Geometry 101

Q&A

Wednesday, 27 July 2011 09:58

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I came across a discussion on geocentrism and stationary satellites between you and Gary Hoge on his web site, catholicoutlook.com.

Marcus Grodi keeps noting the solution of many questions, phrased as either/or, lies in the realization that the situation is truly both/and.

Geocentrism or heliocentrism is another example. Galileo was so overwhelmed with the simplicity of the Copernican description of planetary motion about the sun, that he said it was true and the geocentric description, false. It was either/or. In other words, Galileo claimed that motion is absolute, not relative. He was wrong. It is relative, i.e., it depends on one's choice, within a geometry problem, of a reference point. If motion absolutely had to be referenced to the sun, it would be false to say a person walked across the room, or to say a plane flew from Chicago to LA. Describing the path of such a plane flight in reference to the sun, would be beyond the ability of most of us. Yet, any other description (and even the designation as Chicago to LA) of such a flight would be false! The path in space in reference to the sun, would be totally different in July from the path in space in reference to the sun in October!

In any geometry problem the choice of a reference point is arbitrary. It is as true to say the sun moves about the earth as to say the earth moves about the sun. The proposition, that the earth moves around the sun and not vice versa, is neither true nor false. It is meaningless. It is based on the false proposition that in geometry, the choice of a reference point can be true or false, when it is clearly arbitrary. Specifically, the proposition could only have meaning if motion were absolute about an objectively existing reference point (or coordinate system) of which there were only two possibilities, geocentric and heliocentric. Geometric reference points and coordinate systems have no objective existence. They are constructs of human thought existing only in the human mind.

Hoge argued that a geocentric description is false, because one cannot maintain the validity of the inverse square law of gravitation and the motion of a man-made satellite around the earth, at an angular velocity around the equator, such that the satellite is stationary relative to the surface of the earth, if the earth, itself, is not rotating about its polar axis at that same angular velocity. He concludes: since the earth is rotating, it cannot also be stationary.

What Hoge should have argued was that given the geocentric coordinate system, which he arbitrarily chose, and the satellite motion described, then the earth is rotating on its polar axis relative to that stationary coordinate system, while the earth is stationary relative to the satellite. This conclusion, based on the acceptance of geocentrism, cannot possibly disprove geocentrism. Also, it cannot disprove that one may not chose another geocentric coordinate system, compatible with the inverse square law of gravitational attraction, and in which the earth is not rotating on its axis.

(A) Consider the geocentric coordinate system whose origin is the center of the earth, one positive axis is polar, exiting the earth at the North Pole; one axis is through the equator and exits the earth at the international dateline at time, t; and the other orthogonal axis exits the equator 90 degrees displaced from the international dateline at time, t.

(B) Given the coordinate system of paragraph (A), to have a satellite continuously above the same spot on the equator (i.e., motionless with respect to the earth) and be compatible with the inverse square law, the earth must be rotating on its axis, IF the coordinate system (A) is taken as defining a direction through the international dateline at time, t, and maintaining that orientation, such that six hours later that same axis exits 90 degrees displaced from the dateline and the other axis, which was oriented 90 degrees from the dateline is now 180 degrees displaced. In other words, if the rotation of the earth is taken for granted.

(C) Consider, in contrast, the coordinate system of paragraph (A), but whose equatorial axes exit the earth, one at the dateline and the other 90 degrees displaced from the dateline, not only at time, t, but continually throughout time, (the Sungenis system). The earth and the satellite would be stationary with respect to this coordinate system. Yet, the inverse square law would be valid and applicable, because the location of the satellite would be referenced to an inverse-square-law, geocentric axis, spinning within the stationary earth.

The essential difference between (B) and (C) is: in (B) the earth is rotating relative to a stationary conceptual axis; in (C) the conceptual axis is rotating relative to the earth. MOTION IS RELATIVE, NOT ABSOLUTE! COORDINATE AXES ARE CONCEPTUAL, EXISTING ONLY IN THE HUMAN MIND! The choice cannot be between true and false, but only between more and less aesthetically attractive, i.e. as a matter of personal taste. There is one exception to coordinates being a matter of choice. It is the orientation of the eyes within the human skull, but this is usually and appropriately ignored in the choice of a conceptual coordinate system. It is not heliocentrism or geocentrism that is the ultimate coordinate system, but homocentrism, and actually egocentrism. It is only conceptually that one can have an observation post outside of his own body!

You may recall from analytical geometry that location and motion with respect to any coordinate system may be translated in reference to any other coordinate system. That is not to say it that it would be easy or practical to do so, or that every coordinate system is equally suited to a description of the specific location and motion under consideration. Aesthetics furnishes valid criteria for choice within problems of geometry.

Robert E. Drury

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R. Sungenis: Robert, thank you for your thoughts. I am in agreement with your observations. The only thing I would add is that, if, indeed we have a centrally located and motionless Earth, then by definition, there is no relative motion, only absolute motion (at least in the vicinity of the Earth) since all measurements can be made using the immobile Earth as one of the coordinates. This is the glory, if you will, of the geocentric system. We don't have to have all kinds of Riemann geometry and tensor calculus to figure out where something is located in the universe. All we need do is use Cartesian coordinates that have the immobile Earth as their foundation.

God be with you.

Robert Sungenis