[6] Ellipses and Orbits of Heavenly Bodies

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The path that one heavenly body takes as it goes around another heavenly body is called its orbit. Ancient peoples did not know that the planets orbited the sun. Instead they thought that all the heavenly bodies circled around the earth. There was only one ancient Greek astronomer who went against his contemporaries by espousing his theory that the "wandering stars and the earth" (the planets) circled the sun, namely Aristarchus of Samos c. 280
BCE (see pages 74-75 of Toomer 1996). The only other ancient astronomer who is known to have accepted this sun-centered viewpoint is Seleucus of Babylon c. 150 BCE (see page 391 of Pedersen 1993 and page 247 of Stahl).

When discussing history, it is always best to quote from the original
historical sources or translations of them (these are called primary sources), and then arrive at conclusions. Unfortunately, when the history of ancient astronomy is the topic, problems are encountered that prohibit quoting from original sources before Ptolemy (c. 150 CE). One insurmountable problem is that the important ancient astronomical texts are not written for the purpose of teaching others their methods; there are no ancient textbooks. Instead we find columns or tables of numbers with some occasional notes, and there are records of observations with some notes. The ingenuity of modern historians of mathematics and astronomy has enabled them to determine the meanings of the various columns and the meanings of the scientific terms used.

Modern science has reverse engineered the ancient texts to learn what must have been their ancient methods in order for the columns of numbers and the occasional notes to make sense. While English translations of ancient astronomical texts certainly exist, there would be no benefit to quote from any one text for an understanding of the underlying methods unless one were writing a detailed textbook which required some significant knowledge of
mathematics and astronomy. This difficulty in not being able to quote from the primary sources pertaining to ancient astronomy for the layman makes it necessary to quote and cite modern secondary sources.

For the history of astronomy the original ancient sources are so obscure that a correct interpretation requires great care by specialists in this field, so that scholars who are only historians or only modern astronomers may easily go astray in their conclusions. A generic example of the obscurity is a writing tablet with orderly columns of numbers having some symbol at the top of each column and some miscellaneous remarks. First, one translates the numbers into today's numbers, and also translates the miscellaneous remarks. Second, one determines patterns to the numbers and relates these patterns to known values relating to astronomical time periods of heavenly bodies. Some columns become reasonably easy to interpret or explain, while other columns may remain a matter of modern scholarly debate for 100 years or more because the tablets themselves do not define the meaning of the columns.

Simply publishing a literal translation of the tablet does not do
the layman any good at all. Because of this, when some scholar publishes a paper about the history of ancient astronomy, it may require some years of scholarly debate in order that a clear mutual understanding of the correctness of that paper will emerge. During the twentieth century some papers were published in this subject that were subsequently proven false by the best scholars in this field.

But less knowledgeable writers on the history of science thought that some of these papers were correct before they were proven false, and thus popular published articles, Internet website articles, and books on the history of ancient astronomy are available with information that modern specialists in this field know to be false. Unless a person devotes some years of study to the literature on this subject and keeps up with the latest journals and advanced books related to the history of ancient astronomy, it is easy to be
led astray. I have performed Internet searches and have been greatly dismayed at the widespread misinformation available. I have taken great care to learn who the best authorities are in this field, and I have only used internationally respected specialists for my quotations and sources. I have kept up with the latest literature for the specific details that are especially significant for this study.
Educated people of today know that the earth rotates on its axis once each 24-hour day, but we still speak of the sun rising up in the morning rather than the earth rotating to enable us to see the sun. Thus the sun does not really move fast around the earth so as to truly rise in the morning, but the expressions in our language, which have been handed down to us since ancient times have remained. The NKJV states in Eccl 1:5, “The sun also arises, and the sun goes down, And hastens to the place where it arose”.

Nothing is improper here by saying what appears to happen from the
perspective of an observer on earth. Gen 1:14 mentions the dividing of the daytime from the night, and it says that the lights in the heavens have this purpose. We must not be critical of the Bible here on the grounds that the rotation of the earth on its axis would be explained as the cause today.

Regardless of the physics, the Bible was written in terms of human
perception from the surface of the earth and must be accepted this way. The Bible gives no hint of advanced mathematical or astronomical knowledge from the days of Moses. Ancient people thought that the sun went around the earth in an orbit having the shape of a circle, and that the moon went around the earth in an orbit having the shape of a circle. Ancient Greek astronomers used the mathematics of circles to approximate the predictions of eclipses and other astronomical events, but they had to add some complexity to their mathematical schemes because they eventually
discovered that the speed of the moon around the earth was not constant.

They modified their mathematics in an attempt to make their predictions agree with what they observed later, yet they continued to accept circular motion of the heavenly bodies.
The German astronomer Johannes Kepler (1571-1630) discovered that the orbit of Mars around the sun had the shape of an ellipse. Sir Isaac Newton (1642-1727) proved that all planets of our solar system had an orbit around the sun shaped as an ellipse. Ancient predictions could never become extremely accurate compared to what was achieved by Newton because ancient astronomers did not truly understand the laws of motion, the shape of orbits, the physical reality of what was primarily moving, and the higher
mathematics needed to prove the more precise physical relationships through time. Kepler was innovative and brilliant in using geometry to derive his results about Mars, but without having the calculus that Newton was the first to apply to astronomy, Kepler was greatly handicapped to go beyond his great achievements. But Kepler had at his disposal the very carefully
documented results of many years of fine observations by Tycho Brahe, who used accurate carefully constructed mechanical astronomical instruments, and Brahe was funded by willing donors who were not concerned that the effort was not useful to people at that time. Kepler stood upon the shoulders of Brahe. Newton said that his achievements were only possible because he stood upon the shoulders of giants. The inventions of the telescope and the pendulum clock were a great help to astronomers who gave accurate data to Newton. The invention of the printing press helped to spread scientific achievements far and wide so that brilliant minds in diverse places could rapidly feed upon each other's results. The funding of European universities and the exchange of knowledge among people in a variety of scientific disciplines that was characteristic of the renaissance helped to make this
achievement possible. The ancient world lacked such a critical mass of diverse inventions and published scientific papers that teamed together to enable such magnificent results. A key word of this paragraph is ellipse. A few remarks about the nature of an ellipse may be useful in order for the reader to appreciate certain later comments concerning the moon's orbit around the earth. If the reader does not understand some of the discussion in the next few paragraphs, it is of no great consequence.

Picture a circular white pancake resting on a dark tabletop and consider looking at it from directly above. Its boundary looks like a circle. Then picture yourself standing upright on the floor a short distance from the table while looking at the pancake. If the height of the table is only the size of your big toe, the boundary of the pancake will look very much like a circle, but if the height of the table is only a little below the height of your eyes, the boundary will look like a very squashed circle. At some in between height,
the boundary will look somewhat like an egg. Each boundary shape of the circular pancake viewed from a very low height to one near the height of your eyes is technically called an ellipse in mathematical terminology.

The orbit of the earth around the sun is nearly a perfect ellipse that is somewhat close to being a circle. The orbit of the moon around the earth is nearly a perfect ellipse that is a little less circular. If the moon and the planets did not have gravitational relationship with the earth, then the earth's orbit would be as perfect an ellipse as one could expect for a physical object. If the sun and the planets away from the earth did not attract the moon, then the moon's orbit around the earth would be a nearly perfect ellipse.

However, in a technical sense the last sentence is not quite true because if the sun continues to pull at the earth and would no longer pull on the moon, the moon would fly off away from the earth because the annual orbit of the moon around the sun is based on the sun's pull on the moon, not the earth's pull on the moon.

The position of the sun within the earth's orbital ellipse and the position of the earth within the moon's orbital ellipse are not at the center where one might expect. The following will explain where they are. Picture a straight stick nailed to the center of an ellipse, and picture the length of the stick to only extend from one edge of the ellipse to the other. Now imagine hitting the stick so that it spins around the ellipse, but imagine the length of the stick stretching and shrinking as it turns, so that it always only extends from one edge of the ellipse to the other. The major axis of the ellipse is the stick's line segment when it is longest in its spin, and the minor axis of the ellipse is the stick's line segment when it is shortest in its spin. These axes are perpendicular to one another and cross at the center of the ellipse.

Picture a stick in the position of the major axis, but imagine it to be broken at the center of the ellipse with its two halves loosely glued together so that it may change angle where the glue holds them. Now imagine putting the palm of each of your hands at the ends of the stick and slowly pushing them together as when beginning to clap hands. The clapping movement should be toward the center of the ellipse so that as both hands move at the same speed, the stick rests in the plane of the ellipse, and the glued spot moves up
the minor axis. Stop the movement when the glue touches one end of the minor axis. The two ends of the stick at your palms lie along the major axis, and the two halves of the stick are joined at one end of the minor axis. Now each end at a palm is at a point called a focus of the ellipse. Each ellipse has two foci, both of which are on the major axis and off the minor axis. The procedure described shows that the distance from each focus to an end of the minor axis equals half the length of the major axis. There is only one point
on an ellipse closest to a focus; that is the nearer of the two points at the ends of the major axis. Similarly, there is only one point on an ellipse furthest from a focus; that is the further of the two points at the ends of the major axis.

The sun is at a focus of the earth's orbital ellipse. The earth is at a focus of the moon's orbital ellipse. Thus the sun is never at the center of the earth's orbit and the earth is never at the center of the moon's orbit.