Geocentrism: Flogging a Pink Unicorn by Alec MacAndrew (Ph.D. in physics)

See also Alec's www.EvolutionPages.com (contains another copy of this article)

Also Geocentrism Disproved: Ken Cole vs. Robert Sungenis

(from the Catholic Answers apologetics forums, December 2005, pictures and links added by P)

Introduction



Against my better judgement, I agreed to post a summary of the arguments that demonstrate that geocentrism (the doctrine that the earth is the unmoving centre of the universe) is not a tenable hypothesis for a reasonable person with a moderate knowledge of modern physics. Please note that I am not seeking to show heliocentrism or any-other-centrism, merely that geocentrism is not a tenable hypothesis. Here we go.



The whole argument can be summarised in one sentence, so if you can't be arsed to read the whole thing, just read the next sentence:

In Newtonian mechanics, geocentrism cannot be true for many physical reasons; in General Relativity the centre of the universe has no meaning, so to claim that the earth is the centre of the universe is meaningless; in neither system can the earth be said to be the unmoving centre of the universe.

I'll also argue that the promotion of geocentrism is unnecessary for salvation, is contrary to reason, and represents a major source of scandal, calling ridicule down on the Church and the Faithful.



OK, let's start. (I have posted some of this material before and some of it is new).

Newtonian mechanics

In Newtonian mechanics, geocentrism cannot be true for many physical reasons.



Newtonian mechanics works within Euclidean geometry, which, for our purposes, we can summarise as a two dimensional spatial geometry based on an absolute space. Euclidean space is absolute and independent of matter or energy, which exist within Euclidean space without, in any way, affecting it. In addition, Newtonian mechanics relies on an additional dimension of absolute time.



Note that the concept of the equivalence of reference frames exists in Newtonian mechanics. It is a mistake to think that the idea that reference frames are equivalent is a new finding of Special or General Relativity. Indeed, the concept of relativity and the equivalence of reference frames was first understood by the great scientist, Galileo, whose name is given to the mathematical expressions used to transform between reference frames in Euclidean geometry -- these expressions are called Galilean transformations after him.



Galilean relativity states that relative motions of systems of bodies are the same no matter what inertial reference frame they are in, where an inertial reference frame is one in which the motion of a body not subject to forces is in a straight line and uniform and where the acceleration of bodies is proportional to applied forces. In Newtonian mechanics inertial reference frames move uniformly and rectilinearly with respect to one another.



Newton used this property of Galilean relativity in his calculations of planetary motion. It follows from the definitions of inertial frames and their equivalence that the centre of mass of an isolated system of bodies is at rest in an inertial frame. Newton reasonably approximated the solar system as an isolated system of bodies (this is not strictly true, but the forces and influence of the rest of the universe on relative motions within the solar system are vanishingly small on the scale of years). Within this reference frame, he then calculated the accelerations that would result from the gravitational forces between the bodies. Newton rejected the notion of geocentrism and heliocentrism (neither of which were ever to make an appearance in physics again); instead it is the centre of mass of the system of bodies (in this case the solar system), that is at rest with respect to the reference frame -- all the other bodies (including the sun) experience accelerations and are not therefore at rest in the inertial frame. The sun, of course, is vastly more massive than every other body in the solar system, and so its centre is nearly at the centre of mass of the solar system and nearly stationary with respect to it, but not quite.

So heliocentrism, within the solar system, can be seen as a close approximation to the Newtonian case. All of this is true whether we observe this from an inertial frame at rest with respect to the solar system or the fixed stars, as we can transform between them using the Galilean transformation.



It is unreasonable to hold that the earth is the unmoving centre of the universe according to Newtonian physics, in which there is an absolute space. The arguments against geocentrism in a Newtonian universe are overwhelming and have been rehearsed many times. I do not intend to go into them in detail, but I list some of them below.

Geostationary Orbits and Geostationary Satellites (picture right): To achieve a geostationary orbit, a geosychronous orbit is chosen with an inclination of either zero, right on the equator, or else low enough that the spacecraft can use propulsive means to constrain the spacecraft's apparent position so it hangs motionless above a point on Earth. (Any such maneuvering on orbit is a process called station keeping.) The orbit can then be called geostationary. This orbit is ideal for certain kinds of communication satellites or meteorological satellites. See Basics of Space Flight: Planetary Orbits

(1) Satellites are launched to the east because the earth's rotation boosts the velocity of the satellite and helps it to achieve orbital velocity -- the earth is used as a sling shot

Satellites are launched to the east because the earth's rotation boosts the velocity of the satellite and helps it to achieve orbital velocity -- the earth is used as a sling shot (2) Satellite launch sites are as close to the equator as nationally possible for the same reason as 1.

Satellite launch sites are as close to the equator as nationally possible for the same reason as 1. (3) Points at rest or in uniform motion in inertial frames of reference (which in Galilean relativity are frames of reference in which a point not under the influence of applied force continues in rectilinear and uniform motion), have no unresolved forces

Points at rest or in uniform motion in inertial frames of reference (which in Galilean relativity are frames of reference in which a point not under the influence of applied force continues in rectilinear and uniform motion), have no unresolved forces (4) The earth has obvious unresolved forces (items 3 and 4 have relevance in Riemannian geometry too)

The earth has obvious unresolved forces (items 3 and 4 have relevance in Riemannian geometry too) (5) Foucault's pendulum demonstrates the existence of unresolved forces at the surface of the earth

Foucault's pendulum demonstrates the existence of unresolved forces at the surface of the earth (6) Weather systems always rotate counter clockwise in the northern hemisphere and vice versa in the southern hemisphere owing to the coriolis force of rotation

Weather systems always rotate counter clockwise in the northern hemisphere and vice versa in the southern hemisphere owing to the coriolis force of rotation (7) Oblate earth -- the earth has a greater girth at the equator than across the poles owing to the centrifugal force of the earth's diurnal rotation

Oblate earth -- the earth has a greater girth at the equator than across the poles owing to the centrifugal force of the earth's diurnal rotation (8) Parallax in the star fields as a consequence of earth's rotation round the centre of gravity of the solar system

Parallax in the star fields as a consequence of earth's rotation round the centre of gravity of the solar system (9) Red shift in the star field as a result of ditto

Red shift in the star field as a result of ditto (10) A star field with a radius of 14 billion light years and a mass 3x10^27 times that of the earth rotating around the earth once a day and wobbling with a amplitude of 186 million miles at an angle of 23.5 degrees annually is an untenable dynamical system in Newtonian mechanics

A star field with a radius of 14 billion light years and a mass 3x10^27 times that of the earth rotating around the earth once a day and wobbling with a amplitude of 186 million miles at an angle of 23.5 degrees annually is an untenable dynamical system in Newtonian mechanics (11) Systematic forces which explain the dynamics of retrograde planetary motion are not available in a Newtonian gravitational system

Foucault Pendulum: Jean Bernard Leon Foucault was born in 1819, the son of a French publisher. He showed early skill in making mechanical toys, studied medicine, but shifted to physical sciences at the Paris Observatory. He became one of the most versatile experimentalists of all time. By a Foucault Pendulum, man can demonstrate at any point on the Earth's surface (except on the equator) that the earth rotates. See About Foucault Pendulums

Interestingly, there is a serious sense in Newtonian mechanics that refutes the idea of not just the earth, but any body being the unmoving centre of the universe. Even if we accept, for the sake of argument, that the universe is spatially finite, and we accept that there is a point in absolute space that corresponds to its centre of mass, no object with finite mass can be permanently at rest with respect to that point, because all objects with finite mass necessarily experience accelerations caused by the gravitational forces resulting from the presence of other bodies of finite mass in the universe, and they therefore cannot be permanently at rest in any given Newtonian inertial frame.



Geocentrism is meaningless in General Relativity (GR)



Geocentrism, indeed any-centrism, is meaningless in the formulation of GR that accurately describes the universe structure. So let's see what that is.



First of all, solutions to Maxwell's electromagnetic equations yielded an expression which showed that the propagation of electromagnetic energy (light) is constant irrespective of the frame in which you measure it. So now we have a phenomenon that disobeys the principle of Galilean relativity. The solution to this conundrum is Einstein's special relativity. The inconsistencies between constant c and Galilean relativity are resolved by giving up the idea that length and time are independent of reference frame. The Galilean transformation is replaced by the Lorentzian transformation and Newtonian spacetime by Minkowski spacetime. We have to give up the concept of simultaneity -- events that appear simultaneous in one reference frame do not appear simultaneous in another, so we also lose the concept of absolute time.



Einstein then developed his insight that the force of gravitational attraction is indistinguishable and no different in principle from the force of acceleration.



The Einstein equivalence principle states that in a local inertial reference frame the outcome of any non-gravitational experiment is independent of the velocity of the frame or its position in spacetime and that the laws of nature are those of special relativity. This does NOT mean that rotation is the same as being static nor does it deny the special status of inertial reference frames; in fact, EEP holds ONLY in inertial reference frames



The consequence of this is that in General Relativity, spacetime is not flat as it is in Newtonian mechanics or Special Relativity, but is curved. Moreover, the curvature is determined by the presence of mass. We now have to work in non-Euclidean geometry, with no absolute flat co-ordinate system. In order to calculate the dynamic behaviour of masses we have the complex problem that the presence of the mass curves spacetime in such a way as to create what we observe as the gravitational force (although in GR we shouldn't think of gravity as a force) between them, but also influences the geometry of space and time in their locality. We have to work in Riemannian geometry using tensor analysis the details of which are way beyond the scope of this post.



The Einstein field equation is the generalised formulation of gravitational physics and one of the reasons that it is expressed in terms of tensors is that that allows a co-ordinate free description. It is important that no co-ordinate system is deemed to have precedence, as it is possible, in any such preferred system, to re-introduce the discarded notion of gravitational force. So GR is formalised in a co-ordinate free manner.



From a cosmological perspective, there have been various attempted solutions of the Einstein field equation, the most successful of which, the Friedmann-Robertson-Walker solution closely reflects the observed universe. In the FRW metric, the universe is homogeneous and isotropic, that is, from any point it looks the same in all directions and its properties at all points are the same.



In a homogeneous universe the curvature of space time is invariant with position and determined by the energy density of the universe. Locally however, spacetime is strongly curved by the presence of massive objects.

Stellar Parallax (picture right): As the Earth revolves around the Sun, it moves 2 AU from one side of its orbit to another in 6 months. Viewed from these two different locations, a nearby star would appear to shift position with respect to more distant stars. The amount of the shift is called the "Stellar Parallax." As the distance to a star increases, the amount of parallax decreases. Parallaxes were not observed at the time of Copernicus. The "non-observation of stellar parallaxes" was one of the principal objections to the Copernican heliocentric model. Copernicus and others countered that this was because the stars were too far away to produce measurable parallaxes. Copernicus and others were right: stellar parallaxes were not easily observed because the stars are much more distant than people originally suspected: All stellar parallaxes are less than 1-arcsecond. The nearest star with the largest parallax is Alpha Centauri, with a parallax of 0.76 arcsecond.



The first stellar parallax was observed in 1837 by the astronomer Friedrich Wilhelm Bessel for the star 61 Cygni. Modern measurements of parallaxes use photography or digital imaging techniques. A new generation of "interferometric" techniques is being developed for upcoming space missions that will be able to measure parallaxes with a precision of 1 micro-arcsecond.

Now what about the proposition that the earth is the unmoving centre of the universe? Well, GR states that the effect of a force resisting gravity and the effect of a force accelerating a reference frame are identical and indistinguishable. In GR, spacetime geometry is determined by the distribution of matter/energy in the universe (there is no absolute space) and the spacetime geometry influences the flow of matter/energy. It is therefore utterly meaningless to talk about a spatial centre for the universe because in GR, space has no absolute meaning.



Mach's principle states that inertia is not absolute but depends on matter in the universe. Matter/energy there determines inertia here. There is no such thing as absolute rotation in the universe independent of the distribution of matter, and no absolute space. The closest we can get to a definition of absolute rotation is rotation with respect to the average distribution of matter in the universe: the distant stars; or rotation with respect to a local inertial frame (which is, in fact, very closely aligned to the star field, although this alignment can be slightly perturbed by the influence of large nearby masses)



General covariance applies in all inertial frames of reference. It is extremely misleading, and a characteristic error of geocentrists to claim that in GR, ALL reference frames are equivalent. THEY ARE NOT! Let's do a thought experiment. Let's imagine we are in a spacecraft, with blacked out windows, that is rotating so that the centrifugal force creates an artificial gravity -- we are pinned against the walls of the craft by this force. We then employ the steering motors of the spacecraft to manoeuvre the craft so that all forces that we can measure within the craft disappear. We open the window blinds and what do we see? The craft is not rotating with respect to the stars. The craft is now at rest within what we call a local inertial frame of reference, one in which there are no measurable residual forces due to linear accelerations. According to Mach, matter/energy there determines inertia here, so the inertial frame aligns approximately with the star field (with local perturbations due to large nearby rotating masses -- a phenomenon known as frame dragging).



In GR, an inertial frame is defined as a frame in free-fall in which an object at rest experiences no forces. The equivalence principle applies only in inertial frames. The surface of the earth is absolutely not an inertial frame in GR, because if you are standing on the surface of the earth you experience a force due to the local curvature of spacetime (gravity) as well as coriolis and centrifugal forces. Such forces do not appear in an inertial frame.



Now we have seen that talking about a centre of the universe in GR (or at least as far as the Friedmann- Roberston-Walker metric solution to the Einstein field equation goes) is meaningless, but is it meaningless to talk about absolute rotation? Well when astronomers and cosmologists talk about rotation in the universe they do so with respect to local inertial frames (which we have seen are very closely aligned to the distant stars), or with respect to the star field itself. So in GR, the formal conclusion is that it is meaningless to posit absolute rotation independent of matter in the universe, but that inertial frames are special (in that they uniquely represent conditions with no detectable residual forces), they align with the star field according to Mach's principle, and if absolute rotation means anything at all, it means being in a non-inertial reference frame rotating with respect to the stars; in such a frame forces are detectable. The Earth's surface is just such a non-inertial frame: by this definition it rotates.



Apples are not Frogs



Geocentrists also confuse kinematic transformations with dynamic transformations. Just because a kinematic transformation is possible does not mean that the physics cannot distinguish between the two reference frames. Here's a simple example. A flea leaps off the surface of the earth. Now there is nothing wrong with describing that event kinematically in a reference frame stationary with respect to the flea. In such a reference frame the earth accelerates away from the flea rapidly to a maximum velocity at the point where the flea loses contact with the earth. Thereafter, the earth continues to move away from the flea but more and more slowly until the earth stops and begins to accelerate back towards the flea. The earth eventually hits the flea at about the same speed that they originally parted. The earth then slows down and stops. (The event can be described from an earth frame of reference simply by swapping the words flea and earth).



From a dynamic point of view the reference frames are not equivalent. A point in the flea's reference frame will experience forces associated with the flea's rapid acceleration and deceleration. A point in the earth's reference frame will experience almost zero force as the acceleration of the earth's frame due to the flea's antics is very very very tiny. Dynamically it is not correct to say that the earth leapt off the flea. Strictly speaking, the reference frame that experiences zero acceleration and zero force as a result of this experiment is one in which the centre of gravity of the flea and the earth is at rest.



Similarly, it is not dynamically correct to say, as you must if you hold that the earth is the unmoving centre of the universe in an absolute space, that the impact of a large meteorite on the earth causes an absolute acceleration of the entire universe.



A Sungenis specific error



A particular Sungenis nonsense is reference to the "gyroscopic rotation of the universe stabilising the earth at its centre of mass." First of all, this confuses solid body dynamics with many-body kinematics. Secondly if he really believed in the equivalence of the rotating and static star field reference systems he would acknowledge that the "stabilising forces" would have to exist in both co-ordinate systems -- but where in the reference frame at rest with respect to the distant stars are we to find forces that prevent the earth from wandering off through the universe due to the influence of locally acting forces such as gravitational attraction to large masses. Indeed the measurement of the CMB anisotropy indicates a relative motion between the solar system and the primordial radiation of the early universe of 365 km/sec. (Incidentally, the CMB also aligns with, i.e. does not rotate with respect to the star field and local inertial frames, so we can say that the star field frame and the local compass of inertia is at rest with respect to the spacetime manifold of the primordial universe as described by the FRW model).



Geocentrism harms the church and the faith



Geocentrism is either wrong or meaningless depending on whether you are working in Newtonian mechanics or GR. A belief in geocentrism doesn't harm one's ability to get to heaven any more than a belief in young-earth creationism, a literal belief in Noah's flood or a belief in Santa Claus or pink unicorns (except to the extent that we suppress our reason, we are suppressing one of the important faculties that distinguishes us from other animals).



But neither is holding to the plain error of geocentrism any help to the faithful. Frankly, most people don't care. The majority of people who come across Robert's bunkum will see it as that. But since Robert represents himself as a master apologist for the CC, then it's the CC that gets smeared with the buffoonery. It's certain that Robert causes scandal and damages the Church's reputation amongst the faithful and unbelievers because of his insistence on this scientifically wrong and theologically unimportant point. It is appalling science, poor apologetics, and abysmal evangelism.



He can't hope to convince scientists, because the idea is scientific candy-floss, uninteresting and meaningless in modern cosmology, promoted only by acolytes like Mark whose scientific understanding is not just small but negative.



Summary



To summarise, in order for the "centre of the universe" to have meaning, we need an absolute space. In such a space, Newtonian mechanics (plus special relativity) applies, and there are many compelling reasons in that system which show that the earth cannot be the unmoving centre. In order to refute these reasons, Robert calls on GR, but in GR talk of a centre is meaningless (Robert also vehemently denies GR so logically he shouldn't use it). In an absolute space model the earth cannot be at the centre and in a GR model there is no centre. Robert is caught in a fundamental logical inconsistency.



I leave anyone who is deranged enough to care sufficiently about geocentrism to have read all this, to comment about it to your heart's content.



Here endeth the flogging of the pink unicorn.

Alec MacAndrew (Ph.D. in physics)

See also Alec's www.EvolutionPages.com

Also Geocentrism Disproved: Ken Cole vs. Robert Sungenis

MESSENGER Earth Departure movie (picture right): The Mercury-bound MESSENGER spacecraft captured several stunning images of Earth during a gravity assist swing-by of our planet on August 2, 2005. Several hundred images taken with a wide-angle camera in its Mercury Dual Imaging System (MDIS) were sequenced into a movie documenting the view as MESSENGER departed Earth. Comprising 358 frames taken over 24 hours, the movie follows Earth through one complete rotation. The spacecraft was 40,761 miles (65,598 kilometers) above South America when the camera began rolling on August 2, and 270,847 miles (435,885 kilometers) away from Earth -- farther than the Moon's orbit -- when it snapped the last image on August 3. FLV | WMV Galileo Earth Rotation movie (picture right): Using time-lapse photography, the Galileo spacecraft looked back to capture the rotation of the earth, from a distance of about 4 million miles in December 1990. FLV | WMV At the equator, the circumference of the Earth is 40,070 kilometers (or 24,900 miles), and the day is 24 hours long so the speed is 1670 kilometers/hour (or approx 1040 miles/hour). This decreases by the cosine of your latitude so that at a latitude of 45 degrees, cos(45) = .707 and the speed is .707 x 1670 = 1180 kilometers/hour. You can use this formula to find the speed of rotation at any latitude. If the Earth stopped spinning suddenly, the atmosphere would still be in motion with the Earth's original 1040 mile per hour rotation speed at the equator. All of the land masses would be scoured clean of anything not attached to bedrock. This means rocks, topsoil, trees, buildings, your pet dog, and so on, would be swept away into the atmosphere.

Appendix: Vatican admits Galileo correct (from the Los Angeles Times, October 31, 1992)



VATICAN CITY -- It's official: The Earth revolves around the sun, even for the Vatican.



The Roman Catholic Church has admitted erring these past 359 years in formally condemning Galileo Galilei for entertaining scientific truths it long denounced as anti-scriptural heresy. Pope John Paul II himself turned up Saturday for a meeting of the Pontifical Academy of Sciences to help set the record straight on behalf of the 17th century Italian mathematician, astronomer and physicist who was the first man to use a telescope and who is remembered as one of history's greatest scientists.



"The underlying problems of this case concern both the nature of science and the message of faith," the pope said. "One day we may find ourselves in a similar situation, which will require both sides to have an informed awareness of the field and of the limits of their own competencies."



Thirteen years after he appointed it, a commission of historic, scientific and theological inquiry brought the pope a "not guilty" finding for Galileo, who, at age 69 in 1633, was forced by the Roman Inquisition to repent and spent the last eight years of his life under house arrest. The commission found that Galileo's clerical judges acted in good faith but rejected his theories because they were "incapable of dissociating faith from an age-old cosmology" -- the biblical version of the Earth as the center of the universe.



"God fixed the Earth upon its foundation, not to be moved forever," says one Bible verse contradicted by Galileo's pioneering notion that the Earth spins daily on its axis and makes an annual journey around the sun.



Unable to comprehend a non-literal reading of Scripture, according to the commission, the judges feared that if Galileo's ideas were taught, they would undermine Catholic tradition at a time when it was under attack by Protestant reformers such as Martin Luther and John Calvin.



"This subjective error of judgment, so clear to us today, led them to a disciplinary measure from which Galileo 'had much to suffer,'" Cardinal Paul Poupard, the commission chairman, told the pope. "These mistakes must be frankly recognized, as you, Holy Father, have requested."



Tried on "vehement suspicion of heresy," Galileo was forced to swear that he "abjured, cursed and detested" the errors of his work, which extended the findings of the Polish astronomer Nicholaus Copernicus that the Earth Moves. Legend insists that as he finished his abject, life-saving confession of his errors to the black-cowled Inquisitors, Galileo muttered under his breath: "Nevertheless, it does move." (Latin: eppur se muove, but it does move).



The case was important to him, John Paul said Saturday, because over the centuries it had become "the symbol of the church's supposed rejection of scientific progress, or of 'dogmatic' obscurantism opposed to the free search for truth."

Books and Sources

The Copernican Revolution: Planetary Astronomy in the Development of Western Thought by Thomas S. Kuhn (Harvard Univ Press, 1957)

Physics for Dummies (2004)

The Complete Idiot's Guide to Theories of the Universe by Gary F. Moring (2001)

Relativity: The Special and General Theory by Albert Einstein (Three Rivers Press, reprint edition 1995)

Galileo Was Wrong by Robert Sungenis (three large volumes)

Geocentrism Debunked site by David Palm (responds to many of Sungenis 'scientific' and 'historical' claims)