -- Ptolemy's or Copernicus' -- had to fit a number of considerations:
    • The positions
(latitude, longitude) of the planets over time.
          -- These are the primary data of the star catalogs
    • The change in the planet's apparent speed along its orbit.
          -- All astronomers prior to Kepler assumed a constant speed of the planet along its path. Hence the need for epicycles, or orbits offset from the Sun and/or Earth.
    • The change in the planet's brightness, a function of the distance to the planet and -- for inner planets -- the phase of the planet relative to the Sun (analogous to the phases of the Moon).
          -- The total Earth-planet-Sun distance should relate to brightness.

Curiously, Copernicus still needed epicycles in his model, although fewer than in the Ptolemaic system. In his day the position of the Roman Catholic Church was that the Earth, was the center of the universe. Copernicus avoided conflict with the religious authorities by presenting his calculations as a mathematical tool that was easier to compute than the method of Ptolemy, without (at least publically) asserting that his model was to be equated with reality[FOOTNOTE: the phases of Venus are only visible with a telescope, but the related changes in brightness could be observed with the naked eye.]. Copernicus' major work, de Revolutionibus orbium coelestium was published in the last year of his life at the urging and assistance of  Joachim Rheticus who approached Copernicus at the urging of Philipp Melanchton, an associate of Martin Luther.

As a matter of fact, the Copernicus model was less accurate than Ptolemy's system, which by this time, had been tweaked and tested against astronomical observations for almost 1500 years.

Tycho Brahe and Johannes Kepler
. Even with Copernicus' use of epicycles, and measurement errors of several arc-minutes, it was hard to match up the orbits with the observed data. All solar system models had systematic errors along the orbital paths.

Tycho Brahe's (1546-1601) life mission was to make more accurate star charts. Over many years of observation, he constructed accurate star catalogs with (relative) errors of 1 arc-minute or slightly less. These accurate tables showed that both Ptolemy's and Copernicus' models -- even with Copernicus' epicycles and off-sets -- had systematic errors. The worst case was the orbit of Mars.

Johannes Kepler (1571-1630) attempted to use Tycho Brahe's data to infer a more accurate model for the solar system. Regardless of his painstaking effort, Kepler could not avoid systematic errors of up to 3 minutes -- well beyond the accuracy of Brahe's tables. After years of effort Kepler solved problem by using elliptical planetary orbits with the Sun located at one of the foci and on which the speed of the planet varied with distance from the Sun. He established the three laws of planetary motion that form the foundation for modern orbital calculations, and are known as Kepler's laws. He published these in his treatise Astronomia Nova in 1609, just one year before Galileo transformed astronomy with his telescopic observations, including the discovery of the Galilean moons orbiting Jupiter. About 60 years later, Isaac Newton showed that these three laws are equivalent to his law of gravitational attraction which varies inversely with the square of the distance between the planet and the Sun. The remarkable thing is that Kepler did all this using only naked-eye observations. After he came up with his (correct) model for planetary orbits, he produced the Rudolphine star catalog in 1627. The calculations needed to produce this table were greatly simplified by the discovery and publication of logarithmic tables by John Napier in 1614, with improved tables by Henry Briggs in the following decade.

Kepler's methodology is good for projecting planetary movements into the distant past and future, and is especially useful for predicting lunar and solar eclipses. Modern astronomy programs are based on the Keplerian laws, with adjustments for the Earth's precession and other small variations, and have claimed accuracies of under 10 arc-seconds for projections several thousand years in the past or future.

Astronomy in the Age of Science.

Perhaps the most astonishing advance in Astronomy came with the publication of Isaac Newton's Philosophiæ Naturalis Principia Mathematica, which laid down the foundations of modern physics and wedded progress in physics with mathematics, particularly the calculus. In one fell swoop, science broke the shakles of earth-bound existence, because Newton's physics came to be seen (along with the addition of relativity and quantum mechanics) as applicable throughout the entire universe, and the universe itself was seen to follow precise natural laws, giving an unexpected new illumination of the universe as a precision timekeeper.

Summary: The Silent Speech in Astronomy. [TODO]

There are several instances of God's provision of Silent Speech in this short account.

    • The preservation of historical records is a gracious gift that God has granted to us so that we can learn details of the past that we have no a-priori right to expect. In some instances -- such as the cave paintings -- the full implications may still remain to be worked out.  It is clear that we had no right to expect such graphic details to be preserved for thousands of years, and have clear evidence of the tenuous and vanishing nature of the record, which requires special care to avoid complete loss. It is providential that these records were not recovered centuries ago -- there is no logical reason why they were not -- and in that event they would have been lost and perhaps  been erased from our conscious knowledge, or relegated to fantastic folklore from the distant past.

    • The ability to express nature in mathematical terms that can be evaluated in closed form, is another gift of God. This gets to Einstein's remark about how incomprehensible it is that the universe  is at all comprehensible[FOOTNOTE: See George V. Coyne and Michael Heller, A Comprehensible Universe]. Any mathematician should know that very little of mathematics can be evaluated in terms of analytical expressions. For example, the normal expectation would be that trajectories of planets and stars would require solution of the notoriously difficult many-body problem. Until the very recent age of powerful computers, tackling such problems would have been utterly impossible. Would the computer age ever have dawned if not for the ability to make significant advances using simplified models of reality?


The Zodiac
The Zodiac is the band in which the Sun and Planets move over the course of the year. The journey of the Sun through this band of stars passes succesively through the signs (constellations) of the zodiac along a path called the ecliptic. A sidereal year is the time required for the Sun to complete the circuit through the Zodiac. At the vernal equinox (around March 21), the length of the day equals the length of the night.  This is the beginning of the Jewish religious calendar. The Jewish secular calendar begins at the autumnal equinox (around September 21).

There is indirect, but plausible, evidence that the Babylonian (Sumerian) Zodiac was first formulated at the time when the Sun was located in the Pleiades (see the figure below) during the Vernal equinox.

Ecliptic and Orion-Pleiades

This occurred around 2300 BC. The Pleiades are called in Sumerian "MUL.MUL" or the "star of stars" and stands at the head of their Zodiac, so it is reasonable to infer that the zodiac was established around that time.

Sumerian "MUL.MUL"

It is interesting that the book of Job 38:31-32 mentions three constellations: Orion, Pleiades, and The Bear. The Bear, of course, marks the North Star. Pleiades and Orion are in  the Sumerian Zodiac, with Pleiades in the prominent position. This fact may indicate that Job, as well as the Sumerian Zodiac date to around 2,000-2,500 BC. By the time of the Babylonian Zodiac (around 500 BC), the Earth's precession has put Aries, which heads the Babylonian Zodiac, in the principal position, and both Pleiades and Orion are omitted from the Zodiac. The twelve signs of the Babylonian zodiac are still used today.

Astrologers use the Babylonian zodiac, without adjustment for the earth's precession. This is called the tropical zodiac and is headed by Aries, which is associated with March 21-April 20.  The sidereal zodiac follows the earth's precession. By the turn of the calendar in 1 AD the equinox entered the  Pisces constellation, and currently (2,000 AD) the equinox is at the trailing edge of Pisces and moving towards Aquarius.

The following illustration shows the sidereal zodiac with the 2010 calendar. The Vernal equinox occurs on March 20.

Zodiac - Calendar 2010
Constellations of the Zodiac with the calendar for 2010 AD

The following is another depiction of the Ecliptic and the location of the Vernal Equinox between 4000 BC and 2500 AD.

Precession of the Equinoxes 4000 BC to 2500 AD.

The Date of Jesus' Crucifixion

One consequence of the extreme precision of astronomical calculations is that it is possible to determine with good precision the exact appearance of the heavens at any particular date. The maximum positional error for the solar system and fixed stars between 2,000 BC and 2,000 AD is about 20 seconds in time and a few arc-seconds in position. Readily available astronomy programs, such as Starry Night, can compute positions and movements for any time in this range on a home computer, with a variety of display options.

Frederick A. Larson used astronomy software to investigate the events surrounding Jesus' birth and death. The documentary dvd Bethlehem Star presents the conclusions that he came to in this investigation. I found the discussion of Jesus' crucifixion to be particularly interesting.  Larson (with others) argues that there was a lunar eclipse on the day of Jesus' crucifixion based on the reference to a "blood moon" in Acts 2:20, and that the crucifixion occurred on a Friday that was also the time of the Jewish Passover celebration.  This leads to the conclusion that Jesus' Crucifixion occurred on April 3, 33 AD, a date that is arrived at by a number of lines of argument,  from the time of Isaac Newton to the present -- see the Wikipedia article on the Crucifixion of Jesus. Astronomy programs confirm that a lunar eclipse occurred on this date at about 3 PM and that it was visible in Jerusalem for about 30 minutes after sunset.  Larson also notes that on this date, at the time of the eclipse, the Sun was located in Aries, in the vicinity of the constellation's heart (or liver?), and draws some interesting conclusions from this.

The following is the calendar for 33 AD. The Vernal equinox fell on March 20, and the crucifixion was on Friday, April 3, just before passover celebration on that year, that same evening. There was a lunar eclipse at 3 PM that afternoon, the end of which was visible at Jerusalem for about 30 minutes after Sunset, and appeared as a "blood moon" mentioned by the Apostle Peter in Acts 2:20.  On this date the Sun was in or near the heart of Aries.

Zodiac Calendar 33 AD
Constellations of the Zodiac with the calendar for 33 AD

Accuracy of Positional Measurements recorded in Star Catalogs
Star Catalog
Time Period
Ptolemy's Almagest (naked eye)
c. 200 AD
3-8 arc-minute
some systematic errors due in part to adjustments from Hipparches' sky catalogs. Ptolemy considered the (relative) accuracy of his tables at 10 arc-minutes.
Copernicus'  De Revolutionibus  (naked eye)
1543 AD
3-8 arc-minute
Used Ptolemy's tables, corrected and updated in the intervening years by many (mostly moslem) scientists.
Tycho Brahe
1590 AD
0.5 to 1 arc-minute (relative)
naked-eye measurements.
Circular approximation to Mercury's orbit had maximum systematic errors of up to 3 minutes.
Johannes Kepler
1609 AD
0.5 to 1 arc-minute Discovery of the Elliptical orbits of the planets removed all systematic errors. Fitting the Mars data with the Brahe/Copernican models showed errors up to 8 arc-minute.
Galileo Galilei
1610 AD
3 arc-seconds
Galileo's early telescope was able to resolve satellites of Jupiter that were separated by about 10 arc-seconds. Inherent error due to scintillation of the atmosphere is about ?? arc-seconds.
Planet diameters are: Jupiter - 20 to 40 arc-sec; Venus - 10 to 60 arc-sec; see
Friedrich Bessel (First parallax msmt of 61 Cygni)

First star parallax measured -- 0.3 arc-seconds for star 61 Cygni (distance 11.43 ly). Required precision timepiece(?)
Harrison's regulator clock 1790?
Atmospheric smearing

Atmospheric smearing of starlight is about 0.5 arc-second.
Twinkling (scintillation) can be 0.4 arc-second at clear, high altitude. Overall, a 1 arc-second smearing is considered good.  This affects spectral analysis of starlight as well as pointing.
Hubble Space Telescope
Hipparchus satellite

Present day accuracy 0.001 arc-second
Very Long Baseline Interferometer (VLBI) antenna arrays 2010?
10-6 arc-second Direct geometric distance measurements for certain classes of galaxies, out to 25 million light-years
(2009 Measurement of Galaxy NGC 4258 at 23.5x106 light-years ± 7%)


1, The width of the Moon is about 29.5 to 33.5 arc-minutes. The width of the Sun is about 31.6 to 32.7 arc-minutes. During a full solar eclipse the Sun's corona is visible over the entire perimeter. It remains complete for only a few seconds.
Earth's rotation will cause a star on the Ecliptic to move about 1 arc-minute in 4 seconds, so precise measurements of absolute position were exceedingly difficult and required accurate and reliable clocks, which did not exist until after Harrison's invention of the regulator clock. Tycho Brahe achieved accuracies of 0.5 arc-minutes in relative (star to star) position measurements averaged over a number of observations.
3. Parallax measurements using large baselines require very precise clocks. Cesium atomic clocks (accuracy ??) are used for ???

Direct measurement of Astronomical Distances by Parallax.  Parallax is the direct geometric measurement of changes in the direction of a stellar object when viewed at the extremes of a very long baseline. The first parallax measurements were done in the 1800s to measure the distance to the nearest stars. The accuracy and practical maximum distance that can be measured in this way depends on the length of the baseline and the precision of the angular measurement. The most accurate positioning at present is done in radio frequency astronomy using the Very Long Baseline Interferometer (VLBI) antenna arrays which receive signals from widely separated locations on the Earth. Of course the measurements depend on stellar objects that have suitable coherent radiations in these frequencies. The potential accuracy of current and planned VLBA precision is 10-6 arcseconds which equates to direct distance measurements out to 25 million lightyears. Recently, the galaxy NGC 4258 was measured at  23.5x 106 lightyears ± 7%, based on direct geometric triangulation. According to NASA, VLBI Radio Interferometry is hundreds of times more detailed than the Hubble Space Telescope and the dedicated Hipparcos parallax-measuring satellite.

The Goddard Space Flight Center  VLBI Summary says "VLBI is a geometric technique: it measures the time difference between the arrival at two Earth-based antennas of a radio wavefront emitted by a distant quasar. Using large numbers of time difference measurements from many quasars observed with a global network of antennas, VLBI determines the inertial reference frame defined by the quasars and simultaneously the precise positions of the antennas. Because the time difference measurements are precise to a few picoseconds, VLBI determines the relative positions of the antennas to a few millimeters and the quasar positions to fractions of a milliarcsecond. Since the antennas are fixed to the Earth, their locations track the instantaneous orientation of the Earth in the inertial reference frame."

Reference on various cosmological models and computer simulations.



The Platonic Year:
Plato Timaeus 39d. Plato called  this the "perfect year" when the Sun, Moon and all of the planets return to their original alignment. "And God lighted a fire in the second orbit from the earth which is called the sun, to give light over the whole heaven, and to teach intelligent beings that knowledge of number which is derived from the revolution of the same.  Thus arose day and night, which are the periods of the most intelligent nature; a month is created by the revolution of the moon, a year by that of the sun.  Other periods of wonderful length and complexity are not observed by men in general; there is moreover a cycle or perfect year at the completion of which they all meet and coincide."



Christopher Walker, Ed. Astronomy before the Telescope, St. Martin's Press, 1996.


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