Celestial navigation is allegedly based on the theory that the Round Earth is the center of the universe and that everything is revolving around it.
But I'm not sure if even that model exists. We have tables of the Moon based on historical data, not a mathematical revolving model; at least one that doesn't use epicycles.
The great RE mathematician Isaac Newton used epicycles in his math of the Moon going around the Earth:
https://wiki.tfes.org/Astronomical_Prediction_Based_on_Patterns#Newton.27s_EpicyclesNewton's Epicycles
Historian of Science William Whewell (bio) informs us that Newton used epicycles for the Moon:
History of the Inductive Sciences (1846)
“ 3.— The Epicyclical Hypothesis was found capable of accommodating itself to such new discoveries. These new inequalities could be represented by new combinations of eccentrics and epicycles: all the realand imaginary discoveries by astronomers, up to Copernicus, were actually embodied in these hypotheses; Copernicus, as we have said, did not reject such hypotheses; the lunar inequalities which Tycho etected might have boen similarly exhibited; and even Newton36 represents the motion of the moon’s apogee by means of an epicycle. As a mode of expressing the law of the irregularity, and of calculating its results in particular cases, the epicyclical theory was capable of continuing to render great service to astronomy, however extensive the progress of the science might be. It was, in fact, as we have already said, the modern process of representing the motion by means of a series of circular functions. ”
Take a look at this model of the Moon in
this paper.
See the illustration on page 600 and the caption in the image, and note that the basic model was "adopted ever since."
V. THE MANY MOTIONS OF THE MOON
A. The traditional model of the Moon
A plane through the center of the Earth is determined at an inclination g of about 5 degrees with respect to the ecliptic. The Moon moves around the Earth in that plane on an ellipse with fixed semi-major axis a and eccentricity « of about 1/18. The Greek model was quite similar, except that the ellipse was replaced by an eccentric circle.
The plane itself rotates once every 18 years in the backward direction, i.e., against the prevailing motion in the solar system, while keeping its inclination constant. The perigee of the Moon, its point of closest approach to the Earth, makes a complete turn in the forward direction in about nine years.
The following picture (see Fig. 1) emerges: first we fix the direction of the spring equinox or some fixed star near it as the universal reference Q in the ecliptic: counting always from west to east, we determine the angle h from Q to the ascending node, i.e., the line of intersection for the Moon’s orbit with the ecliptic where the Moon enters the upper side of the ecliptic; from there we move by an angle g in the Moon’s orbital plane until we meet the perigee of the Moon; and finally we get to the Moon by moving through the true anomaly f. All these three angles have a double time dependence: linear (increasing for f and g, while decreasing for h) plus various periodic terms that average to 0.
~
D. The evection—Greek science versus Babylonian astrology
The Babylonians knew that the full moons could be as much as 10 hours early or 10 hours late; this is due to the eccentricity of the Moon’s orbit. But the Greeks wanted to know whether the Moon displays the same kind of speedups and delays in the half moons, either waxing or waning. The answer is found with the help of a simple instrument that measures the angle between the Moon and the Sun as seen from the Earth. The half moons can be as much as 15 hours early or late. With the Moon moving at an average speed of slightly more than 308 per hour (its own apparent diameter!), it may be as much as 5° ahead or behind in the new/full moons; but in the half moons, it may be as much as 7°308 ahead or behind its average motion. This new feature is known as evection.
Ptolemy found a mechanical analog for this peculiar complication, called the crank model. It describes the angular coupling between Sun and Moon correctly, but it has the absurd consequence of causing the distance of the Moon from the Earth to vary by almost a factor of 2. In the thirteenth century Hulagu Khan, a grandson of Genghis Khan, asked his vizier, the Persian all-round genius Nasir ed-din al Tusi, to build a magnificent observatory in Meragha, Persia, and write up what was known in astronomy at that time. Ptolemy’s explanation of the evection was revised in the process. In the fourteenth century Levi ben Gerson of Avignon in southern France seems to have been the first astronomer to measure the apparent diameter of the Moon (see Goldstein, 1972, 1997). Shortly thereafter Ibn al-Shatir of Damascus in Syria proposed a model for the Moon’s motion that coincides with the theory of Copernicus two centuries later. The crank model was replaced by two additional epicycles, yielding a more elaborate Fourier expansion in our modern terminology (see Swerdlow and Neugebauer, 1984).
With the improvements of the Persian, Jewish, and Arab astronomers, as well as Copernicus, the changes in the Moon’s apparent diameter are still too large with +/- 10%. As in Kepler’s second law, the Fourier expansion (12) has to include epicycles both in the backward and in the forward direction, in the ratio 3:1.
"The crank model was replaced by two additional epicycles, yielding a more elaborate Fourier expansion in our modern terminology."
"With the improvements of the Persian, Jewish, and Arab astronomers, as well as Copernicus, the changes in the Moon’s apparent diameter are still too large with +/- 10%. As in Kepler’s second law, the Fourier expansion (12) has to include epicycles both in the backward and in the forward direction, in the ratio 3:1."
That epicycle Moon model was used in antiquity before gravity, and was used by Newton with his gravity model, and appears to be still used, judging by the quotes on the
Astronomical Prediction Based on Patterns page in our Wiki. So I'm not entirely sure that the revolving model you think exists actually ever did exist. It appears as if they couldn't really get it to work cleanly even before gravity theory.
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