Electric Comets & A Break for the Holidays...

I'm taking a break for a few weeks for the holidays, and hope to polish up a number of posts that have been long overdue (how many times have I said that?).

Recently I have been participating in the Electric Comet thread over at the International Skeptics Forum.

Electric Comets III: Mass vs. Charge

Stuart Robbins at Exposing PseudoAstronomy has posted Part 2 of his critique of James McCanney's odd claims about electric comets and the rest of the universe.  Definitely worth a listen.

Meanwhile, I'll address some of the claims floating around about the measured mass and density of Comet 67P (Wikipedia).  By measuring the motion of the Rosetta spacecraft around the comet, they have been able to estimate the mass of the nucleus at about 1e13 kg or 10 trillion kilograms.  Current measurements suggest this value is accurate to within about 10%, so future estimates should fall in the 9-11 trillion kilogram range, with some smaller probability that they fall outside that range.
Rosetta Blog: Determining the Mass of Comet 67P/C-G

This will not be the final word on the comet mass as at various times during the mission, Rosetta will be moved to locations where more precise measurements are possible.  Note that the standard model for comets will also expect some rate of mass loss.

Using that mass estimate and the measured volume of the comet constructed from imagery, we get a mean density of 0.4 gm/cm^3, significantly less than water and around what you expect for the 'dirty snowball' model.

When I saw this estimate, I considered the possibility that the Electric Universe crowd might claim that this low mass was an artifact of assuming that the attraction was purely gravitational and did not include contributions due to electrostatic repulsion which might occur in one of the many 'electric comet' models.  Shortly after I started work on this analysis, I was notified that this was indeed being claimed by some Electric Comet supporters.

While Electric Universe supporters continue to make excuses, people with real training in physics can use such claims to determine physical parameters.  So we ask the question:

How much charge would that take to make a dense object appear to be a given lower mass object? 

First, we setup the force equation so the gravitational acceleration between the mass of the spacecraft, m, and the perceived mass of the comet, M', vs the real mass, M.

This equation balances the forces so 'real' masses M & m appear to have apparent masses, M' and m (assuming the spacecraft mass, m, is unchanged), if they are carrying charges Q and q, respectively.  The fact that both force laws are inverse-square allows distance between the masses, r, to cancel out.  This leaves:

Then we can re-arrange the terms to solve for the product of the charges Q & q:

Using the fact that mass is density times volume, we can recast this equation into a form more useful for exploration of our question:


Now we have an expression that can tell us about the charge on the comet nucleus and the spacecraft, based on other numbers which we can measure as well as some hypothetical 'real' densities.  We don't obtain the actual value of the charge of the comet nucleus, but we now have a constraint that can be combined with other data to tell us more. 

From the form of the equation itself, we see that for the apparent density to be less than the real density, Qq will always be positive, meaning that the charge on the spacecraft and comet must be of the same sign, both positive or both negative.  This makes intuitive sense, as the electrostatic force will be repulsive in both cases.  But if the charges are of opposite signs, the apparent density will be higher than the real density since now the two objects must be attracting each other through the electrostatic force.

Let's plug in some numbers.  We have the 'apparent density' of the comet, based on the allegedly flawed assumption that gravity is the only important quantity for steering the Rosetta spacecraft.

We have a mass for the spacecraft, m=1230 kg (assuming the spacecraft is the dry mass defined in Wikipedia)

Apparent comet nucleus density = 0.4 gm/cm^3 = 400 kg/m^3

Combined with the mass, we can estimate the volume of the nucleus.
V = (1e13 kg / 400 kg/m^3) = 2.5e10 m^3

Let's assume the real density is closer to that of rocks, say 2 gm/cm^3 or 2000 kg/m^3.  Then, using the SI units where epsilon0 = 8.854187817e-12  farads/m, we find

Qq = 4*3.14159* (8.854187817e-12  F/m ) (6.673e-11 N(m/kg)^2)*(1230 kg)* (2.5e10 m^3) (2000 - 400) kg/m^3
      = 3.65e-4 F*N*m

We can also plot the charge constraints, examining the requirements for several different densities.  In the graph below, we plot the spacecraft charge on the x-axis vs. the charge on the comet nucleus (y-axis) for several different values of 'real' density.  Plotted logarithmically, different values of Qq form straight lines for the different density values.

While we don't know the charge on either the comet nucleus or the Rosetta spacecraft, we now know the product of these quantities.  This provides us with options to examine. 

One thing we should note is the surprisingly small value of this quantity.   If the comet carried a charge of 1 coulomb, then the spacecraft would be charged to 3.65e-4 coulombs.  You can charge a small capacitor to one coulomb.  It isn't that much charge.  If the comet were charged to 100 coulombs, then the spacecraft would be charged to 3.6e-6 coulombs, or 3 millionths of a coulomb.  The higher the charge on the comet nucleus, the smaller the charge on the spacecraft must be to  explain the density discrepancy Electric Comet supporters advocate.  Similarly, we could place more charge on the spacecraft than the comet.

Of course, this claim has loads of other implications, none of which we've seen explored by the Electric Comet advocates or their 'theorists'.  Let's examine some of these questions.  We'll see if we get any real answers from Electric Comet supporters.  Some of these I'll explore in a future post.

The comet nucleus is traveling through the solar wind, which is a plasma, free electrons, free protons, and a fraction of heavier ions.

• How much of this plasma does the comet nucleus intercept?  How long would it take for the charge on the nucleus to neutralize?  You need to compute or at least estimate the projected geometric area of the comet nucleus.
• Step it up a notch and consider not just how much of the solar wind will be intercepted by the comet's geometrical profile, but how much additional charged material is attracted to the nucleus from beyond this region due to the electrostatic attraction of the comet.  Now how long will it take for the nucleus to neutralize charge?  What happens then, and why?
• Is the amount of additional charge attracted (most likely solar protons) sufficient to explain the amount of OH and water production measured per the Thornhill model for the comet OH emission? (see Electric Comets II. Of Water & Ice).
• The constraint above means a very small amount of charge could be on comet as well as spacecraft.  In the solar wind plasma, one might expect that non-uniformities in the solar wind might fluctuate substantially, perhaps even occasionally charging up objects with the OPPOSITE charge.  If it manages to do that on only one of the objects in the comet/spacecraft system, this repulsion can suddenly become attraction.  Therefore, in the electric comet model it is possible that the comet might suddenly appear MORE massive.  With such small values of charge on the comet or spacecraft sufficient to explain the density discrepancy, it may certainly be possible for one of the objects to accumulate charge of the opposite sign and make the comet appear not just more massive, but significantly more massive.  What navigational issues does this present for Rosetta?

And of course there's the persistent question about Electric Universe models that remain unanswered:

• How would/could a net charge on the comet nucleus be maintained in interplanetary plasma?
• Where's the battery or generator that maintains the potential between the comet nucleus and the solar wind?

Exercise for Readers
It might be tempting for Electric Universe supporters to use the analysis above as evidence that planetary bodies might carry significant electric charge which alters our estimates of planetary masses.  While the analysis above works easily for two bodies, I'll suggest it as an exercise for the reader to determine what happens for three or more bodies which will disrupt simplistic attempts to re-interpret solar system dynamics.
 
Other Notes:

• For another challenge for the geniuses of the Electric Universe, see my response to a comment from Lodaya. 
• Rosetta Blog
• Plasma instrument on Rosetta
• A long-running and recently restarted Electric Comet discussion is ongoing over at the International Skeptics Forum.

For reference, here's some of the standard Electric Universe Excuse set I've seen:

1) The irregular shape of the nucleus makes it impossible to determine precise values for the area/spacecraft mass/some other variable.
 - We're just trying to get estimates here.  Real scientists and engineers do these types of estimations all the time.  You can at least estimate a maximum and minimum for the area and examine the implications of that.

2) The problem is non-linear and therefore unsolvable.
- Real scientists and engineers solve non-linear systems all the time.  Multi-target spacecraft trajectories, weather forecasting, etc.  'Non-Linear' is not a total roadblock for people who know what they're doing.

3) This model does not include effect 'X', therefore it does not apply to Electric Comets and they will not address it.
- Then include effect 'X'.

4) These problems come from someone who is an enemy of Electric Universe theory/fails to treat Electric Universe theories with appropriate respect so therefore their objections can be ignored.
- Bad news dudes, if other scientists who actually do spacecraft missions saw your claims and actually looked at them, they would insist on answers to these questions and more before they trust electric comet advocates to multi-million dollar/euro equipment.

5) Electric Universe 'theorists' have no way to verify that these claims would actually be made by other scientists so they will not be addressed by Electric Universe supporters.

Geocentrism: According to Hoyle?

This is another post in the followups to the claim that Geocentrists @ Galileo Was Wrong (GWW).  Specifically, this is a partial response to the post:

GWW: Newton versus Einstein: The “Physics” of Alec MacAndrew

I found this post particularly entertaining as Mr. Sungenis wants to lecture someone with actual training in physics when the Geocentrists' understanding of the topic is so poor that they must do their 'physics' by copying old texts (see Geocentrism: Flunking the Lagrange Point Challenge) and trying to pass off the standard, non-Geocentric, technique of computing the Lagrange points as supporting Sungenis' particular flavor of Geocentrism.

To clarify, when I'm talking about the equivalence of coordinate systems in the relativistic sense, I try to refer to it as geocentric with a lower-case 'g', since this treatment works for ANY point you which to choose as a center.  If I'm talking about geocentrism where the claim is Earth a center in some kind of absolute sense, I'll use Geocentric, with an upper-case 'G'.  I'll try to avoid using these terms at the start of sentences, where ambiguity might result.

But the topic I wish to specifically address in this post is Mr. Sungenis' quote-mining of Fred Hoyle (wikipedia) to support his position.   Sungenis does this using HIS twisted definitions of terms rather than those meant by the person he is quoting, but then this is the standard for the practice of quote-mining (Wikipedia).

The particular reference Sungenis uses is Fred Hoyle's book, "Nicolaus Copernicus: An Essay on his Life and Work" written in 1973 (Google Books).

In this book, written for popular audiences, Hoyle invokes relativity (the equivalence of ALL reference frames) to make the point that we can just as easily consider the universe as centered on the Earth, as well any other point.  

The most telling example of Sungenis' distortions is, in quoting Hoyle from "Nicolaus Copernicus: An Essay on his Life and Work", p. 82. he quotes Hoyle a little TOO much...

"we can take either the Earth or the Sun, or any other point for that matter, as the center of the solar system." (emphasis mine). 

Sungenis quotes, but conveniently ignores, the full implications of Hoyle's meaning with this statement, instead choosing Hoyle's mention of the equivalence of the 'geocentric' view to spin the statement into claiming Hoyle supports Geocentrism with Earth as some absolute cosmic center.  I'm surprised Sungenis didn't make that clause disappear with ellipsis...

Hoyle was not a Geocentrist in the sense of claiming the Earth can be the center of the universe in any absolute sense, but advocating geocentrism as a frame of reference chosen for convenience (much the same as Phil Plait's argument at Geocentrism?  Seriously? and Geocentrism: Does NASA use Geocentrism?) where we can chose Earth, or any other point, as the origin for our coordinate system.  THAT is the underlying basis of relativity which Sungenis tries to ignore and evade.  Hoyle could just as correctly chosen Mars, or Saturn, or gamma Andromedae or the M33 galaxy as the center, with no loss of generality.  But, since Hoyle was writing for a lay audience, he probably chose Earth for familiarity.

Of course, that freedom of choosing the 'center' at another location comes with a price, most notably the additional mathematical complexity.  In Newtonian physics, it is the inclusion of such things as centripetal forces.  But in the Einstein and Mach formulation, the metric (Wikipedia) actually carries this information along.  All the complex terms which appear in the Newtonian formulation don't show up until you explicitly derive the equations of motion for a specified coordinate system and frame of reference.

This makes the Geocentrists failure of the Lagrange Point challenge even funnier.  If they want to argue relativity now, even if incorrectly, they should have done a relativistic derivation of the Lagrange points.  Though it probably would have been quite a challenge to find one already worked out for them to copy unless they know a graduate student doing General Relativity who might have done it as part of a homework assignment...

Fred Hoyle is often quoted by creationists and similar pseudo-scientists for his opposition to Big Bang cosmology.  Creationists conveniently ignore that one of the reasons Hoyle, and a number of others who argue against BBC, do so because of its suggested religious analogies (Is Big Bang Cosmology a 'Creationist' Model?).  Fred Hoyle was an interesting individual, who had made a significant professional reputation for himself in nuclear astrophysics, but was also often fighting for the underdog or for someone whom he feels was wronged by 'the system'.  In this area, Hoyle is probably best known for his support for Jocelyn Bell (wikipedia) for credit on the discovery of pulsars. 

Other References and Notes

• MacTutor: Sir Fred Hoyle
• The expression "according to Hoyle" may be familiar to card game enthusiasts (Wikipedia: Edmond Hoyle).
• Some Personal recollections of Fred Hoyle:  I had the opportunity to meet Fred Hoyle when my Ph.D. advisor invited him to Clemson in 1992.  Hoyle even autographed my copy of his book "Diseases from Space".  The fact that I have this book does not mean I endorse any or all the ideas presented within.