Exactly 101 years ago, German scientist Alfred Lothar Wegener, sailed against the prevailing wisdom of his day when he posited that not only have the Earth’s continental plates receded from each other over the course of the Earth’s history, but that they are currently in a state of motion relative to one another. To explain this, Wegener set forth the hypothesis that the Earth must be expanding as a whole. Wegener’s inability to provide an adequate explanation of the forces and energy source responsible for continental drift and the prevailing belief that the Earth was a rigid solid body resulted in the acrimonious dismissal of his theories. Today, that the continents are generally receding from each other is no longer a point of debate but a sacrosanct pillar of modern geology and geophysics. What is debatable is the energy source driving this phenomenon. Herein, we hold that continental drift is a result of the Earth undergoing a secular radial expansion. An expanding Earth hypothesis is currently an idea that is not accepted on a general consensus level. Be thatas it may, we show herein that the law of conservation of angular momentum and energy entail that the Earth must not only expand as a consequence of the secular recession of the Earth-Moon system from the Sun, but invariably, that the Moon must contract as well. As a result, the much sort for energy source driving plate tectonics can (hypothetically) be identified with the energy transfers occurring between the orbital and rotational kinetic energy of the Earth. If our calculations are to be believed—as we do; then, the Earth must be expanding radially at a paltry rate of about +1.50 mm/yr while the Moon is contracting radially at a relatively high rate of about -410 mm/yr.
As is well known—since about the late nineteenth century [
The laws of conservation of angular momentum and energy, when applied to the problem of the recession of the Earth-Moon system from the Sun; the pointer, strongly appears to point to the seemingly difficult-to-dismiss fact that the Earth must expand radially as a result, at a nominal rate of ~1.50 mm/yr—this is about the average growth rate of human nails [
The energy source of the expansion of the Earth and the shrinking of the Moon is not thermal in origin or emergent from any other mechanism other than the unlocking of the bound gravitational energy locked up in the orbit of the Earth-Moon system. Since the Earth-Moon system is receding from the Sun [
Since about 1596, scientists have long recognised that the opposing margins of continents fit together, e.g., [
Though the idea of plate tectonics had been known since about 1596, in its modern form, it was given a new birth certificate—alas, an almost stillborn birth certificate, by the perspicacity and tenacity of the now celebrated German astronomer, turned meteorologist Alfred Lothar Wegener (1880-1930). Though widely rejected by his contemporaries, Wegener [
While generally not accepted, Wegener’s ideas did attract a handful of respected and credible supporters such as the renowned Afrikaner geologist, Alexander Logie du Toit (1878-1948) from South Africa (whose work is summed up in the book [
Despite Wegener’s ideas being generally criticized on both geophysical and geological grounds, he presented a large and significant body of very strong ponderable evidence in support of continental drift, but the mechanism driving these plates remained elusive. To this day, the energy source driving continental drift is not known and its search is one of the “holy grails” of modern plate tectonics theory. What is the energy source driving the motion of plates? For example, planets generally consist of concentric shells of matter, except for the Earth which has its unique, two-component surface, comprising of about 41% continental rock and with the reminder being quite different ocean floor basalt. To the present day, there has been no satisfactory explanation for the partial, crustal continental rock layer, except by assuming that in the distant past, the Earth was smaller and subsequently expanded [
As already afore-stated, the principal impediment and shortcoming to this otherwise interesting idea of an expanding Earth is and has always been the lack of knowledge of a mechanism that could provide the necessary energy [
“Thus, if expansion on the postulated scale occurred at all, a completely unknown energy source must be found.”
This view, is as valid today as it was in 1982 when Scheidegger made this pronouncement. To that end, amongst others, this reading seeks to furnish the energy source driving the expansion. As we shall argue herein, this energy must be coming from the locked-up gravitational binding energy that is being unlocked in the energy transfers occurring between the orbital angular momentum and the spin angular momentum of the Earth.
In-closing the present section; from Scheidegger [
While it is well known that an EEH can in principle explain a number of currently inexplicable geophysical phenomenon such as plate tectonics (e.g., [
If the expansion of the Earth required to explain plate tectonics is significantly smaller than the observed +0.20 mm/yr or is of the same order of magnitude as the sensitivity of the measurement, then, the current position that the Earth is not expanding requires much more sensitive measurement before sending this idea to the “Science Museum of Great but Failed Ideas”. Or, if the expansion rate of the Earth is significantly less than Fukumori [
As will be demonstrate herein, it appears that Fukumori [
Therefore, the Earth may very well be expanding and the source of the energy of this expansion being the lost orbital angular momentum of the Earth-Moon system which is a result of the secular recession of this system from the Sun. If the Earth is expanding, then, evidence of this expansion should come not only in the form of relative motion of the landmasses, but also in the form of a Hubble-type motion of the landmasses. Therefore, this study is a preparatory study of a possible future study that will seek to quantity whether or not the continents are undergoing a Hubble-type flow from one another. If this can be ascertained, it would be the most revealing evidence yet that indeed, the Earth is undergoing an expansion.
Last and most important of all is that, current plate tectonics theory is incomplete in that it provides no appreciable and adequate energy source for geodynamics and it critically depends on the assumption of mantle convection. There is need to identify the energy source. It is the goal of this study to suggest or identify a plausible energy source driving the continents apart.
That the continents are moving relative to each other is no longer a point of debate. What is debatable is the energy source driving this phenomenon. Herein, we hold that continental drift is a result of the Earth undergoing radial expansion. This expansion is driven or powered by energy transfer occurring between the rotational kinetic of the Earth’s spin and the rotational orbital angular momentum kinetic energy. It is well established fact that the Moon is receding from the Earth at a rate of about
If the Earth is expanding globally, then, evidence of this expansion should come not only in the form of relative motion of the landmasses, but also in the form of a Hubble-type motion of the landmasses. That is, if one has a sphere of radius
The Hubble-type motion of the continental landmass assumes that the continental landmass is sitting on an expanding sphere. Therefore, a direct verification or refutation of a globally expanding Earth is to undertake a study that seeks to quantify whether or not the continents are undergoing a Hubble-type flow relative motion. A Hubble-type flow of the landmasses is but the clearest signature yet, of an expanding solid Earth. If this can be ascertained, it would be the most revealing evidence yet, that indeed, the Earth is undergoing an expansion and this expansion is causing the continents to drift apart. Hence, this work serves as a precursor or preparatory work for a future quantitative study of global plate tectonics with the aim of a verifying or refuting the hypothesis of a globally expanding Earth.
Other than a radial expansion of the Earth, it is possible that other geodynamic forces may come into play and contribute to plate tectonics such as mantle conventional currents which are thought to be the major driving force of plate motion. Lateral density variations in the mantle are believed to result in these convectional currents which if they exist, will lead to the angular displacement
If a graph of
Before we leave this section, it is perhaps important to make a glimpse into what to expect for the expansion rate of the Earth—we have to make a crude calculation. We know that current plate tectonic measurements indicate that the plates are moving at a rate of
This study explores the viable possibility of a secular expansion of the Earth. This secular expansion is hypothesised to be a direct consequence of the observed secular recession of the Earth from the Sun. The supreme and paramount aim of the study is to suggest or posit that the observed continental drift may very well be a result of an expanding Earth.
The objectives of this study (as enshrined in the three part series of readings) are as follows:
1. Judiciously apply the law of conservation of angular momentum to the Earth-Moon system - posteriori justified; the sole aim of which is to unearth a plausible astrophysical link to global geo-plate tectonics.
2. Calculate the implied radial expansion and or contraction of the of the Earth and the Moon.
3. Show that the rotational kinetic of the Earth-Moon system is a viable, potent and plausible source energy capable of driving global plate tectonics.
4. By way of a literature study, set the stage for further work on the possibility of an astrophysical link to global geo-plate tectonics.
5. Present a new plausible theory on the way the Earth-Moon system might have formed. A backward extrapolation of the evolution of the Earth-Moon system for an expanding Earth, contracting Moon and a receding Earth-Moon leads to a very interesting paradigm that might explain many puzzles about the nature of the Earth-Moon system.
Since the idea of plate tectonics was given birth to, the source driving this activity has eluded those that have made the endeavour to decipher the source. Finding this source is not only of great importance to geology and geophysics, but to science in general because it would lead to a better understanding of the forces operating in our terrestrial habitat. Thus, the paramount nature and justification of the present endeavour cannot be under or overstated.
Our present approach to the problem of finding a plausible energy source that is driving the drifting of continental plates is purely a theoretical one; where-after, it is anticipated that data will be gathered (from existing geophysical stations and from Global Positioning System satellites) in the near future to consolidate the ideas propagated herein. We demonstrate that from the embellished, sacrosanct and cherished law of conservation of angular momentum and energy, that, the Earth is expected to expand radially if the Earth-Moon system is receding from the Sun as determined from the observations of Pitjeva; Standish; Krasinsky and Brumberg [
Only until recently, it has become clear that our understanding of the gravitational phenomenon is in serious dearth. The emerging picture was now that where our knowledge of the gravitational phenomenon appeared to be taking a good shape. Alas, the opposite is actually the case. This position has been brought about because of the improvement in our advancement in technology. There has been a recent upsurge of gravitational “anomalies” and this is a direct result of the higher resolution measurements brought by the aforesaid technological advancements. Gravitational anomalies have puzzled the scientific community for quite sometime now.
First, was the discovery of the so-called darkmatter by the Swiss astronomer Fritz [
The widely accepted and dominate gravitational model in contemporary physics is Einstein [
The present reading is organised as follows. In the subsequent section, we lay down the proposed theory that we put forward as a plausible explanation of global plate motion. It is not a new theory in the traditional sense of bringing new exotic concepts, but merely a direct application of the law of conservation of angular momentum on the Earth-Moon system. In
Both Newtonian and Einsteinian gravitation assume that the orbital angular momentum of a planet orbiting the Sun must be a conserved quantity, thus the emergence of the recession of the Earth-Moon system from the Sun and as-well the recession of the Moon from the Earth has come as nothing short of a Newtonian and Einsteinian surprise. Recessional motion of the Earth-Moon system and the Moon from the Earth have implications on the angular momentum. Since the magnitude of the orbital angular momentum
where
In the reading [
The next central idea is the conservation of energy. An object orbiting some central massive body is going to have some rotation kinetic energy
Actually, the assumption of the conservation of the total energy associated with the orbit of test body is central not only to Newtonian gravitational but Einsteinian gravitation as-well, so this idea is sound and valid.
The next conservation is that of the energy associated with the spin of the orbiting and spinning test body. From what has been stated above, the rotational orbital kinetic energy
Thus the present theory is summed up in the three conservation Equations (3), (4) and (5). Undoubtedly, the foundation of our theory is not without a firm and valid basis.
We are now going to apply the ideas of the presiding section to the Sun-Earth-Moon system. Our first port of call is to establish a single value for the recession of the Earth-Moon system from the Sun. The mean distance from the Sun of the Earth-Moon system is referred to as the Astronomical Unit and denoted by the symbol AU. Let us represent the secular change in the Astronomical Unit byδAU. As stated earlier, at present, there are two values for this quantity, that is, the Russian astronomers Krasinsky and Brumberg [
Assuming that these two measurements are governed by Gaussian statistics and that the errors in the measurements random and independent, then, the best estimate of these two measurements can be obtained by taking the weighted mean of the two values. For example if
Applying this prescription to the two measurements of Standish; Krasinsky and Brumberg [
We shall from heron adopt this value (6) as representative of the change in the mean distance between the Sun and Earth-Moon system.
The maximum distance of the Earth from the Sun
Now, lets compute the spin angular momentum of the Earth-Moon system
We here derive the expansion rate formula for the Earth from the two concepts to be used the conservation of angular momentum and energy of the Earth-Moon system. The total angular momentum of the Earth-Moon system comprises six components, that is: (1) the orbital angular momentum of the Earth-Moon system
In the about, the components
For our purpose here, we shall make a simplifying assumption, namely that the axial tilt of both the Earth and the Moon has remained constant, that is, it does not change, this means we shall take
angle of these celestial bodies is changing. In the present expedition, we find no reason to invoke this possibility, thus, we simple let it to the rest, in which event, the resulting calculations are much easier to handle.
Now, let us define the quantity
Written in full,
We give here the results emerging from the derived formulae (A.25) and (A.26) for the Earth and the Moon systems in section (5.1) and (5.2) respectively. In section (5.3), we give an analysis of the results.
Now, from (A.25), the expansion terms can be split into two, that is, Solar and Lunar contribution terms, that is:
By inserting the relevant values, one finds that for the Solar contribution, we will have:
and for the Lunar contribution, we will have:
Clearly, the Lunar contribution is far weaker than the Solar contribution, it is so weak so much that, we can, for our purposes here, neglect it altogether. From this, we can safely conclude that, whatever force is driving the recession of the Earth-Moon system from the Sun, it is this same phenomenon that should lead to the Earth to expand. Therefore, the recession of the Earth-Moon system from the Sun leads to the expansion of the Earth which in-turn leads to plate tectonics. From (13), the corresponding rate of expansion of the Earth is:
At its conception, this reading never meant to touch seriously on matters to do with the Moon. Actually, after we had calculated and demonstrated that the Earth might be expanding, we felt that was enough, the reading must be sent off for publication. On second thoughts, we felt that the reviewers might ask, “Since this is within the realm of your calculation, what does your calculation give for the Moon?”. It is only then, that we felt, we must address this matter before we are compelled to do so. We had envisaged a simple reading where we report that the Earth-Moon drift from the Sun, most certainly is the driver to geo-plate tectonics. The same calculation as that for the expansion rate of the Earth, was conducted for the Moon when upon we arrived as (A.26).
Substituting the relevant figures into this formula, one notices that as in the case of the Earth, the Lunar recession’s contribution is minute compared to that Solar recession term, that is:
and:
The Lunar recessional term leads to an expansion of +0.20 mm/yr while the Solar recessional term leads to a contraction of
At the time we performed this calculation, our ideas of the geology of the Moon where the pre-2010 ideas; we thought the Moon must be a geological dead piece of rock. Our first reaction to the idea that the Moon might be contracting was that of scepticism. The Moon can not be contracting, especially at such a significant rate of
As any researcher would do nowadays, we “hit” google. Much to our surprise, elation and delight, we found out that only recently have Watters et al. [
The LROC photographed Lunar scars known as lobate scarps. Lobate scarps occur when the surface of the geological body experiences a compressional force, causing one part of the upper surface to fold and fracture above the other part. In the absence of significant tectonics on the Moon, Watters et al. [
Lobate scarps have been observed on the surface of the Moon before i.e., from images taken by the panoramic cameras aboard the Apollo 15, 16 and 17 missions Watters et al.; Binder and Gunga [
Other than lobate scarps, the Lunar surface has recently been shown to contain a significant number of grabens [
“We think the Moon is in a general state of global contraction due to cooling of a still hot interior. The graben tell us that forces acting to shrink the Moon were overcome in places by forces acting to pull it apart. This means the contractional forces shrinking the Moon cannot be large, or the small graben might never form.4
In conclusion on the matter of Lunar contraction, i.e., the Lunar contraction rate as calculated herein, we have this to say. While we are very skeptical of a Lunar contraction rate as high as ~410 mm/yr, if we have to learn from history, we have to place aside our skepticism and accept the result pending verification or refutation from observations. This calculation is inferred from the law of conservation of angular momentum and energy, we have no choice but to place, not our faith in the calculation, but our confidence in the calculation, confidence that, it is highly likely that this result will in the near future be verified. Our skepticism or any that can be brought forth is nothing but skepticism whose strong foundations is based on prejudice of a scientific nature.
Is it not scientific prejudice that denied Albert Einstein (1879-1955) the monumental and once in a lifetime opportunity to predict that the Universe might be expanding? Is it not scientific prejudice that stalled Wegener’s hypothesis of continental drift? Is it not scientific prejudice that might have lead to the rejection of the celebrated French Prince, Louis Victor Peirre Raymond de Brogile (1872-1946)’s wave-particle duality leading to a great stagnation in the developed of quantum mechanics? While not endless, the list is long. Sometimes, we must accept the bare facts before us, and if Nature is to embarrass us, we must be humble enough to accept this as an honour rather than a dishonour. We would rather be “embarrassed” by Nature than by anything else. Nature is the greatest teacher of all, we must learn from the best.
The energy to drive plate tectonics must come from the energy locked-up in the spin of the Earth. This energy is unlocked when the Earth-Moon system recedes from the Sun. The total energy locked up in the spin is
This is at a rate of about
In the case of the Moon which is must be contracting at a rate of
All this energy that drives the expansion of the Earth and the contraction of the Moon is drawn from the lost orbital kinetic energy of the Earth-Moon system
For example, the Earth’s internal heat comes from a combination of factors, the dominant of which are the residual heat from planetary accretion which contributes about
It has been urged in [
Below we present a general discussion, the conclusion drawn thereof, and the recommendations we make for future studies and endeavours toward investigations into the possibility that the Earth might actually be undergoing a secular expansion as inferred herein.
Judiciously and with great equanimity, allow us to say this at the outset of the present section, namely that, while the ideas propagated herein spring-forth from non-exotic nor exogenous ideas but directly from the provinces of the well accepted Physical Laws, if proven correct—as we strongly believe they will; it goes without saying that their implications are nothing short of asymptotically pivotal insofar as our understanding of geo-plate tectonics is concerned. Judging from the rich history of the introduction of new ideas, we should say that, we do not expect a smooth passage and acceptance of the present ideas but more a fierce defence against them.
Be that it may, one thing is however certain—that is, the interpretation and subsequent implication of the recession of the of the Earth-Moon system here conducted, is nothing but a logical and straight forward interpretation despite the nature of the conclusion drawn thereof. To ourself, we merely have made the simplest and logical imaginable endeavour to interpret facts from within the accepted provinces of contemporary physics by applying the sacrosanct and embellished law of conservation of angular momentum. As to whether or not the ideas should be accepted or rejected, this we shall safely leave in the hands of our contemporaries and posterity to decide.
When one traces the history of the Earth as depicted by the present ideas, they can not help but entertain the idea that it is highly likely that all the lands of the Earth most certainly emerged from beneath the waters that once covered all of the Earth—the Earth should have constituted a perfect geoid5. If one imagines the Earth’s crust as comprising a firmament6, and knowing very well that beneath and within the Earth’s crust lies some complex waters systems, then, the emergent picture is that where in the beginning, the waters once where above and below the firmament, the firmament once separated the waters from the waters. With the progression of time, a portion of the firmament must have emerged above the waters (which lie above the firmament) to form the lands we inhabit today and so much cherish as a sacrosanct priceless ancestral possession and heritage.
The idea of an expanding Earth, contraction Moon, receding Moon and receding Earth-Moon system has serious implications on the formation of the Earth-Moon system if one where to wind back the hand of time for such a setting. Initially, we had included a section on this but on second thoughts we felt this would lead to a difficult reading. So, we decided to separate this into a stand-alone reading where this issue of the formation of the Earth-Moon system is tackled. This reading on the formation of the Earth-Moon system shall follow the present reading. Thereafter, we shall present the final part of our three part series of papers, where the issue of whether or not data from geophysical stations around the world supports or refutes a Hubble type flow of the World’s continental plates.
Assuming the correctness of the present ideas, then, we hereby make the following conclusions:
1. Spin-orbit interaction should lead to the expansion (or contraction) of not only the Earth, but other celestial bodies in the Solar system and elsewhere in the Universe. Plate tectonics is thus not expected to be peculiar to our planet but must be abundant in the cosmos for as long as planetary recession from their parent bodies is present.
2. The global contraction of the Moon which has been confirmed by NASA, may very well be driven by gravitational decompression which comes about as a result of changes in angular momentum occurring due to the loss of orbital angular momentum of the Earth-Moon system as they drift from the Sun—this lost orbital angular momentum be transferred to the spin of the respective bodies leading to changes in their physical volume. This same phenomenon must be causing the Earth to expand, leading to global plate tectonics.
3. The lost orbital kinetic energy due to the recession of the Earth-Moon system from the Sun which according to hypothesis made herein, is converted to the kinetic energy of the spin of the Earth-Moon system, most certainly is the driver of plate tectonics, the contraction of the Moon and as-well the observed recession of Moon from the Earth.
If the ideas propagated herein are correct (as we believe) or are to prove to tend to that end, then, we hereby make the following recommendations:
1. To improve on the values obtained for the expansion and contraction of the Earth and Moon respectively, it is necessary to drop the assumption that
2. Measurements hoping to detect any secular expansion of the Earth must have a threshold of sensitivity of about
3. There is need to collect data from the different stations around the World on continental drifts and check whether or not the measured movement of plates does conform to a Hubble-type flow If these data reveal a Hubble-type flow, it would be a strong indicator that the Earth may very well be expanding.
4. It is very much likely that the recession of the Earth-Moon system is not peculiar to this celestial system alone, but is a phenomenon occurring to all the Solar planets. If this were the case, it would be interesting to calculate and most certainly speculate on the possible plate tectonic activities on these planets.
5. The present calculation hinges on the measured rate of recession of the Earth-Moon system. Thus, if accurate values are to be obtained from the calculation conducted here, there is need obtain a much more accurate value of the recession rate of the Earth-Moon system from the Sun. Krasinsky and Brumberg [
We have:
Since
In the above, we have made use of the verifiable fact that
Since
Now, we have to apply the Law of Conservation of Energy as laid down in (4) and (5). The Earth spins with a kinetic energy
where
where, as usual,