by Alec MacAndrew (7 Nov 2014)

Let it work;

For ’tis the sport to have the enginer

Hoist with his own petard, an’t shall go hard

But I will delve one yard below their mines

And blow them at the moon.

– *Hamlet Act 3 Scene 4*

Camille Carlisle is the Science Editor for Sky and Telescope, the leading US magazine for amateur astronomers. She is a Catholic and has recently published a scathing review of The Principle movie, “Protecting Faith from Pseudoscience: A Review of The Principle” on a Catholic blog here. The review points out both the scientific and the philosophical errors in the geocentrist position, and is well worth reading. Ms Carlisle makes similar scientific arguments to my articles here and here. (The comment box on the blog is also entertaining: Rick DeLano rolled up and made the nonsensical assertion that Einstein, Mach, Thirring and Born would support the gravitational argument of the geocentrists, and two of the other commenters squashed him like a flea.)

True to type, Bob Sungenis can’t bear to let any criticism go and has written a response to Ms Carlisle in his usual prolix style (he quotes the original piece in full, and makes up some sort of response for every single paragraph of it). His piece contains many of his usual fallacies and won’t disappoint aficionados of his scientific blunders, but it also contains a new and farcical argument to entertain us. Mr Sungenis calculates the force that would be required to keep the Sun in a daily orbit around the Earth and finds that it is a million, million times more than the gravitational attraction between the Sun and the Earth (his calculation is badly wrong as we’ll see below). In order to explain why the Sun doesn’t fly off into interstellar space, he invokes an invented entity, the “Planck medium”, which he claims “absorbs” the Sun’s centrifugal force by some vague and unquantified mechanism. You can explain anything at all, to your own satisfaction, if you make it up as you go along. Let’s look at this train wreck in more detail.

Sungenis writes:

*In Newtonian dynamics, since the Sun is revolving around the universe’s center of mass (where Earth is positioned in the geocentric system), the Sun will have a centrifugal force acting upon it that keeps it away from the Earth.*

*The centrifugal force is calculated by the mass of the Sun multiplied by linear speed multiplied by the radius from the center, or Centrifugal Force = mlr** or Mw^2r (where w measures angular speed).*

*The mass of the Sun is 1.98 x 10^30 kilograms. The linear speed is 30 kilometers/sec. The radius (which includes both the equatorial radius of the Sun and the Earth) is 1.5 x 10^8 kilometers.*

*Hence, the centrifugal force on the Sun is 1.18 x 10^34 Newtons.*

Sungenis blunders right from the outset. The bolded part of his statement above is completely wrong. The centrifugal force in the rotating frame is *F _{c}=mv^{2}/r*, where

*m*is the mass,

*v*the tangential speed (or linear speed as Sungenis would have it), and

*r*is the radius of the orbit. The expression

*mvr*, or

*mlr*as he states it, doesn’t even give the right dimensions for force so it is obviously wrong[1]. Sungenis mangles not just freshman college physics but high school physics – pure ignorance.

I assume Sungenis tried to calculate the force using the alternative expression *F _{c}=mω^{2}r*, as he gets the numeric part correct within rounding errors. But the exponent is wrong by a factor of a million. Yes, that’s right – unbelievably, Sungenis, in a dismal display of incompetence, gets this trivial sum wrong by a factor of a million. Let’s do the sum in tedious detail so we can be sure that he really is this wrong.

*m = *1.98 x 10^{30} kg (the mass of the Sun).

*ω = *1.99 x 10^{-7} rad s^{-1} (in his cockamamie sum, Sungenis is attempting to calculate the putative *annual* orbit of the Sun on the ecliptic plane, as his reference to 30km/s as the tangential speed shows – that is the tangential speed of the annual orbit. He also claims that the Sun orbits the Earth *daily* on the equatorial plane – we’ll come back to that later. In the annual case, *ω* is 2π rad/year, so 2π/(365.24x24x60x60) rad s^{-1})

*r* = 1.496 x 10^{11} m the mean distance from Sun to Earth, centre to centre.

*v* = 2.98 x 10^{4} m s^{-1} (*v* = 2π*r*/(365.24x24x60x60) = circumference of orbit/period in seconds)

Now, whichever expression you use to do the sum, whether you use *mv ^{2}/r *or

*mω*, you get F

^{2}r_{c}= 1.174 x 10

^{28}N, a factor of a million less than Sungenis confidently but incorrectly states. (N stands for Newton, the unit of force, which is the force required to accelerate 1kg with an acceleration of 1m s

^{-2})

He manages to calculate the gravitational force between Sun and Earth correctly within rounding errors (*F _{g }= Gm_{e}m_{s}/r^{2}*), where

*G*is the gravitational constant (6.674 x 10

^{-11}m

^{3}kg

^{-1}s

^{-2}),

*m*and

_{e}*m*are the masses of Earth and Sun and

_{s}*r*is as before. F

_{g}= 3.53 x 10

^{22}N.

Now even though Sungenis managed to get the centrifugal force wrong by a factor of a million, it is true that the centripetal force required to hold the Sun in annual orbit around the Earth is much greater than the gravitational force between Sun and Earth, in fact about 332,000 times greater. In other words, it makes no sense in Newtonian dynamical terms to say that the Sun revolves around the Earth once a year. (Sungenis also claims elsewhere that the Sun revolves around the Earth once per *day* on the Earth’s equatorial plane instead of the Earth rotating on its axis once per day – in this case the centrifugal force would be 1.57 x 10^{33} N, about 45 *billion* times greater than the gravitational force between Sun and Earth.)

The factor of 332,000 is not arbitrary, but is the ratio of the masses of the Sun and the Earth – if you swap the Earth for the Sun as the revolving body the forces are in dynamical balance as we’ll see later. Of course this problem is worse for other stars which are further from the Earth than the Sun is. For example, as I point out here (on page 20), the centripetal force required to keep a solar mass star at z=0.1 in a daily orbit round the Earth is 1.3 x 10^{47} N, a vast force for which there is no source.

How does Sungenis explain the Sun’s annual revolution around the Earth, which requires a centripetal force not twice, not ten times, not 100 times, but 332,000 times greater than gravity provides? The geocentrists have invented an entity, which they call the “Planck medium”, and Sungenis claims that it “absorbs” the centrifugal force. Needless to say, he doesn’t describe the physical properties of this medium which allow it to “absorb” the centrifugal forces. Does it do so gravitationally, by viscous drag, by electrostatics or magnetics? Who can say? How can it “absorb” these stupendous dynamic forces, and yet be completely undetectable? Only Bob knows.

Sungenis claims that the invented medium consists of Planck particles, so what are Planck particles? A Planck particle is a hypothetical entity, a black hole with its Schwarzschild radius equal to its Compton wavelength (link). (The Schwarzschild radius, r, of a black hole is the radius at which light cannot escape the black hole. For a black hole of mass m, *r = 2Gm/c ^{2}*. The Compton wavelength of a particle, λ, is the wavelength of a photon which has the same energy as the rest mass of the particle,

*λ = h/mc*where h is Planck’s constant and c the speed of light. Setting

*2Gm/c*gives the mass and Schwarzschild radius of a Planck particle). The Planck particle mass would be 3.85 x 10

^{2}= h/mc^{-8}kg and its Schwarzschild radius would be 5.73 x 10

^{-35}m.[2] Its uniform density would be 4.9 x 10

^{94}kg/m

^{-3}= 4.9 x 10

^{91}g/cm

^{-3}which Sungenis gets wrong by a factor of about 100 – does he ever get anything right? Such a density would make the mass in one cubic centimetre filled with Planck particles a stupendous factor of 10

^{36}greater than the ordinary mass in the entire observable universe.

But in any case, this is moot, because physicists don’t think that such things as Planck particles actually exist in the outrageous bulk densities quoted by Sungenis. Why? Because measurements of the CMB[3], as well as measurements based on supernovae[4] and Baryon Acoustic Oscillations[5] show that the geometry of the Universe is flat or close to flat and this means that the mean mass-energy density is close to the critical value of a little less than 10^{-26} kg/m^{3} or about five hydrogen atoms per cubic metre (the critical value of mass-energy density in the Universe is that required to result in a flat geometry and Euclidean space). In order to answer the challenge that the Sun orbiting the Earth is dynamically absurd, Sungenis has to invoke an ad hoc explanation, using a medium for which there is not the slightest shred of evidence, and which, in spite of its supposed mind-boggling density, is completely undetectable, directly or indirectly. He proposes no quantified mechanism by which this medium “absorbs” these vast centrifugal forces while allowing planets and satellites to move freely through it. No-one else performing real, complicated celestial mechanics calculations (like NASA or ESA for example!) has to invoke this fantasy. This made-up medium, this fairy dust has no physical interaction other than magically doing just what he needs it to do while remaining completely undetectable whenever he doesn’t need it – way to go, Bob.

Now let’s consider that when geocentrists like Sungenis talk about the “Planck medium”, which is a term used almost exclusively by geocentrists, they are probably referring to the hypothesised vacuum energy or zero point energy of the vacuum that arises from a naïve interpretation of Quantum Field Theory[6]. A naïve calculation results in an *infinite* energy density for the vacuum, and a slightly less naïve calculation yields a finite but stupendously large value. Since the energy of the vacuum is *measured* to be actually rather small (see above – 10^{-26 }kg/m^{3} is the upper limit of the density of the vacuum) it is clear that there must be a problem in the renormalisation step of the QFT calculation at these scales. QFT does not include gravity which is expected to unify with electromagnetism and the strong and weak nuclear forces at these scales. Most physicists agree that in the absence of a theory of Quantum Gravity, QFT on its own is unable to model the density of the vacuum which remains undetermined in QFT[7].

And in any case, it is empirically clear that the vacuum doesn’t have the viscous or drag properties that Sungenis wants it to have. Even if the zero point energy is what he means when he speaks of the “Planck medium”, he has imbued it with properties that it doesn’t have, even as a highly hypothetical entity in QFT.

There are two ironies which illustrate Sungenis’s contempt for consistency and coherence. First of all, he rather hypocritically invokes Planck particles – which are black holes by definition – *even though he regularly derides the existence of black holes, insisting that they’re completely unevidenced*.

Secondly, he often criticises cosmologists’ hypotheses of dark matter and dark energy, claiming that they are poorly evidenced ad hoc solutions to the problem of missing mass in galaxies and the accelerating expansion of the Universe. But here he is, proposing a solution to the dynamical problem of a revolving Sun, where he has to explain the problem that the gravitational force is a whopping 332,000 times too small to maintain the Sun in a an annual geocentric orbit, by invoking an entirely arbitrary, undetectable, unquantifiable and, frankly, magical idea. That’s ironic, because although the composition of dark matter is unknown, its presence can be and has been detected and quantified throughout the Universe by its gravitational interaction with other matter and with radiation. It is an entirely reasonable hypothesis that is consistent with other things that we know about the Universe – whereas Sungenis’s Planck medium not only lacks evidence but is *incompatible* with observations.

And while Sungenis hoots at the dark energy hypothesis of the Standard Cosmological Model, he wants us to accept his undetectable hypothetical entity which is *120 orders of magnitude* denser than dark energy[8]. Moreover this is invoked by Sungenis to explain two phenomena, the Earth’s rotation and its revolution round the Sun, which already have good Newtonian explanations, gravity and the conservation of angular momentum, whichi date back over three hundred years. It’s an unnecessary and ridiculous solution looking for a non-existent problem.

So here’s the kicker – the thing that Sungenis fails to bring out in his buffoonery: we have already seen that **the gravitational attraction between the Sun and Earth is 3.53 x 10 ^{22} N** (given by

*F*). So let’s calculate the centrifugal force if the Earth is revolving round the Sun once a year. We have seen that

_{g }= Gm_{e}m_{s}/r^{2}*F*and in this case:

_{c}=mω^{2}r*m* = 5.97 x 10^{24} kg

*ω = *1.99 x 10^{-7} rad/s

*r* = 1.496 x 10^{11} m

**So the centrifugal force of the Earth’s annual revolution is (5.97 x 10 ^{24}) x (1.99 x 10^{-7})^{2} x (1.5 x 10^{11}) = 3.54 x 10^{22 }N**. Therefore, the gravitational attraction between the Sun and Earth is equal to the centrifugal force of the Earth’s annual revolution.

Is this an amazing coincidence? Of course it’s not. It’s the simple consequence of Earth’s orbit around the Sun – the force of the Sun’s gravitational attraction is exactly equal to the centripetal force required for the Earth’s annual orbit at its distance of ~150 million kilometres from the sun – no magical media to “absorb” the centrifugal force is required, just straightforward orbital mechanics based on standard Newtonian physics, such as can be applied to all the planets, including the Earth.

That’s physics, not geocentric wishful thinking. Since the same condition equating the gravitational force for each planet and the centripetal force required at that planet’s orbit holds in the case of every planet, including the Earth, it beats me why anyone would think that the Earth is a special case not orbiting the Sun. In carrying out these calculations (very badly), Sungenis has been hoist with his own petard – it has blown up in his face.

## Notes

[Notes for pedants: I use some approximations in the various calculations above. In no case does the approximation affect what I am saying in any significant way. Examples of approximations include rounding figures to a few significant places, assuming that the Earth’s orbit is circular rather than elliptical (it’s nearly circular), and referring to the Earth’s orbit around the centre of the Sun rather than round the Sun-Earth centre of mass (since the Sun is about 332,000 times more massive than the Earth this approximation has little effect).]

[1] The dimensions of *mvr *are kg m^{2} s^{-1}. But the dimensions of force are kg m s^{-2}. Getting the dimensions of an expression wrong or entirely ignoring dimensional analysis is characteristic of a pseudoscientist.

[2] See http://en.wikipedia.org/wiki/Planck_particle . Some people use the reduced Compton wavelength which is defined by the reduced Planck constant ħ = h/2π in deriving the mass and dimensions of a Planck particle: http://math.ucr.edu/home/baez/planck/node2.html

[3] For popular web-pages that explain the geometry of the Universe and what we can conclude from WMAP data, see http://map.gsfc.nasa.gov/universe/uni_matter.html and http://map.gsfc.nasa.gov/universe/uni_shape.html . For examples of the numerous technical papers which report the flatness of the Universe, see Komatsu et al*, Five-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Cosmological Interpretation, *arXiv:0803.0547v2 and Larson et al,* Seven-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Power Spectra and WMAP-Derived Parameters*, arXiv:1001.4635v2

[4] Sullivan et al*, SNLS3: Constraints on Dark Energy Combining the Supernova Legacy Survey Three Year Data with Other Probes*, arXiv:1104.1444v2

[5] Percival et al, *Baryon Acoustic Oscillations in the Sloan Digital Sky Survey Data Release 7 Galaxy Sample*, arXiv:0907.1660v3

[6] Sungenis and Bennett, *Galileo Was Wrong*, 10^{th} Edition. Chapter 6

[7] For a formal treatment, see a QFT textbook, for example: Michio Kaku, *Quantum Field Theory; A Modern Introduction*, Oxford University Press, ISBN-0-19-509158-2, particularly pages 67-68, 87, 196 et seq. Unfortunately, a grounding in tensors, spinors and group theory (particularly Lie algebras) is needed to follow the formal physics. Alternatively John Baez’s popular page sets out the discussion in layman’s terms http://math.ucr.edu/home/baez/vacuum.html and Sean Carroll’s pedagogical paper can be followed by someone with some grounding in university level maths for physicists: http://relativity.livingreviews.org/Articles/lrr-2001-1/index.html

[8] As energy and mass are equivalent we can refer to the density of the vacuum either as an energy density (joules m^{-3}) or a mass density (kg m^{-3}). The upper limit of the observed vacuum density is about 10^{-26} kgm^{-3} which is 10^{-9} joules m^{-3}. Sungenis’s medium is 4.9X10^{94} kg m^{-3} or 4.4×10^{111} joules m^{‑3}