Continued from previous post ...
Stockwell's calculations were fit into an empirical formula and published by Simon Newcomb.
The value of T
in the above formula represents the number of centuries from 1900 A.D. with positive (+) values for centuries AFTER 1900 A.D.
and negative (-) values for centuries BEFORE 1900 A.D.
For example, to calculate earth's expected axial tilt in 1500 A.D, a T
value of -4 (i.e. 1500 - 1900 = -4) would be used.
Newcomb's formula for the calculation of axial tilt values (past and future) had been accepted for many years as the international standard and was
the one used by Dodwell in his original calculations.
However, an improved version of the formula was derived by L.J. Lieske in 1976 with a base year of 2000 A.D. (Newcomb's Formula used 1900 A.D)
Note that in my re-examination of Dodwell's data, I replaced his use of the Newcomb Formula with that of Lieske's in the hope of
achieving an improvement in axial tilt calculations for previous eras.
Now I'll present a table containing 71 data points used in the analysis.
Column 1 represents the source of the axial tilt measurement.
Column 2 represents the year that the measurement was taken.
Column 3 represents the OBSERVED axial tilt measurement in standard degree, minute and second format.
Column 4 represents the EXPECTED axial tilt measurement for that year derived from the Lieske Formula.
Column 5 represents the difference (in minutes and seconds) between the observed axial tilt and the Lieske Formula values.
Please note that the reason for the inclusion of the Stonehenge and Amun-Ra sources (highlighted in green) will be explained later.
A cursory examination of column 5 will show that looking backwards in time from 1976 towards the mid 1600's, the difference between the observed and
calculated axial tilt values are fairly minimal and fall within the expected range of deviation. However, from the mid 1600's and looking backwards
once again, we can see a sudden and progressive difference becoming very evident and a definitive divergence taking place between what the Lieske
Formula tells us that the earths axial tilt SHOULD have been during those time periods; and what was actually observed and recorded by astronomers of
So, we have somewhat of a mystery on our hands ... either the actual observed axial tilt values as we head further back in time are in error ... or
the internationally accepted Lieske Formula is in error.
Before we continue with the analysis, I'm sure that by now, some of you may be wondering just HOW does one go about measuring the amount that the
earth's axis is tilted by ... and especially how were ancient astronomers able to measure it more than 3000 years ago ? Surely it must take
sophisticated devices and advanced mathematics to work out how much the earth is tilted ?
To answer these questions, I'll try and provide a brief explanation.
Surprisingly, the simple answer is that essentially all it takes is nothing more than a long wooden pole (or
" as it's normally referred to) and some very simple geometry. It is one of the
first scientific instruments ever made, originating with the Chaldean astronomers of Babylon and then soon spreading to the ancient Greek, Chinese,
Indian, Arab and Egyptian civilizations. All of them were perfectly capable of making the necessary observations and arriving at accurate answers.
Indeed, this ancient method was the precursor to the simple sun-dial and has been in continuous use over the millennia.
Essentially, all that needed to be done was to ensure that an area of ground was prepared so that it was perfectly flat and the pole to be placed
absolutely vertically in that flat area of ground. There were many simple ways that both of these preparations could have been easily accomplished
even thousands of years ago.
Once the pole has been fixed in place, all that was then required was to wait until the day of either the
summer or winter solstice
and measure the length of the shadow cast by the pole at
local noon on those particular days. Knowing the length of both the shadow and the pole, extremely simple geometry would provide the angle of the sun
in the sky.
The following diagram should help illustrate just how simple and easy it is to determine and measure the angle of the earths axial tilt.
By measuring the angle formed by the corresponding summer and winter solstice
shadows (in this case 47 degrees), then dividing that angle in half, will give the angle of the earths axial tilt of approximately 23.5 degrees.
Naturally it goes without saying that the more accurate the measurement of the summer and winter solstice shadows cast by the pole, then the more
accurate the resultant value of the tilt.
It needs to be emphasized MOST strongly that using the above procedure, it would have been EASILY within the capabilities (both technical and
mathematical) of ALL of the ancient civilizations to arrive at extremely accurate measurements of the earths axial tilt. Saying that because
measurements were made many thousands of years ago that they therefore could not possibly be accurate is doing a great disservice to the astronomers
of those ancient times. Just take a look at the incredibly accurate measurements that would have been necessary in the construction of the Egyptian
pyramids and monuments thousands of years ago to show quite clearly that people of those times were more than capable of measuring with extreme
accuracy something as simple as the angle of a shadow cast on the ground by a wooden pole.
It should be mentioned at this point that even though the above method of determining the earths axial tilt is, in practice, simple and
straightforward - that there are still potential sources of measurement errors that could impact the accuracy of the final value.
As an example, except for the last few hundred years, the concept of solar parallax and atmospheric refraction were unknown to the ancient astronomers
and therefore were NOT factored into their observations and calculations when determining the sun's ACTUAL altitude and not just the OBSERVED
altitude in the sky. Both solar parallax and atmospheric refraction cause light rays traveling through the atmosphere to bend slightly and therefore
causing the altitude of the sun (to an observer) to appear slightly higher than it actually is, and so this had the effect of introducing slight
errors into their calculations.
A simple example is that when we observe the sun just touching the horizon and about to set, in actual fact the sun has already set below the horizon
but because of the effects of atmospheric refraction, we "see" the image of the sun as if it was still just above the horizon.
Dodwell was well aware of these (and other) potential sources of error in ancient observations and therefore ensured that all observed values of
earths axial tilt had been corrected for parallax and atmospheric refraction. It is these corrected values that appear in column 3 of the data table
Continued next post ...