The diagram depicts that a streaming count of lunar weeks (or lunar quarters) can effectively be used to define a cycle of 50 years. It seems that a jubilee cycle (of 50 years) can be counted out in segments of 7 years using a fixed count of lunar weeks. (For additional information, refer to Chapter One).
It is here significant that the cited jubilee calendar of lunar weeks inherently would represent a fully perfect solar-year interface if any one--or a combination--of the following spin-orbital configurations did exist:
- The synodic month was equal to a target rate of 29.53043 days.
At the rate of 29.53043 days per synodic month each lunar quarter or lunar week can be predicted to elapse in 7.38261 solar days. It then follows that each jubilee-calendar year which contains 49.4733333 lunar weeks (on the average) would be equivalent to 365.2422 days. (Note that 49.47333 lunar weeks per calendar year times 7.3826075 solar days per lunar week is equal to 365.2422 days per solar year). Thus, at the rate of 29.53043 days per synodic month, the length of each jubilee-calendar year would exactly correspond with the length of the solar year of 365.2422 solar days.
What is here remarkable is that the Earth-Moon can actually be predicted--in average time--to define the cited target rate of 29.53043 solar days for the synodic month. A prior shift in the definition of the spin-orbits (a trend) toward the cited target rate (29.53043 days per synodic month) can perhaps be recited from the record of very recent bivalve fossils. This indication from the fossil record of a recent shift toward the target definition of 29.53043 days is evident from the following diagram:
____________________________________________________________
-- DAYS IN THE SYNODIC MONTH --
From 11,000 years to 1,800,000 Years Ago
(Based Upon Bivalve Fossil Data)
1. = experimental value, interpreted as (days/month),
(Berry and Barker 1975).
2. = experimental value, interpreted as (days/month),
(Pannella 1972 and Thompson 1968).
____________________________________________________________
PLEISTOCENE FOSSILS (-11,000 to -1,800,000 Years)
1 = 29.5 Days Sandstone near Punta Cholla, Sonora
1 = 29.5 Days Palos Verdes Formation, California
1 = 29.6 Days San Pedro Sandstone, California
2 = 29.1 Days YPM-IP-26310
2 = 29.6 Days YPM-IP-26307
2 = 29.0 Days YPM-IP-26305
2 = 29.3 Days YPM-IP-26312
2 = 29.2 Days YPM-IP-26309
2 = 29.1 Days YPM-IP-26304
2 = 29.4 Days YPM-IP-28493
____________________________________________________________
The definition of the synodic month when projected into the prehistoric past can thus be interpreted to perhaps come closer to the target rate of 29.53043 solar days.
- The solar year was equal to a target rate of 365.2442 days.
If the solar year elapsed in 365.2442 days then a perfect interface would inherently exist between the modern lunar week of 7.38265 days--where 49.4733333 lunar weeks at this rate equals 365.2442 days.
It is here significant that Earth's spin can be recited to lose about 0.0017 seconds per century on average. This means--through some time range of the prehistoric past--the solar year was once equal to the cited target rate of 365.2442 days. The time of perfect interface--based upon the cited slowing rate of 0.0017 seconds per century--can be predicted to have occurred some 292 centuries ago.
Note that because Earth's spin loses 0.0017 seconds each century, and because the rate of the solar year is 365.24 days then the definition of the solar year is changing at the rate of 0.6209 spin-seconds for each century. It follows that the target rate of the solar year (365.2442 days) minus the current rate of the solar year (365.2422 days) is equal to a net change of 181.44 spin-seconds. This set of assumptions and parameters then indicates that at 292 centuries ago the solar year was equal to 365.2442 solar days. (Note 181.44 spin-seconds divided by 0.6209 seconds per century is equal to 292 centuries).
Of course, the time range during which the cited jubilee calendar might average out to exactly correspond with the rate of the solar year cannot explicitly or exactly be determined. It is however apparent that a time range extending toward the prehistoric past may be indicated.
The possibility of Supernatural regulation
It is possible to interpret--as cited above--that during a range of prior centuries the lunar week did perfectly interface with the rate of the solar year. A perfect interface would have occurred in the past on the basis of indicated shifts (or shift trends) away from the current spin-orbital configuration.
The indicated (perfect) lunar week interface seems significant in the regard that a calendar of lunar weeks appears to exactly overlay a jubilee time grid (as diagrammed).
The indication of functional time design makes it possible to interpret that the spin-orbits are experiencing (or have experienced) a degree of Supernatural regulation. After all, the definition of a perfect jubilee interface is very unusual. (Can it possibly be that the spin-orbits have been designed to conform with a determined time plan or schedule?)
An explicit description of the cited jubilee interface can be found in the Bible Book of Leviticus--and in other ancient literature! For additional information, refer to the online publication entitled: 'A Significant Jubilee Cycle'.
Ultimately, jubilee time design and the associated precision limits (once perfect?) tends to indicate that the Genesis account of a perfectly configured Earth-Moon system is within the realm of possibility. Essentially, an intelligently designed lunar-based progression can be interpreted to have existed in satisfactory interface with the passage of each annual cycle across a number of millennia in the past!
For pertinent information that points to the possibility that the spin-orbital configuration has remained relatively unchanged for perhaps millions of years, refer to the online document entitled: 'The Slowing Spin of the Earth'.
The age of the Earth-Moon
The cited interpretation of an enduring jubilee schedule does not have to mean that the age of the Earth-Moon might be younger than several thousand years.
In fact, there is geological evidence which seems to show that the Earth-Moon could be extremely old (and much, much older than a mere number of millennia).
Prior differences in the spin-orbital rates can be recognized from the record of coral and bivalve fossils--as cited--where daily growth leaves a record (like tree growth rings).
The fossil record ultimately indicates that a rather different Earth-Moon configuration (or configurations) has (or have) existed in the distant past. In the older Earth-Moon system (or systems), the day count appears to have been greater for the annual cycle (and also for the lunar period). As an example, the record of mollusk fossils interpreted to have once lived 65 million years ago indicate that the synodic period did then elapse in a cycle of about 30 days.
For additional information concerning the fossil record and possible evidence of a prior configuration (or configurations) of the Earth-Moon, refer to the online document entitled: 'The Slowing Spin of the Earth'.
An enduring jubilee schedule?
As is cited throughout previous sections and chapters, it seems possible to interpret that the Earth-Moon inherently defines a unique jubilee schedule. Clearly, the cited cross-reference between the lunar week and the jubilee schedule is a very durable interface.
What here is remarkable is that the Bible appears to contain an explicit description of the jubilee-time cycle. For additional information of the biblical description of 7 sets of 7 years (plus 1 year), refer to the online document: 'The Jubilee Time Cycle'.
_________________________________________________________
CHAPTER FIVE
A Functionally Composed System
Modern knowledge of the composition of the Earth-Moon system raises a number of questions concerning the ultimate origin of this system. The size and relative position of the Earth and the Moon, their material makeup, the tilt of the Earth, the synchronized rotational rate of the Moon, and the unique lunar orbit all remain to be--at least to some degree--science mysteries.
What you see is...
When viewed from the Earth, the Sun and the planets appear to rise and set (always from east to west).
The Moon appears to shine, but in actuality its surface is reflecting light from the Sun. The "shining" portion of the lunar surface--as viewed from the Earth--changes night-after-night (as the illuminated portion of the Moon's surface waxes and wanes according to a periodic cycle known as the lunar-month cycle).
As the Moon celebrates light from the Sun--in the waxing half of the lunar-month cycle--the lunar surface increases in luminance for two weeks before becoming wholly illuminated (at the full phase). In the waning half of the lunar-month cycle, the lunar surface subsequently decreases in luminance for two weeks before becoming wholly dark (at the new phase).
The lunar-month cycle--referred to as the synodic month--completes in 29.5 days. The actual obit of the Moon around the Earth is called the sidereal month and completes in 27.3 days. The synodic month is longer than the sidereal month because the Earth is moving around the Sun and the relative positions of Earth and the Sun throughout 27 days are altered, and consequently the Moon must travel farther in order to come again into alignment (between the Earth and the Sun). Thus, from the perspective of an observer stationed on the Earth, the synodic month, or lunar month (of 29.5 days) is the apparent or perceived lunar cycle and is therefore significant to the observer.
It is significant that the annual cycle passes through four distinct seasons (in each solar cycle), and likewise, the lunar-month cycle passes through four distinct quarter phases. The four phases of the lunar-month cycle are: (1) New phase; (2) First-quarter phase; (3) Full phase; and: (4) Last-quarter phase.
The lunar-month cycle first begins when the Moon moves closest to the Sun. At this time the Moon appears to be dark (with no portion of its surface reflecting any light from the Sun). The Moon--as viewed from the Earth--is at its new phase on this special day. Night-after-night more of the crescent shaped Moon is illuminated as it appears after dusk higher-and-higher in the western sky. After one week of waxing, the Moon--at dusk--appears directly overhead between the western and eastern horizons. At this time, the Moon arrives at its distinct first-quarter phase. At the first-quarter phase, the Moon is no longer crescent shaped, and it appears one-half illuminated (exactly like the letter 'D'). Following the first-quarter phase, the Moon, night-after-night, continues to wax in luminance and at dusk it appears closer and closer to the eastern horizon. Seven days following the first-quarter phase, the Moon appears on the eastern horizon at dusk, and its surface now appears wholly illuminated (the full phase). When the Moon is fully illuminated (the full phase), the Moon appears between the eastern and western horizons for an entire evening of viewing. After the unique full phase, the Moon begins to wane and--night-after-night--less of the Moon is illuminated. Also, the Moon rises from the eastern horizon about fifty minutes later evening-after-evening. After a week of waning, the Moon arrives at its distinct third-quarter phase. At this time, the Moon again appears one-half illuminated but the illuminated half appears in reverse from the first-quarter phase (like a backwards letter 'D'). At the third-quarter phase, the Moon doesn't rise from the eastern horizon until the middle of the nighttime. Following the third-quarter phase, the Moon again becomes crescent shaped, and less-and-less of the crescent shaped Moon becomes illuminated as it continues to wane night-after-night. Seven days following the third-quarter phase (or the last-quarter phase), the Moon arrives once again at its special new phase.
The four distinct quarter phases of the Moon can be predicted to appear throughout the four seasons of the year (as described below):
- New phase (rides high in sky in summer and low in winter, and it reaches an intermediate height in spring and fall).
- First-quarter phase (rides low in the fall and high in the spring, and it takes a middle course during summer and winter).
- Full phase (rides low in summer, the same as the Sun at noon in midwinter; and rides high in winter, comparable with that of the Sun at noon in the summer; and it takes an intermediate height in spring and fall).
- Last-quarter phase or third-quarter phase (rides high in the fall and low in the spring, and it follows an intermediate height in summer and winter).
The significance of Earth's environment
As is cited above, processes which are apparent to an observer stationed upon the Earth--such as day and night, lunar phases, lunar months, seasons, and annual cycles--may not be very apparent to an observer stationed in space (and from the perspective of an observer stationed in space, what is real in the solar system--such as the size of the Sun and Moon, sidereal days, sidereal months, and sidereal years--would be perceived very differently than to an observer stationed on the Earth).
Subsequent paragraphs and sections will then attempt to show more of how significant Earth's environment appears to be for interpreting the apparent Moon and Sun.
As an example, the Earth's rotational axis happens to be tilted at 23.5 degrees relative to the Sun's orbit. As the Earth orbits around the Sun, an Earth's resident experiences seasonal differences due to the cited 23.5 degree tilt.
Another example of the significance of Earth's environment concerns the Moon's apparent diameter--where, from the Earth, the Moon appears to have the same size diameter as the Sun's diameter. Essentially, to an observer stationed on the Earth, both orbs (the Sun and the Moon) appear to have the same angular size (of 0.5 degrees).
Equal angular sizes--perceivable only to an observer stationed on the Earth--seems to reflect that both the Sun and the Moon are specifically positioned (relative to the Earth).
The phenomenon of equal Moon and Sun sizes--whereby both orbs appear to have the same angular size--is integral in the periodic formation of a solar eclipse. It is here significant that the orbit of the Moon happens to be tilted at only 5 degrees with the Sun. The peculiar angle of the Moon orbit (in close alignment with the Sun) is ultimately necessary for the formation of a solar eclipse on the Earth. (If the orbit of the Moon did not closely align with the Sun then the Moon would never move into direct position between the Sun and the Earth; and consequently, a solar eclipse would never occur).
The Earth/Moon/Sun configuration is such that solar eclipses can only occur at the appearance of the new phase of the Moon, and lunar eclipses can only occur at the appearance of the full phase of Moon. The combined number of eclipses (including partial eclipses) of the Sun and the Moon cannot be less than two, or be more than seven, in a calendar year. Solar eclipses repeat their cycle every 223 lunar months.
It is then most unusual that in order for a total eclipse of the Sun to be observable from the Earth, the Moon's apparent diameter must equal or exceed the Sun's apparent diameter (and this is so--as explained above). In addition, the angle of the Moon's orbit must uniquely align with Earth's orbital plane around the Sun (and this also is so!).
In summary, the formation of a solar eclipse appears to be unique. This phenomenon requires a somewhat rare combination of diameter sizes, relative positions, and tilt of orbits. This amazing combination happens to exist--even in concert with the 23.5 degree tilt of the Earth's axis.
Of possible significance to a study of functional time design is that the cited saros cycle of 223 synodic months can effectively be metered out using a lunar-weeks count (or a lunar-quarter count) of 99 times 9 plus 1.
The Moon's rotational rate
A most remarkable mystery concerns the Moon and its rotational period.
The sidereal orbital period of the Moon around the Earth completes in 27.321666 days while the rotational period of the Moon also completes in 27.321666 days!
Essential, the Moon rotates once upon its axis every time it orbits around the Earth.
This means that as the Moon progresses throughout its orbit about the Earth the same side of the Moon shows toward the Earth at all times. (If the Moon did not rotate upon its axis in synchronization with its orbit then its opposite side would eventually revolve into view from the Earth).
Due to the Moon's synchronized orbit and rotation, only about 59 percent of its surface is ever visible from the Earth. (Note that a bit more then one-half of the normal face of the Moon is visible throughout time because of the Moon's slightly elliptical orbit). This tipping face of the Moon is known as "libration in longitude" and as "libration in latitude"--where over a long period of time "libration" permits the viewer to see a little bit farther around the edges of the normal face of the Moon.
It isn't known just why the Moon rotates in correspondence with a synchronized orbital rate but it is possible that the cited synchronization is the result of Earth's gravitational pull--where the diameter of the Moon is estimated to be bulged toward the Earth (by the amount of about one-third mile).
This unique Earth-Moon arrangement--where the Moon perpetually faces the Earth--is a facet of considerable wonderment. Here, a mysterious tie or connection seems to exists between the Earth and the shining Moon--which perpetually faces the Earth in its continuous orbit.
Moon geography
The geography of the Moon consists of level plains, valleys, and mountain peaks (similar to those on the Earth) but it possesses many geological features which are different.
The features viewed as "the man in the Moon" are a combination of craters, mountain peaks, deep narrow valleys, and level plains, or maria. The largest of the maria is... about 700 miles in diameter. There are some 20 other prominent maria on the side of the Moon that faces the Earth... The maria are surrounded by huge mountains... with peaks up to 30,000 feet. Tens of thousands of craters are scattered over the Moon's surface, often overlapping one another... [Some] craters have rays. These are light-hued lines radiating from the craters like the spokes of a wheel. Some rays are more than 1,000 miles long. None is more than about 12 miles wide... The large craters range from less than a mile to nearly 150 miles in diameter. Like the maria, they are surrounded by high peaks. There are more than a thousand deep valleys, called rills, or clefts, on the Moon. They are 10 to 300 miles long and 2 miles or less wide... depths are unknown... During a solar eclipse, Sunlight shining down valleys on the edge of the Moon may form a circle of bright points known as Baily's beads... (Compton's Encyclopedia, 1995).
The geography of the Moon is somewhat unique in the regard that the near side of the Moon (or the side of the Moon that continuously faces the Earth) has geological features which differ from those of the far side of the Moon (or the side of the Moon that perpetually faces away from the Earth).
A number of 1 to 5,000,000 scale lunar maps (both shaded relief maps and geologic maps), are available. (Maps can be ordered from USGS Information Services).
Most unusual is that the far side of the Moon lacks the large flat places (or the maria) that appear on the near side of the Moon.
The largest flat spot on the Moon is known as Mare Imbrium (Sea of Rains). This flat place happens to be about 1200 km (or 750 miles) wide. This huge flat place, and a number of other prominent features, can be viewed and recognized from the Earth without the aid of magnified viewing.
Another facet about the unusual geography of the Moon is that the far side of the Moon is lighter colored.
Thus, the features that appear on the near side of the Moon--or the features that can be viewed from the Earth--are somewhat unusual in comparison with those that cannot be seen on the far side of the Moon.
The Earth-Moon arrangement can be recognized to be unusual. In its ongoing celebration of light from the Sun, not only does the same side of the Moon perpetually face the Earth but the features of the Moon that can be viewed from the Earth appear to be unique.
The size and orbit of the Moon
The Moon has a large comparative size relative to the size of the Earth--where the Earth is almost 8,000 miles in diameter, and the Moon's diameter is some 2,160 miles. The size of the Moon is therefore about one-fourth the diameter of the Earth, and this comparative size is larger than for any of the other planets in our solar system.
The Moon is not as dense as the Earth (about 3/5 as dense), and it only has about 1/81 the mass of the Earth.
The Moon's diameter is only very slightly enlarged (by only one-third mile), and this implies that the Moon is solid below the surface (otherwise gravity would have produced a far greater effect upon its diameter).
The large comparative size of the Moon and its nearness to Earth affects tides on the Earth (which are largely caused by the pull of the Moon--rather than the pull of the Sun). The ratio of the tide-raising pull of the Moon to that of the Sun is 11 to 5.
The Sun tends to pull the Moon away from the Earth (when the Moon is between the Earth and the Sun) and the Sun tends to pull the Moon toward the Earth (when the Moon is on the far side of the Earth). The effects of this pull are called perturbations.
The orbit of the Moon is approximately circular. It is--however--slightly elliptical (221,600 miles at perigee, and 252,950 miles at apogee). At perigee the Moon is nearest the Earth, and when it reaches apogee the Moon is the most distant--where these exact distances vary from month to month.
The Moon's orbit does not align with the Earth's equator, but rather aligns more closely with the Earth's path around the Sun (the ecliptic)--where it intersects the plane of the ecliptic at an angle of only 5 degrees.
The two points at which the Moon each month crosses the plane of the ecliptic are called the lunar nodes.
The orbit of the Moon is a bit complicated in that it does not remain in a completely flat plane. Instead its orbital plane oscillates slowly. This movement is sometimes called the regression of the nodes, since the nodes move constantly westward around the ecliptic. A full cycle of oscillation requires about 230 months (or 18.61 years) to entirely complete.
Of possible significance to a study of functional time design is that the Moon inherently rises at a rate that is about 50 minutes slower than the rate of the solar day (a rate equal to 1.03505 days on the average). A time span of 230 synodic months can thus effectively be metered out in correspondence with a count of 9 times 9 times 9 times 9 rises plus 1 rise (or 6562 rises).
Due to the oscillation, the Moon in some years ranges farther north or south in the sky, and this oscillation ultimately accounts for the occurrences of eclipses.
The nearly circular orbit of the Moon is somewhat of a science mystery. The close proximity of this orbit to the Earth cannot be explained purely through a capture process... as if the Moon were somehow captured into Earth's orbit. Essentially, computer simulations indicate that the Earth isn't large enough to capture and hold a large Moon. (Even if the Moon were somehow captured and held, it is unlikely that a close circular orbit of the current angular momentum would result. It seems that during the process of a capture the Moon would simply crash into the Earth).
The origin of the Earth-Moon system
A number of ideas have been set forth to explain the composition and configuration of the Earth-Moon system.
One of the popular early theories attempted to document the Moon as a world that formed in Earth's orbit (simultaneously as the Earth formed). However, based largely upon information gained during the latter part of the twentieth century, it now seems that the lunar and the terrestrial histories have been quite different. (The Moon has been discovered to be less dense than the Earth... and it seems to be lacking an inner core of iron--as does the Earth).
Another hypothesis has been that the Moon was captured into orbit around the Earth. This theory appears to still be under investigation by some researchers; however, this respective theory no longer represents the mainstream view. It is believed that the Moon could not have been captured for the following primary reasons:
- The Moon's orbit is in close proximity to the Earth.
- Computer simulations indicate that capture or condensation could not produce the nearly circular orbits of the Earth and the Moon.
- Capture or condensation ideas do not explain why the Earth's axis is tipped 23.5 degrees.
- It is now known that lunar rocks have a strong similarity to materials found near the Earth's surface, and it seems unlikely that this material originated from somewhere else in space.
Another theory has investigated the possibility that in early stages the Earth flung off the Moon. However, studies by astrophysicists indicate that the escape of the Moon from the Earth is improbable (as it is most difficult to find mechanical processes by which an object such as the Moon could be removed from the Earth).
Throughout the last two and one-half decades, a new theory--the giant impact hypothesis--has grown in popularity. This theory is that the Moon was created when the primal Earth was hit by a huge fast moving body. (The Earth is believed to have been hit a glancing strike from a body larger than the size of Mars).
According to the giant impact hypothesis, an off-center strike was necessary to cast-off (or gouge-out) enough of the Earth's outer material to form the Moon. This glancing collision ejected Earth's material at speeds exceeding Earth's escape velocity (or 25,000 mph). Following this raking-off of the Earth's material, the large impacting body fragmented, and some of the cast-out material eventually formed a Moon in Earth's orbit.
The giant impact hypothesis is perhaps the best of all the theories to explain the near orbit of the Moon.
Based upon computer simulations, it seems that an off-center strike could have cast off enough of the Earth's outer material to form the Moon in close proximity to the Earth (and this explains the near orbit). This blow could also have produced about 18 degrees of the 23.5 degree tilt of the Earth (but subsequent impacts are required to ultimately achieve the additional 5 degrees of tilt).
A giant impact, if actually true, means that the Moon is composed from outer material from the Earth, and this is in part supported by modern knowledge of the composition of the Moon--which indicates the inner-core of the Earth is more dense than the Moon.
The giant impact hypothesis throughout recent months and years is coming under more serious investigation. The idea seems to falter in that--while the density of the lunar material is approximately the same as the Earth's outer material--the ratios of rare materials seem to be wrong (and there are other problems).
Essentially, the riddle of the Moon's origin continues to be debated. A plausible theory must somehow account for the Moon's close orbit, synchronized rotation, angular momentum, composition, and its large size relative to the Earth's.
While the giant impact hypothesis is perhaps the best idea to date, this theory of a raked-off Moon doesn't completely explain all of the mechanical and material makeup of Earth-Moon system.
The best theory to account for the origin of the Moon is probably the giant impact theory. However, in order to account for the Moon's origin, a sequence of the following processes is required:
- A "raking-off" of Earth's outer material.
- The "formation" of a round Moon.
- A "fine-tuning" (to produce additional tilt of the Earth's axis).
- A "refinement" of the material makeup of the Moon (which is similar to the Earth's outer material--but not quite).
Can it be possible that the processes required to create the Earth-Moon are reflective of the actions of a Creator rather than reflective of the results of a giant impact?
A functionally composed system?
From the perspective of an observer on the Earth, rates of days, months, and years can be recognized to all interrelate together--as has been shown in the previously presented Chapter One.
In addition to the cited definition of interrelated time structures, other plausible examples of functional design can be recited from the mechanical makeup and the material composition of the Earth-Moon system.
One example of functional composition concerns the angular sizes of the Sun and the Moon. It here seems to be very unusual that the Moon's apparent diameter--as viewed from the Earth--appears to have the same angular size as the Sun's diameter. Essentially, to an observer stationed on the Earth, both orbs appear to have an equal angular size--of about 0.5 degree. (As has been explained in the current chapter, equal angular sizes of both the Sun and the Moon is integral in the formation of total solar eclipses, and in the rare formation of ring eclipses).
Another example of functional design can be recited from the orbit of the Moon (which perpetually remains synchronized with the rotational rate). As is shown in a section from above, the sidereal orbital period of the Moon around the Earth completes in 27.321666 days. It here is amazing that the rotational period of the Moon appears to exactly be synchronized with the sidereal orbit. (The Moon rotates only one time every 27.321666 days--and this is the very same rate as the sidereal orbit). Because both rates--the sidereal orbit and the rotation--are exactly the same, the Moon can be predicted to progress throughout its orbit with the same face of the Moon showing toward the Earth at all times.
A number of science mysteries (or questions that do not have scientific answers) seem to surround the current composition of the Earth-Moon system.
One of these mysteries concerns the size of the Earth-Moon pair. (How is it that a true planet the size of the Earth holds a relatively large, almost perfectly round Moon in its orbit?)
The size and density of the Earth-Moon system, the Moon's close orbit, and the nearly circular orbit of the Moon--though beneficial in stabilizing Earth's tilt and spin--are rather unique as compositional characteristics.
The close proximity of the Moon's orbit to the Earth cannot be explained through a capture process... as if the Moon were somehow captured into Earth's orbit. Essentially, computer simulations indicate that the Earth isn't large enough to capture and hold a large Moon. (Even if the Moon were somehow captured and held, it is unlikely that a close circular orbit of the current angular momentum would result).
It is here evident that the Earth-Moon was probably created through a chain of multiple processes. However, the explicit creative process (or processes) by which the Earth-Moon system was initially formed remains in the realm of theory.
A clue to the origin of the Earth-Moon can seemingly be recognized from the spin-orbital configuration. It is straightfoward to interpret that interrelated time structures are generated from out of interfacing rates solar days, synodic months, and solar years. The clear possibility then seems to be that time cycles generated by Earth-Moon are reflective of a system that has been functionally designed.
For additional significant information concerning what appears to be interrelatedness amid Earth and Moon cycles, refer to the following online publications:
- 'An Interrelated Earth-Moon System'
- 'The Moon as a Time Meter'
- 'Functional Time Design'
- 'Time Portals or Annual Gates'
- 'Significance of 40 Days'
- 'The Slowing Spin of the Earth'
- 'A Significant Circle-of-Seven'
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APPENDIX A
EXCESS OF THE DURATION OF THE DAY TO 86400S AND
ANGULAR VELOCITY OF THE EARTH'S ROTATION
(SINCE 1623)
Borrowed from: International Earth Rotation Service (IERS)
This table gives mean annual values of the duration of the day D, which are available for the last four centuries. For the interval 1623-1955, the data are those provided by L.V. Morrison, Royal Greenwich Observatory, interpolated for the middle of the year. The mean solar time has been referred to the dynamical time scale derived from the time argument of the lunar ephemeris.
The duration of the day has been obtained:
- from 1623 to 1860, by derivative of cubic splines fitted on individual values of the difference between mean solar time and dynamical time (13 knots),
- from 1861 to 1955, by a 5-point quadratic convolute.
More information on the computation of the duration of the day is available in Stephenson and Morrison (1984), with an estimation of the accuracy of these evaluations.
From 1956 up to present, the duration of the day has been obtained from the BIH/IERS values of UT1-TAI ; the table gives annual averages. At the level of precision of these values of the duration of the day, the unit of the dynamical time and the unit of TAI can be considered as having the same duration. Thus D is expressed in present SI units. The table gives also the values of the angular velocity of the Earth's rotation w derived from the listed values of D.
DATE D [[omega]] DATE D [[omega]] DATE D [[omega]]
(years) (ms) (prad/s) (years) (ms) (prad/s) (years) (ms) (prad/s)
72 921.. 72 921.. 72 921
1671.5 -3. 154. 1721.5 0.2 151.3
1672.5 -3. 154. 1722.5 0.2 151.3
1623.5 -11. 161. 1673.5 -3. 154. 1723.5 0.1 151.4
1624.5 -11. 161. 1674.5 -3. 154. 1724.5 0.1 151.4
1625.5 -10. 160. 1675.5 -3. 154. 1725.5 0.1 151.4
1626.5 -10. 160. 1676.5 -3. 154. 1726.5 0.1 151.4
1627.5 -9. 159. 1677.5 -3. 154. 1727.5 0.1 151.4
1628.5 -9. 159. 1678.5 -3. 154. 1728.5 0.2 151.3
1629.5 -8. 158. 1679.5 -2. 153. 1729.5 0.2 151.3
1630.5 -8. 158. 1680.5 -2. 153. 1730.5 0.2 151.3
1631.5 -8. 158. 1681.5 -2. 153. 1731.5 0.2 151.3
1632.5 -7. 157. 1682.5 -2. 153. 1732.5 0.2 151.3
1633.5 -7. 157. 1683.5 -2. 153. 1733.5 0.2 151.3
1634.5 -7. 157. 1684.5 -2. 153. 1734.5 0.2 151.3
1635.5 -6. 157. 1685.5 -2. 153. 1735.5 0.2 151.3
1636.5 -6. 157. 1686.5 -1. 152. 1736.5 0.3 151.2
1637.5 -6. 157. 1687.5 -1. 152. 1737.5 0.3 151.2
1638.5 -5. 156. 1688.5 -1. 152. 1738.5 0.3 151.2
1639.5 -5. 156. 1689.5 -1. 152. 1739.5 0.3 151.2
1640.5 -5. 156. 1690.5 -1. 152. 1740.5 0.3 151.2
1641.5 -4. 155. 1691.5 -1. 152. 1741.5 0.3 151.2
1642.5 -4. 155. 1692.5 -1. 152. 1742.5 0.3 151.2
1643.5 -4. 155. 1693.5 0. 151. 1743.5 0.4 151.1
1644.5 -4. 155. 1694.5 0. 151. 1744.5 0.4 151.1
1645.5 -4. 155. 1695.5 0. 151. 1745.5 0.4 151.1
1646.5 -3. 154. 1696.5 0. 151. 1746.5 0.4 151.1
1647.5 -3. 154. 1697.5 0. 151. 1747.5 0.4 151.1
1648.5 -3. 154. 1698.5 0. 151. 1748.5 0.4 151.1
1649.5 -3. 154. 1699.5 0. 151. 1749.5 0.4 151.1
1650.5 -3. 154. 1700.5 0.1 151.4 1750.5 0.4 151.1
1651.5 -3. 154. 1701.5 0.2 151.3 1751.5 0.4 151.1
1652.5 -3. 154. 1702.5 0.2 151.3 1752.5 0.4 151.1
1653.5 -3. 154. 1703.5 0.3 151.2 1753.5 0.4 151.1
1654.5 -3. 154. 1704.5 0.3 151.2 1754.5 0.4 151.1
1655.5 -3. 154. 1705.5 0.3 151.2 1755.5 0.4 151.1
1656.5 -3. 154. 1706.5 0.3 151.2 1756.5 0.4 151.1
1657.5 -3. 154. 1707.5 0.3 151.2 1757.5 0.4 151.1
1658.5 -3. 154. 1708.5 0.4 151.1 1758.5 0.4 151.1
1659.5 -3. 154. 1709.5 0.3 151.2 1759.5 0.4 151.1
1660.5 -3. 154. 1710.5 0.3 151.2 1760.5 0.4 151.1
1661.5 -3. 154. 1711.5 0.3 151.2 1761.5 0.4 151.1
1662.5 -3. 154. 1712.5 0.3 151.2 1762.5 0.3 151.2
1663.5 -3. 154. 1713.5 0.3 151.2 1763.5 0.3 151.2
1664.5 -3. 154. 1714.5 0.3 151.2 1764.5 0.3 151.2
1665.5 -3. 154. 1715.5 0.2 151.3 1765.5 0.3 151.2
1666.5 -3. 154. 1716.5 0.2 151.3 1766.5 0.3 151.2
1667.5 -3. 154. 1717.5 0.2 151.3 1767.5 0.3 151.2
1668.5 -3. 154. 1718.5 0.2 151.3 1768.5 0.3 151.2
1669.5 -3. 154. 1719.5 0.2 151.3 1769.5 0.3 151.2
1670.5 -3. 154. 1720.5 0.2 151.3 1770.5 0.3 151.2
1771.5 0.3 151.2 1821.5 -0.81 152.15 1871.5 -2.59 153.65
1772.5 0.2 151.3 1822.5 -0.99 152.30 1872.5 -2.55 153.62
1773.5 0.2 151.3 1823.5 -1.16 152.45 1873.5 -2.10 153.24
1774.5 0.2 151.3 1824.5 -1.32 152.58 1874.5 -2.03 153.18
1775.5 0.2 151.3 1825.5 -1.42 152.67 1875.5 -1.77 152.96
1776.5 0.2 151.3 1826.5 -1.49 152.72 1876.5 -1.37 152.62
1777.5 0.2 151.3 1827.5 -1.50 152.73 1877.5 -1.24 152.51
1778.5 0.2 151.3 1828.5 -1.48 152.72 1878.5 -0.90 152.23
1779.5 0.2 151.3 1829.5 -1.41 152.66 1879.5 -0.49 151.88
1780.5 0.2 151.3 1830.5 -1.30 152.56 1880.5 -0.23 151.66
1781.5 0.2 151.3 1831.5 -1.14 152.43 1881.5 -0.06 151.52
1782.5 0.1 151.4 1832.5 -0.94 152.26 1882.5 -0.15 151.59
1783.5 0.1 151.4 1833.5 -0.73 152.08 1883.5 -0.33 151.75
1784.5 0.1 151.4 1834.5 -0.52 151.91 1884.5 -0.24 151.67
1785.5 0.0 151.5 1835.5 -0.34 151.75 1885.5 -0.15 151.59
1786.5 0.0 151.5 1836.5 -0.18 151.62 1886.5 -0.05 151.51
1787.5 -0.1 151.6 1837.5 -0.04 151.50 1887.5 -0.04 151.50
1788.5 -0.2 151.6 1838.5 0.09 151.39 1888.5 -0.18 151.62
1789.5 -0.3 151.7 1839.5 0.19 151.31 1889.5 -0.25 151.68
1790.5 -0.5 151.9 1840.5 0.27 151.24 1890.5 -0.48 151.87
1791.5 -0.6 152.0 1841.5 0.33 151.19 1891.5 -0.58 151.96
1792.5 -0.7 152.1 1842.5 0.37 151.15 1892.5 -0.42 151.82
1793.5 -0.9 152.2 1843.5 0.39 151.14 1893.5 -0.13 151.58
1794.5 -0.9 152.2 1844.5 0.40 151.13 1894.5 0.33 151.19
1795.5 -1.0 152.3 1845.5 0.41 151.12 1895.5 0.86 150.74
1796.5 -1.0 152.3 1846.5 0.41 151.12 1896.5 1.53 150.18
1797.5 -1.0 152.3 1847.5 0.40 151.13 1897.5 2.16 149.64
1798.5 -1.0 152.3 1848.5 0.39 151.14 1898.5 2.64 149.24
1799.5 -1.0 152.3 1849.5 0.38 151.15 1899.5 3.00 148.94
1800.5 -0.87 152.20 1850.5 0.36 151.16 1900.5 3.31 148.67
1801.5 -0.75 152.10 1851.5 0.33 151.19 1901.5 3.60 148.43
1802.5 -0.61 151.98 1852.5 0.30 151.21 1902.5 3.70 148.34
1803.5 -0.46 151.86 1853.5 0.26 151.25 1903.5 3.69 148.35
1804.5 -0.34 151.75 1854.5 0.23 151.27 1904.5 3.55 148.47
1805.5 -0.23 151.66 1855.5 0.20 151.30 1905.5 3.40 148.60
1806.5 -0.14 151.59 1856.5 0.17 151.32 1906.5 3.48 148.53
1807.5 -0.06 151.52 1857.5 0.15 151.34 1907.5 3.57 148.45
1808.5 -0.01 151.48 1858.5 0.11 151.37 1908.5 3.65 148.39
1809.5 0.03 151.44 1859.5 -0.02 151.48 1909.5 3.71 148.34
1810.5 0.05 151.42 1860.5 -0.34 151.75 1910.5 3.77 148.29
1811.5 0.05 151.42 1861.5 -0.81 152.15 1911.5 3.86 148.21
1812.5 0.04 151.43 1862.5 -1.19 152.47 1912.5 3.89 148.18
1813.5 0.01 151.46 1863.5 -1.35 152.61 1913.5 3.62 148.41
1814.5 -0.04 151.50 1864.5 -1.61 152.83 1914.5 3.18 148.78
1815.5 -0.11 151.56 1865.5 -2.13 153.26 1915.5 2.92 149.00
1816.5 -0.18 151.62 1866.5 -2.76 153.80 1916.5 2.74 149.15
1817.5 -0.28 151.70 1867.5 -2.89 153.91 1917.5 2.35 149.48
1818.5 -0.39 151.80 1868.5 -2.60 153.66 1918.5 2.05 149.74
1819.5 -0.51 151.90 1869.5 -2.59 153.65 1919.5 1.76 149.98
1820.5 -0.65 152.02 1870.5 -2.51 153.59 1920.5 1.48 150.22
1921.5 1.51 150.19 1971.5 2.90 149.02
1922.5 1.28 150.39 1972.5 3.13 148.83
1923.5 0.98 150.64 1973.5 3.05 148.89
1924.5 0.93 150.68 1974.5 2.72 149.17
1925.5 0.81 150.78 1975.5 2.69 149.20
1926.5 0.56 150.99 1976.5 2.91 149.01
1927.5 0.18 151.32 1977.5 2.77 149.13
1928.5 -0.22 151.65 1978.5 2.88 149.04
1929.5 -0.35 151.76 1979.5 2.61 149.26
1930.5 -0.19 151.63 1980.5 2.30 149.53
1931.5 -0.10 151.55 1981.5 2.16 149.64
1932.5 -0.07 151.53 1982.5 2.16 149.64
1933.5 -0.06 151.52 1983.5 2.28 149.54
1934.5 -0.08 151.53 1984.5 1.52 150.18
1935.5 0.00 151.47 1985.5 1.45 150.24
1936.5 0.08 151.40 1986.5 1.23 150.43
1937.5 0.22 151.28 1987.5 1.36 150.32
1938.5 0.47 151.07 1988.5 1.32 150.35
1939.5 0.78 150.81 1989.5 1.53 150.18
1940.5 1.09 150.55 1990.5 1.94 149.83
1941.5 1.25 150.41 1991.5 2.04 149.75
1942.5 1.31 150.36 1992.5 2.22 149.59
1943.5 1.35 150.33 1993.5 2.37 149.47
1944.5 1.41 150.28 1994.5 2.17 149.64
1945.5 1.41 150.28 1995.5 2.31 149.52
1946.5 1.35 150.33 1996.5 1.83 149.92
1947.5 1.30 150.37 1997.5 1.84 149.91
1948.5 1.25 150.41
1949.5 1.20 150.45
1950.5 1.15 150.50
1951.5 1.10 150.54
1952.5 1.05 150.58
1953.5 0.99 150.63
1954.5 0.92 150.69
1955.5 0.86 150.74
1956.5 0.89 150.72
1957.5 1.34 150.34
1958.5 1.37 150.31
1959.5 1.31 150.36
1960.5 1.19 150.46
1961.5 1.09 150.55
1962.5 1.30 150.37
1963.5 1.54 150.17
1964.5 1.92 149.85
1965.5 2.21 149.60
1966.5 2.41 149.43
1967.5 2.37 149.47
1968.5 2.48 149.37
1969.5 2.67 149.21
1970.5 2.71 149.18
_________________________________________________________
APPENDIX B
Universal Time and Delta-T
Atomic Time, with the unit of duration the Systeme International (SI) second defined as the duration of 9,192,631,770 cycles of radiation corresponding to the transition between two hyperfine levels of the ground state of cesium 133.
TAI is the International Atomic Time scale, a statistical timescale based on a large number of atomic clocks.
Universal Time (UT) is counted from 0 hours at midnight, with unit of duration the mean solar day, defined to be as uniform as possible despite variations in the rotation of the Earth.
UT0 is the rotational time of a particular place of observation. It is observed as the diurnal motion of stars or extraterrestrial radio sources.
UT1 is computed by correcting UT0 for the effect of polar motion on the longitude of the observing site. It varies from uniformity because of the irregularities in the Earth's rotation.
Coordinated Universal Time (UTC) differs from TAI by an integral number of seconds. UTC is kept within 0.9 seconds of UT1 by the introduction of one-second steps to UTC, the "leap second." To date these steps have always been positive.
Dynamical Time replaced ephemeris time as the independent argument in dynamical theories and ephemerides. Its unit of duration is based on the orbital motions of the Earth, Moon, and planets.
Terrestrial Time (TT), (or Terrestrial Dynamical Time, TDT), with unit of duration 86400 SI seconds on the geoid, is the independent argument of apparent geocentric ephemerides. TDT = TAI + 32.184 seconds.
Barycentric Dynamical Time (TDB), is the independent argument of ephemerides and dynamical theories that are referred to the solar system barycenter. TDB varies from TT only by periodic variations.
Geocentric Coordinate Time (TCG) is a coordinate time having its spatial origin at the center of mass of the Earth. TCG differs from TT as: TCG - TT = Lg x (JD -2443144.5) x 86400 seconds, with Lg = 6.969291e-10.
Barycentric Coordinate Time (TCB)is a coordinate time having its spatial origin at the solar system barycenter. TCB differs from TDB in rate. The two are related by: TCB - TDB = iLb x (JD -2443144.5) x 86400 seconds, with Lb = 1.550505e-08.
Delta-T = (TDT-UT).
________________________________________________________
APPENDIX C
Value of Delta T
(Table and Text--as shown below--borrowed from
Fred Espenak, NASA/Goddard Space Flight Center)
As Earth rotates on its axis, tidal friction is imposed on it through the gravitational attraction with the Moon and, to a lesser extent, the Sun. This secular acceleration gradually transfers angular momentum from Earth to the Moon. As Earth loses energy and slows down, the Moon gains this energy and its orbital period and distance from Earth increase.
R. F. Stephenson and collaborators have produced a number of seminal works in the field of Earth's rotation over the past several millennia. In particular, they have identified hundreds of eclipse and occultation observations in early European, Middle Eastern and Chinese annals, manuscripts, canons and records. In spite of their relatively low precision, these data represent our only record to the value of delta-T during the past several millennia.
In Atlas of Historical Eclipse Maps East Asia 1500 BC - AD 1900, Stephenson and Houlden (1986) present two empirically derived expressions to describe the behavior of delta-T prior to telescopic records (pre-1600):
(1) prior to 948 AD
delta-T (seconds) = 1830 - 405*t + 46.5*t^2
(t = centuries since 948 AD)
(2) 948 AD to 1600 AD
delta-T (seconds) = 22.5*t^2
(t = centuries since 1850 AD)
More recently, Stephenson presents a new analysis of most if not all known solar and lunar eclipses that occurred during the period -700 to +1600 (Historical Eclipses and Earth's Rotation, 1997). The new analysis uses a spline to fit the observations.
The following table lists values of delta-T (seconds) derived from Stephenson and Houlden (1986), along with Stephenson (1997) for comparison.
Year delta-T delta-T
(1986) (1997)
-2000 54181 - (all values in seconds)
-1900 51081 -
-1800 48073 -
-1700 45159 -
-1600 42338 -
-1500 39610 -
-1400 36975 -
-1300 34433 -
-1200 31984 -
-1100 29627 -
-1000 27364 -
-900 25194 -
-800 23117 -
-700 21133 -
-600 19242 -
-500 17444 16800
-400 15738 15300
-300 14126 14000
-200 12607 12800
-100 11181 11600
0 9848 10600
100 8608 9600
200 7461 8600
300 6406 7700
400 5445 6700
500 4577 5700
600 3802 4700
700 3120 3800
800 2531 3000
900 2035 2200
1000 1625 1600
1100 1265 1100
1200 950 750
1300 680 470
1400 455 300
1500 275 180
1600 140 110
References for Delta-T
- Morrison, L.V. and Ward, C. G., "An analysis of the transits of Mercury: 1677-1973", Mon. Not. Roy. Astron. Soc., 173, 183-206, 1975.
- Stephenson F.R and Houlden M.A., Atlas of Historical Eclipse Maps: East Asia 1500 BC - AD 1900, Cambridge Univ.Press., 1986.
- Stephenson F.R., Historical Eclipses and Earth's Rotation , Cambridge Univ.Press, 1997.
_______________________________________________________
APPENDIX D
Using Coral as a Clock
===============================================================================
Author: Hannu K. J. Poropudas
Title: Using Coral as a Clock
===============================================================================
APPROXIMATE ANCIENT TIME FORMULA BASED ON FOSSIL DATA
Hannu K. J. Poropudas
(R&D Engineer, Nokia Telecommunications)
(E-Mail Address: poropuda@tnclus.tele.nokia.fi)
Vesaisentie 9E, 90900 Kiiminki, Finland
ABSTRACT
Time formula, also called fossil formula, gives an answer to the question:
how many mean solar days are in a tropical year at a certain point in time.
It is the simplest possible expression that has been worked out from
experimental fossil points (Eicher/Wells 1976, Pannella MacClintock
Thompson 1968 and Scrutton 1978).
The formula is intended for use mainly in the experimental fossil point's
area, which goes back, at maximum, as far as the approximately 3.556 (+ 0.032)
-
billion years old Warrawoona stromatolite fossils (The Cambridge Encyclopaedia
of Earth Sciences 1982 diagram page 357, Schopf 1983).
At the present, the time formula have been tested over an interval as far
back as 850 (+ 50) million years and consistency with the experimental points
-
looks good (formula's safe area of use).
TIME FORMULA
The time formula is the following expression given over the widest
possible time area. The time area can be limited on the basis of
experimental measurement data, if the deviations of the measured results
are, for example, greater than five to ten days.
2
M - A(T)* T - B(T)* T
N(T) = ---------------------
1 + C(T)* T
N(T) = Number of mean solar days in tropical year at the point T
T = time in uniform centuries
M = 365.2422
Here is taken into account lengthening of measured uniform mean
solar day as a first approximation (Allen 1973).
15 1 -8
1 + C* T = 1 + ----- * ----- * T = 1 + 1.7361 * 10 T
10000 86400
The uniform shortening formula of the tropical year (Allen 1973)
-6
365.24219878 - 6.16 * 10 T
has been corrected by one nonlinear term and also the coefficient of the
linear term has been corrected. As a first approximation the coefficients
A(T) and B(T) are also assumed to be constants.
If (N1, T1) and (N2, T2) are two fossil points and if C(T) is assumed
constant value then the coefficients of the formula have the following
values:
A = T2(M-N1)/T1/(T2-T1) - T1(M-N2)/T2/(T2-T1) + C*(N2T1-N1T2)/(T2-T1)
B = (M-N2)/T2/(T2-T1) - (M-N1)/T1/(T2-T1) + C*(N1-N2)/(T2-T1)
The coefficients of the terms are achieved from two reliable fossil points.
1. From coral fossil data approximately 400 million years ago. It has been
estimated that there were little over 400 days in a year at that time.
These fossil corals were ancient marine invertebrates that secreted
a microscopically thin layer of calsium carbonate each day; the layers laid
down in summer were thicker than those laid down in winter.
Estimations are based on careful countings of calcium carbonate layers in
fossil corals formed due to the changes of lightness of night and day
(The Cambridge Atlas of Astronomy 1985, Pages 55 and 54, Photograph:
J. C. Revy. The specimen is from the collection of the Brittish National
Museum of the Natural History).
2. From fossil data approximately 180 million years ago, when there were
approximately 381 days of that time in a year (Wells 1963).
-6 -13
A = 2.46 * 10 and B = 1.79 * 10 (in first time formula).
If fossil points from (Eicher 1976) are used.
1. From fossil data approximately 190 million years ago, when there were
approximately 382 days of that time in a year (Eicher/Wells 1976).
2. From fossil data approximately 395 million years ago, when there was
approximately 401 days of that time in a year (Eicher/Wells 1976).
then
-6 -14
A = 2.28 * 10 and B = 4.74 * 10 (in second time formula)
(see for basis growth increments in fossils: Rosenberg Runcorn 1975).
This seems to be a good form for the approximation even when C is afterwards
set to depend on T. This new setting is possible because the formula allows
quite wide range of variations of C's magnitude and it still gives a good
fit to the fossil data.
A(T) = T2(M-N1)/T1/(T2-T1) - T1(M-N2)/T2/(T2-T1) + C(T)*(N2T1-N1T2)/(T2-T1)
B(T) = (M-N2)/T2/(T2-T1) - (M-N1)/T1/(T2-T1) + C(T)*(N1-N2)/(T2-T1)
The best C(T) is achieved from Geologic Rock and Fossil Record Data, if
the distance between Earth and Moon can be estimated at different points
on the geologic time scale. Solar tides must also be accounted because
these tides speeds up Earth's rotation (see fossil data of past 500 million
years: Pannella MacClintock and Thompson 1968, and Scrutton 1978, Fig 8,
Page 185).
The coefficient of the asymptotic straight line for the month formula is
-7
about 2.60 * 10 from (Scrutton 1978) and the little uncertain period of
4
oscillation about this line is roughly 429.4 * 10 centuries from
(Pannella MacClintoc and Thompson 1968).
-7 4
P(T) = 29.53 - 2.60 * 10 * ( 1 - e*sin ( 2 P T / (429.4 * 10 )))* T
P(T)= number of mean solar days per synodic month at a certain
point T of time
0 <= e <= 1, (e = 1 in first approximation)
P = 3.14159 radians
(This month formula is not used because it is still under testings).
4
If dT = + 5 * 10 centuries and dN = + 0.5 mean solar days/tropical year
- -
are the accuracy of determination of the absolute age of the fossil samples,
and latter is roughly the accuracy of determination of the number of days in
year from fossil samples, then calculations gives the same order error
magnitudes as A and B themselves are, so at present accuracy the coefficients
cannot be estimated very reliable.
The coral and bivalve fossil data suggests that the value of derivative
of the time formula at the point T = 0 is (Schopf 1983):
-6
-(9.5 + 0.9) * 10 (coral data)
- -6
-(10.0 + 1.2) * 10 (bivalve data)
-
Further data (Schopf 1983):
(d W / dt) / (dW / dt) = 42 + 11 (coral data)
Earth Earth-Moon -
= 46 + 8 (bivalve data)
-
= 51 + 5 (modern astronomical data)
-
= 48 (present day value predicted by Kepler's third law and the
conservation of angular momentum)
TABLE OF CALCULATED VALUES COMPARED WITH THE FOSSIL DATA (FIRST TIME
FORMULA, WELL'S CORAL FOSSIL DATA)
The time formula give the following table with different values of T:
TABLE 1
4
1. = T / 10 (centuries)
2. = calculated value from the first time formula (days/year)
3. = calculated value from the second time formula (days/year)
7. = experimental value (days/year), (Wells 1963). 8. = era (end time).
1. 2. 3. 7. 8.
------------------------------------------------------------------------
0 365.24 365.24 365.24 Cenozoic
------------------------------------------------------------------------
- 65 370.95 370.89 371 Cretaceous
------------------------------------------------------------------------
-135 377.07 377.07 377 Jurassic
------------------------------------------------------------------------
-180 381.00 381.10 381 Triassic
------------------------------------------------------------------------
-230 385.34 385.63 385 Permian
------------------------------------------------------------------------
-280 389.67 390.22 390 Pennsylvanian
------------------------------------------------------------------------
-310 392.26 393.01 393 Mississippian
------------------------------------------------------------------------
-345 395.27 396.28 396 Devonian
------------------------------------------------------------------------
<-405 400.42 401.96 >400
------------------------------------------------------------------------
-405 400.42 401.96 402 Silurian
------------------------------------------------------------------------
-425 402.14 403.88 Ordovician
------------------------------------------------------------------------
-500 408.53 411.15 412 Cambrian
(the fossil can be older)
------------------------------------------------------------------------
-600 416.99 421.08 424 Precambrian
(no fossil evidence)
------------------------------------------------------------------------
-390- 399.14- 400.53->400 Devonian (The Cambridge Atlas of)
-400 400.00 401.48 Astronomy 1985, p.55 and p.54)
------------------------------------------------------------------------
WELL'S CORAL FOSSIL SAMPLES:
TABLE 2
WELL'S CORAL FOSSIL SAMPLES (1. Wells 1963 and 2. Wells 1970):
Era 1. Sample 1. Data 1.
-------------------------------------------------------------------------
Pensylvanian Caninia 385 day layers
-------------------------------------------------------------------------
Pennsylvanian Lophophyllidium 390 day layers
-------------------------------------------------------------------------
Middle-Devonian Heliophyllum halli usually about 400 day layers,
(13 annual growth
increments) ranging between extremes of 385
Eridophyllum archiaci and 410
Favosites
-------------------------------------------------------------------------
Lower-Silurian Holophragma calceoloides
-------------------------------------------------------------------------
Cambrian An estimation= 21-hr Cambrian day
(Munk MacDonald 1960).
Era 2. Sample 2. Data 2.
-------------------------------------------------------------------------
Mississippian Lithostrontion 398 day layers.
-------------------------------------------------------------------------
Mississippian Lophophylldium 380 and 390 day layers.
-------------------------------------------------------------------------
Middle-Devonian Heliophyllum halli average of 398 with a range from
Eridophyllum archiaci 385 to 405.
(Fig. 3.)
Cylindrophyllum
Favosites
-------------------------------------------------------------------------
Middle-Silurian Holophragma calceoloides.
(Fig. 1. and 2.)
-------------------------------------------------------------------------
Middle Silurian Ketophyllum about 400 day layers.
-------------------------------------------------------------------------
Upper Ordovician Streptelasma about 412 day layers.
-------------------------------------------------------------------------
Cambrian Escherichia coli An estimation = 21-hr Cambrian
day (Halberg Conner 1961).
TABLE OF CALCULATED VALUES COMPARED WITH THE FOSSIL DATA, (SECOND TIME
FORMULA, WELL'S CORAL FOSSIL DATA)
The time formula the following table with different values of T:
TABLE 3
7. = experimental value (days/year), (Eicher/Wells 1976).
1. 2. 3. 7. 8.
------------------------------------------------------------------------
0 365.24 365.24 365.24 Cenozoic
------------------------------------------------------------------------
- 65 370.95 370.89 371 Cretaceous
------------------------------------------------------------------------
-136 377.16 377.16 377 Jurassic
------------------------------------------------------------------------
-190 381.87 382.00 382 Triassic
------------------------------------------------------------------------
-225 384.91 385.18 385 Permian
------------------------------------------------------------------------
-280 389.67 390.22 390 Pennsylvanian
------------------------------------------------------------------------
-325 393.55 394.41 394 Mississippian
------------------------------------------------------------------------
-345 395.27 396.28 396 Devonian
------------------------------------------------------------------------
-395 399.57 401.00 401 Silurian
------------------------------------------------------------------------
-435 402.99 404.84 405 Ordovician
------------------------------------------------------------------------
-500 408.53 411.15 412 Cambrian
------------------------------------------------------------------------
-570 414.46 418.07 421 Precambrian
------------------------------------------------------------------------
Three coral species from Middle Devonian rocks of New York and Ontario,
the numerous counts range between 385 and 410 and they accumulate near the
median of 398.
AWRAMIK'S AND VANYO'S STROMATOLITE DATA FROM THE BITTER SPRINGS FORMATION,
(Anabaria Juvensis), CALCULATED AND THE FOSSIL DATA COMPARED
(FIRST AND SECOND TIME FORMULA)
(Vanyo Awramik 1985, error limit of the age determination 50 million years)
This research was supported in part by the NSF Grant EAR 83-03754 and is
contribution no. 145 of the Preston Cloud Research Laboratory.
All samples are in collections of the Preston Cloud Research Laboratory.
TABLE 4
7. = experimental value (days/year), (Vanyo Awramik 1985).
1. 2. 3. 7.
------------------------------------------------------------------------
-850 437.83 447.19 435 (best) or 454 or 409 or 485
------------------------------------------------------------------------
This, approximately 850 million years old, stromatolite
investigated by Vanyo and Awramik had a wavy sinusoidal year growth
"wave length" of 87 mm in the best sample and the depth of a days growth
was 0.2 mm. This gave about 435 days in year at that time. Extreme values
were measured to be 409 and 485, and one measurement gave the value 454.
This wavy nature of the growth is due the point of view that the growth has
been directed towards the Sun and the same direction is repeated annually.
THE STROMATOLITE FROM THE AREA OF GREAT SLAVE LAKE (Hearne Formation) GSM 77325
(Jones 1981 and Schopf 1983, age determination is too inaccurate)
The specimen is stored in the collection of Institute of Geological
Sciences.
TABLE 5
7. = experimental value, Highest count=(days/month) ?,(Jones 1981,
Schopf 1983).
8. = experimental value, Mode=(days/(month/2))-(days/month) ?,
(Jones 1981, Schopf 1983).
9. = experimental value, Tidal cycles per year=( months/year ) ?,
(Pannella 1972 b).
1. 2. 3. 7. 8. 9.
------------------------------------------------------------------------
-1790- 510.60- 567.10-
-2170 536.42 629.58 13
------------------------------------------------------------------------
Pannella has estimated (Pannella 1972 b) that there have been about 13
tidal cycles in a year at that time. He has always counted two groups of
laminae of the stromatolite as a unit. The very clear accumulation in the
magnesium spectrum of the stromatolite laminations at the number 25 remains
unclear.
GSM 77325 spectrum:
Mg: 21-25-(33-34)-44-51-(75-76).
? -------
Si: 5-8-10-17-21-25-(26-28)-(35-36)-(43-45)-54-73-100.
-------
Al: 5-19-21-25-27-29-(30-36)-41-50-53.
----------
Ca: 8-11-17-21-25-27-34-43-46-(50-51)-66-81-101-121.
--
( )= between.
BULAWAYAN STROMATOLITE BUL-6/BUL-7 OR UCLA-BUL
