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Heliocentric problem no. 5 - Schröter's Effect

Dr. Neville Thomas Jones, Ph.D., D.I.C., M.Sc.(Phys), M.Sc.(Comp), B.Sc.(Hons),
formerly of the Clarendon Laboratory, Oxford University, England.

When I first began questioning the heliocentric myth in early 2002, I spent a lot of time reading and re-evaluating what I 'knew'. Upon reaching the conclusion that we are being taught rubbish, I eagerly related this revelation to my wife. Her reply? "[She] knew it all along. Ever since [she] was five!"

Anyway, the source of most confusion regarding the starry heavens is rooted in the following:

  1. Although the civilizations of the past maintained a centrally-located, non-moving World, this cosmology was effectively done away with by Canon Mikolaj Kopernik (usually given the Latin name, Nicolas Copernicus), who wrote in his infamous book, Die Revolutionibus Orbium Coelestium, published in 1543, that the Sun was "the visible god" and that it should be placed "upon a royal throne, [to] truly guide the circling family of planets, earth included" (Book 1, Chapter 10).

  2. Others had tried to propound this Sun-centred model well before Kopernik (for example, Aristarchus of Samos, in the third century B.C.), but the idea only started to be taken seriously after acquiring the fervent support of Johannes Kepler, Galileo Galilei and others.

  3. Indeed, the textbooks today persist in wrongly instructing people that Galilei demonstrated the geocentric model to be flawed in 1610, when he observed the phases of Venus through a telescope. By 1610, Ptolemy's geocentric system of deferents, epicycles and equants had reigned supreme for almost 1,500 years and the exceptionally detailed observational data of the Danish astronomer, Tycho Brahe (1546-1601), further verified the predictive capabilities of that system (with only slight, proposed changes), as Kepler well knew (being Brahe's assistant). It is inconceivable, therefore, that Galilei was ignorant of either the Ptolemaic or Tychonic models, a fact which implies that Galilei's original claim may have been designed by him to be deliberately misleading.

  4. That Ptolemy's constructs were ungainly is not denied, but citing the phases of Venus as being the conclusive scientific evidence for heliocentrism is the astronomical equivalent of the Peppered Moth 'evidence' used to support the ludicrous idea of organic evolution. It is simply not true. 

  5. In the nineteenth and twentieth centuries, observational data showed that the Sun is not positioned at the centre of the universe, and numerous experiments had still failed to demonstrate any motion of the World through the aether. In respect of the latter, Albert Einstein came to the rescue by developing the theory of special relativity, which 'saved' James Clerk Maxwell's brilliant electromagnetic theory by doing away with the very thing that Maxwell's theory is built upon - the luminiferous aether. (No one, to the best of my knowledge, has ever explained just how Einstein saved Maxwell's theory by removing its foundations.)

  6. However, this still was not enough and, in order to preserve the humanistic, atheistic philosophy and edifice that had been lovingly built upon Kopernik's suggested cosmology, the acentric paradigm was born. This asserts that anywhere can be considered, with equal validity, as being at the centre of the universe, since the universe is taken as being infinitely large and thus possessed of no actual centre.

  7. What is lost in all this is the fact that geostatic and heliocentric cosmologies are not equivalent. The common claim that we cannot tell the difference between a heliocentric and a geocentric theory of the universe, and that they are both manifestations of the same, acentric cosmology, is obscuring a deeper reality.

We are advised that, "The World is firmly established; it cannot be moved" (1 Chronicles 16:30, Psalm 93:1, Psalm 96:10), but if the World is not rotating, then the heavens are. The movement of the heavens is then real, not apparent, and the direction is east to west (by simple observation), not west to east (as they are by necessity in the heliocentric case).

There are, then, three cosmologies to consider: heliocentric, geocentric and geostatic. In each of these systems, various celestial bodies are moving. Actually moving, by definition (this is what the whole particular scenario is built upon). Relative motion has little or nothing to do with the initial construction of the model. Let us consider these three models.

Case 1: Heliocentric

Case 2: Geocentric

Case 3: Geostatic

Whether you think the last one is crazy or not is of no importance at this stage. The geostatic model is a legitimate scheme, because:

  1. It must, by its very nature, completely describe and account for everything we can observe from the World. Motion under this scenario can always be attributed to the thing which appears to move;
  2. Either the cosmos has the World at its centre, or it just appears to have the World at its centre. The very same acentric premise, that informs us that the latter is 'reality', must also, by its definition, support the former contention;
  3. No experiment or observation has ever disproved it.

Hence, the heliocentric scenario must agree in all observational respects with the geostatic case, and not the other way round.

The next step is to start thinking about what is really happening in each of these models. We will begin with the geostatic case. This is an example of what is termed, in the computer industry, WYSIWYG (what you see is what you get). The World does not move. Everything else moves. We observe the Sun rising in the east, travelling across the sky and setting in the west, because the Sun rises in the east, travels across the sky and sets in the west. Just like the Ronseal varnish advertisement ("it does exactly what it says on the tin").

Since the Moon does the same sort of thing, but more slowly, the Sun gains on the Moon, catches it (at which time we can sometimes obtain a solar eclipse) and overtakes it. Of all possible models of celestial motion, the geostatic scenario (where everything else does the moving) definitely has to be allowed. Indeed, it is a requirement of all other configurations that they agree with the predictions of the geostatic system, if for no other reason than the fact that this is what we all observe. In particular, the heliocentric system must agree with the geostationary system. Any fundamental difference appearing between the two would tend to disprove heliocentrism, because geostaticism is supported by experiment, observation and our senses.

Although the heliocentric and geocentric descriptions of the so-called 'solar system' are probably dynamically equivalent (it may be beneficial here to read On the equivalence of the heliocentric and geocentric models ), the geostatic scenario can only be satisfied by adopting a clockwise, rather than anticlockwise, orbital motion of the Sun and Moon (when viewed from the north ecliptic pole). Heliocentric and geostatic models are therefore not dynamically equivalent, since they vary considerably in their predictions of orbital speed and direction. This is because, in the geocentric case, as indicated in the paper linked to in this paragraph, the World has gone from non-rotating to rotating, seemingly without many people noticing, or bothering about it.

Hence, to say that the heliocentric scenario must be correct, because observations that can assume a geostatic perspective support reality, is wrong. The equivalence between the two breaks down, as a consequence of the fact that one system has a movement that the other does not have (namely a rotating World), and that both magnitude and direction of actual rotations is different between them.

That a physical system must be independent of the geometrical reference frame by which one mathematically attempts to describe its behaviour, was covered in depth by the German physicist, Ernst Mach (of speed of sound fame). Called Mach's Principle, this was influential in the work of Poincaré, Lorentz and Einstein around the end of the nineteenth century.

The classic example usually quoted, to illustrate to a general audience the significance of Mach's Principle, is that of a small boy in a school playground, bouncing a tennis ball up and down on the ground and catching it again. Clearly it does not matter if we create a system of rectangular coordinates that will allow us to specify at any instant where, in three-dimensional space, the boy, the tennis ball, the ground, etc., are positioned. Furthermore, the coordinate system, or reference frame, that we construct is not unique, the only thing that is unique is that the positions we derive from it are valid only for that particular coordinate system. If we fix the frame to another centre, or we use spherical polar coordinates, for example, we simply get different mathematical formulations of the same physical equations of motion, but the boy continues to bounce the ball up and down, totally oblivious to our abstract geometrical frame of reference. We also notice that, although the point of contact has various means of being represented in a mathematical way, the physical spot on the surface of the World does not change. In other words, and this is the important point to grasp, there exists a physical location within the system from which one can observe a reality, in this particular case, the ball is either touching the ground at regular intervals of time, or it isn't.

The same is true, though it is perhaps not quite so obvious to see, if we use a rotating frame of reference. In this case, although the boy looks different, depending upon the angle we are viewing him at, he is still behaving in exactly the same way. To see this, imagine that we have painted tennis court lines on the playground. The ball is hitting a point on the tennis court which is completely definable in terms of the fixed positions of the lines. We can specify it as, say, 2 metres in from the base line and 1 metre in from the inner tram line on the right hand, far side court as we look at it (thus the necessity for the problematic concept of an 'observer'). No matter how we adjust our vantage point, the ball hits the ground at the same physical location (albeit different coordinates, depending on the geometry used). The physical place of contact between the ball and the ground is a consequence of the mechanical system being observed and is irrespective of the reference frame used to describe the observation and behaviour of the system. This is Mach's Principle and it is used to declare that geocentric and heliocentric frameworks are dynamically equivalent (i.e., that from the perspective of the World we can not distinguish between them).

To see the fallacy inherent when applying this argument to a geostatic and heliocentric comparison, we can imagine the following four cases:

Cases A and B are dynamically equivalent. Any reference frame will give the same results for A as it does for B.

Cases C and D are dynamically equivalent. Any reference frame will give the same results for C as it does for D.

Taking either case A or case B, I don't care which, is that case dynamically equivalent to case C ? If not, then why not ?

Take a look again at cases 1, 2 and 3. Consider how they fit in (or not) with cases A, B, C and D.

The whole point is that we are not dealing just with relative motions of three bodies. We are dealing with two different physical systems. A physical system will behave in a certain way. For example, if a toy train set is assembled on the floor and current sent through the motor, the train will travel in a particular direction. Whenever the power is switched on, the train will travel in the same direction. However, if the voltage polarity is reversed across the motor, the train will go the other way. The set has the same components, but behaves differently. After any time, t1, the front of the engine will be at (x1,y1,z1) in the first configuration, but at (x2,y2,z1) in the second. For any t1, with the exception of those values of t1 which correspond to n half-circuits around the track, (x1,y1,z1) will not equal (x2,y2,z1). They are different points on the surface of the World. Mach's Principle is irrelevant. They are two differently behaving physical systems, albeit with the same components. We can see the difference between them, because we stand on the floor and look down on the system, but if we were shrunk down in size and were travelling on the train, then we could not tell, as long as all we can see are the components of the train set. If we could see a fixed point upon which to attach the coordinates of our observations, then we could still tell.

How does this fit in with the heliocentric/geostatic problem? Well, consider the motion of the Moon about the World. In one scenario it is actually travelling clockwise, whereas in the other it is actually travelling anticlockwise. They are different configurations of the same three objects (World, Sun and Moon). Can we stand anywhere at all within the universe and observe a discernible difference between the heliocentric model and the geostatic reference system? Mach's Principle has nothing to do with it. If we can find just one undeniable anomaly, then the heliocentric model can be ruled out.

The problem now becomes one of proving scientifically that there is indeed a way to discriminate between the reference system and the heliocentric model.

Unfortunately, there is such an amalgamation of alleged movements now, albeit not a single one we are to believe can be detected with our senses, that it is difficult to find a phenomenon that will be demonstrably different in a heliocentric model to how it is in the geostatic reality.

The acentric scheme allows us to have the World as the centre of the universe. Figure 1 depicts this situation. A little later, in this model, and we get the configuration shown in Fig. 2, where the background celestial sphere has rotated east to west, as well as the Sun and Moon rotating east to west. The stars go full circle in 23h 56m 4.091s (the sidereal day), but the Moon only goes around once every 24h 50m 28.5s. Therefore the Moon seems to travel west to east, with respect to the background stars.

Figure 1: Motion of the Moon, Sun and 'background' stars in a geostatic (i.e., non-moving World) framework, looking 'down' from the north ecliptic pole.


Figure 2: As with Fig. 1, but a few hours later. All motion is real, not apparent.


To account for the diurnal motions of a geostatic scenario, the heliocentric model, depicted in Fig. 3, must impose two components of motion on the World - it must rotate on an axis and revolve annually about the Sun.

Figure 3: In the heliocentric idea, the centre of the universe coincides with the centre of the Sun, and the Moon traverses an epicycle, that is centred on a deferent, centred on the Sun.


I believe that the solution which will enable us to demonstrate that the heliocentric and geostatic scenarios are not equivalent to each other, lies with this (non) rotation of the World. The heliocentric system requires of necessity a spinning globe, in order to satisfy nightly, observational facts. But if there exists a motion-related phenomenon that would be the same, irrespective of whether the World spins or not, then the correct model will be the one that functions properly with this extra circumstance, whereas the counterfeit model will almost certainly fail. Hence, we will now turn our attention to something which does not depend upon the World's supposed rotation; namely, the phases of Venus. To explain this whole area, however, we will, for simplicity, first consider the phases of the Moon.

The Moon is illuminated by the Sun, such that one hemisphere of the Moon is brightly lit and the other is in almost complete darkness. What we perceive of as being the Moon's phase is therefore determined by the geometry shown in Fig. 4, below, where A represents the Moon and B represents the Sun.

Figure 4: A solid sphere, whose centre is at A, is illuminated by a spatially extended light source, centred on B, and observed by someone standing on the surface of the World, the centre of which is at C.


In the absence of background reflections, or other light sources, the illumination of a solid sphere depends primarily upon the angle, CAB, since we can vary angle ABC almost at will, by sliding the light source along AB, without in any appreciable way affecting what is lit up, whereas fixing ABC and altering CAB, by sliding the light source up and down BC, will drastically change the illuminated hemisphere. (In a similar fashion, by sliding the observer up and down AC, we deduce that angle ABC has very little influence, too, on what we observe, given the distances involved.)

Again, from Fig. 4 and the law of cosines, we get

a2 = b2 + c2 - 2bc cos CAB ,

which enables us to calculate CAB (or ABC , by use of a similar expression) for any given position of the centres of the World, Sun and Moon. The centre of the World is at (0,0) in the geostatic system, and the centre of the Sun is at (0,0) in the heliocentric system. The distances a and b are constant in each model, and within our forthcoming simulations are assumed to be those that are considered well-established. The rotation rates, calculated to six decimal places, facilitate the determination of the position of the relevant objects in each system. Thus, a high-level computer program was developed to compare the two cosmological models. The graphical user interface for this program is shown as Fig. 5.

Figure 5: GUI for the phase analysis program, showing angle CAB for the Moon, one mean solar hour at a time, over twelve months. (Times of dichotomy are shown by dotted lines.)


Now the phases of Venus are very interesting, because of "a well observed and measurable effect known as Schröter's Effect." Geoff Kirby, as contained in Chapter 6 of his online biography, emphasis mine.) "In fact the observed phase [of Venus] is usually slightly less than the predicted phase. The size of this anomaly varies. So for example the time when the Venus disk is seen to be 50% illuminated is sometimes several earth-days different from the predicted time. Explanations of this anomaly generally propose that [it] is caused by the atmosphere of Venus." (Simon Edgeworth.)

The following quotations should provide the reader with the essence of the puzzlement of this phenomenon: "The curiosity is that the apparent phase is always less than the theoretical phase. If we define the phase as the fraction of the apparent planetary diameter illuminated, then the observed fraction (or phase) is about 0.03 to 0.05 less. This is quite dramatic around the time of dichotomy which is the time when the planet should be exactly half phase, i.e. the phase is 0.5 and the angle Sun-Venus-Earth is 900. The apparent phase appears to be about 0.45 so that Venus is very slightly a crescent." (Geoff Kirby.)

"The so-called phase anomaly is another interesting topic for the observer of Venus. It has long been known that the time when Venus shows a half phase in the telescope frequently occurs later than the predicted time when Venus is west of the sun; and half phase is earlier than expected when Venus is east of the Sun. The half phase is called dichotomy. The results of two observers are shown [in a graph on the website] for autumn 1999. Both observers agree in timing dichotomy at 2nd November 1999, approximately three days 'late'." (The British Astronomical Association.)

"The observed phase may differ slightly from the predicted value, the phenomenon being known as the Schröter effect. Dichotomy is seen to occur a few days early at eastern elongation and likewise late at western elongation." (David Graham, et al.)

"Another old mystery regarding Venus is the Phase Anomaly. This is most noticeable at dichotomy when the planet's terminator (the line dividing day and night) should be a straight line. At that time the planet is so placed with respect to the Earth that it should look exactly like a half-moon with the terminator running straight down the middle of the planet. Astronomers have long been aware that for some unknown reason this never happens at the predicted time. Theoretically we know Venus' orbit with such accuracy that the exact time of dichotomy can be predicted to within hours. But in practise it can be out by a week or more. The problem is that there is nothing wrong with Venus' position in its orbit - so what can be causing this problem?"

"A further aspect of the Phase Anomaly problem is that astronomers have commented at various times on the difficulty of determining Venus' exact phase. Sometimes it seems to be ahead of its predicted phase and at other times behind. The British Astronomical Association has looked into this for the better part of [the 20th] century." (Unknown author.)

In his website, Geoff Kirby makes a good case for daylight masking being the cause of about 40% of Schröter's effect. Certainly, I consider that his experimental method and associated reasoning are sound. This, however, still leaves the remaining 60% unaccounted for, with perhaps the most viable explanation so far offered being the possible scattering characteristics of the Venusian atmosphere (Giuseppe Marino and Fabio Salvaggio, for instance). There is, though, another possibility - one that correlates with previous, experimental results.

Figure 6 shows a run of the program which plotted out the angle a for two years and indicates the points of dichotomy for the heliocentric model. The second dichotomy line is the one relating to eastern elongation (this simply depends upon the initial configuration of the three bodies - World, Sun and Venus - in the program code).

Figure 6: Variations in the phase angle a for the heliocentric system over a two year period from the starting (all aligned) position.


What is hugely significant here is that the time of dichotomy in the geostatic model (637 days) is 2 days before what it 'should' be according to the heliocentric model (639 days) and, since theoretical calculations assume a heliocentric 'solar system' (that can be worked out from a geocentric perspective, if the World rotates), the geocentric, geostatic scenario correctly agrees with observation, whereas the almost universally taught paradigm (heliocentrism, or acentrism, to be more precise) does not.

As a test of the program code, we should expect there to be very little difference in the angle ABC over most of this two-year period, simply because the heliocentric scenario is specially formulated to account for the angular velocities of celestial bodies. Figure 7 confirms that, between days 110 and 644 at least, there is indeed hardly any difference between the heliocentric and geostatic values of this Sun-World-Venus angle.

Figure 7: Testing the mathematical models by plotting the differences in angle ABC.


(The jumps that can be seen to occur at each year-end, in Fig. 7, have still to be resolved.)


Preliminary Conclusions

The heliocentric idea was known of in at least the third century B.C., but was rightly dismissed as being insane. The publication of a multi-volume book, in 1543, by a Sun-worshipping astrologer who knew nothing about physics, then sowed the seed of the present-day misconception that we are taught as being 'fact'. One after another, physicists placed meat on Kopernik's bare bones, with many contorted and ad hoc components of motion.

In this sea of relativism, what is needed is an immovable rock on which to anchor ourselves. That rock is The Almighty and the spiritual anchor is Truth. The anchor and the rock are inseperable, just as We are the ship and are connected to the anchor via the unbreakable rope of spirit (this is the 'Councillor' that Christ talks of in the fourth canonical gospel). The sea is mankind, which acts to toss us about all over the place. If we choose to ignore the safe anchorage point, then we will either drown in the sea, or be dashed to pieces on the outcrop of lies all around us, whilst the anchor and rope lie unused at our disposal. These lies sit in the ocean like a coral reef, never going away, evolving in terms of size and form as extra layers are laid down, difficult to spot, but capable of destroying many a ship.

To disprove heliocentrism similarly requires us to latch onto a small entity in a universe in which we are told that everything is mere relative motion and purposeless chance. We need something that is not relative, but behaves in a discernibly different way in a heliocentric (or geocentric) scheme to how it behaves in a geostatic scheme.

Differences, such as the actual times of dichotomy in each model, can be expected to show up because the geostatic and heliocentric(/geocentric) systems work in a different way. In particular, extra components of motion must be assigned to the World, in order for the heliocentric model to tally with reality. Here, though, we have deliberately sought a phenomenon that does not depend upon one such ad hoc motion (namely, the supposed rotation of the World about an axis), and investigated the behaviour of the two conflicting models.

The correct model will agree with all observations. The phase 'anomaly' of Venus is an undeniable, observational fact, that has been known of for at least two hundred years (from the time of its description by Schröter). The heliocentric idea does not predict what actual observations consistently show. On the other hand, the geocentric, geostatic model, insofar as it has been tested, correctly matches the data.

These investigations remain on-going, but appear extremely promising. It has been known for some time that the Sun is not at the centre of the universe, but for the heliocentric model to suffer further rejection because of the research presented here could not be more fitting, or ironic, for the observed phases of Venus is the exact same phenomenon that Galilei originally (and misleadingly) claimed disproved a geostatic cosmos!



  1. Kirby, G., "The Phase Anomaly of Mercury and Venus," J. Brit. Astron. Assn., 80 (4), 293-295.
  2. Smart, W.M., 1977, "Textbook on Spherical Astronomy," sixth ed., revised by R.M. Green, Cambridge University Press, Cambridge, England, ch. 2, p. 38.