Newton’s equations give the speed of gravity as infinite. For example, in Cartesian coordinates, suppose a gravitating mass 2M is at the origin up until time t=0. At that time, the mass splits into two masses of mass M, one going in the +x direction at speed v the other in the -x direction at speed v. For times greater than 0, the gravitational potential is given by the sum of the two gravitational potentials:

(1)

At any distance, the above depends on t so the gravitational potential (and it is easy to show the gravitational force) is instantaneously changed at all distances from the origin. The speed of gravity is therefore infinite in Newton’s theory.

This is the “mysterious action at a distance” problem for Newton’s gravity. Einstein solved the riddle with general relativity, which gave the speed of gravity as the same as the speed of light. Another way of saying this is that in general relativity, gravity waves travel at the speed of light.

In the weak field limit, Newton’s law of gravitation needs to match Einstein’s law. Given that the two theories postulate a speed of gravity that is widely different, it is a little surprising to find that they match fairly well. Rather than going into this, let me instead link in a simple discussion of this by Steve Carlip on Baez’s website.

**The Aether Theories and Longitudinal Gravity Waves**

Some of the aether theories that existed before Einstein assumed that light was the transverse wave in the aether, while gravity was the longitudinal wave. The 19th century physicists were well familiar with transverse and longitudinal waves in infinite solids, and since the longitudinal waves always travel faster than the transverse waves, those who treated gravity as a longitudinal wave assumed that it travelled faster than light.

For example, from a Kaye and Laby article on sound speeds, here are the speeds of longitudinal and transverse sound waves for some common materials in meters per second:

(2)

In the earth, longitudinal waves are known as P-waves, while transverse waves are S-waves. The P stands for “primary” and S for “secondary”, since the longitudinal waves travel faster and arrive first. Geophysicists sometimes remember these as P standing for “push” and S standing for “shake”. The rule is that the first earthquake wave you feel will move the earth back and forth in the direction of the earthquake’s center, and the secondary waves will move the earth back and forth perpendicular to the direction of the quake center. More complicated waves can travel near the surface of the earth. See L Braille’s website at Purdue University for nice pictures.

**Longitudinal Wave Speed Calculations**

If one knows the stress strain elasticity tensor and all that for a classical infinite isotropic homogenous 3-dimensional solid, one can verify that medium supports two wave types, transverse and longitudinal, and that the speed of the longitudinal waves are greater than the speed of the transverse waves. The calculation uses tensors and is shown in section 5.5.4 of these engineering class notes by A. F. Bower at Brown University. One finds that:

(3)

where is Young’s modulus, is the mass density, and is Poisson’s ratio. Thus the ratio of the two speeds depends only on Poisson’s ratio:

(4)

Suppose that we have a cube of aether, and it is compressed by 1% in the z direction. Poisson’s ratio gives the percent that the aether expands in the x and y directions. If the aether is perfectly compressible, then it doesn’t expand at all, and Poisson’s ratio is 0. If the aether is perfectly incompressible, then the 1% compression in the z direction becomes 0.5% expansion in the x and y directions (to keep the volume constant to first order in the compression), and Poisson’s ratio would be 0.5.

From these arguments, classical physicists saw that a Poisson ratio for the aether of 0.5 would give longitudinal waves with an infinite speed. This matches the speed of gravity for Newton’s equation, so most of their theories assumed that Poisson’s ratio for the aether was 0.5.

**Jupiter and the Speed of Gravity**

At this time, no gravity waves have been observed. Since we haven’t seen the waves, it would follow that we haven’t measured their speeds. However, a few years ago this point was debated in the literature at some length. Clifford Will’s review article on tests of the general theory of relativity, Living Rev. Relativity 9, (2006), 3 tells the story:

In 2001, Kopeikin [152] suggested that a measurement of the time delay of light from a quasar as the light passed by the planet Jupiter could be used to measure the speed of the gravitational interaction. He argued that, since Jupiter is moving relative to the solar system, and since gravity propagates with a finite speed, the gravitational field experienced by the light ray should be affected by gravity’s speed, since the field experienced at one time depends on the location of the source a short time earlier, depending on how fast gravity propagates.

…

However, several authors pointed out that this 1.5PN effect does not depend on the speed of propagation of gravity, but rather only depends on the speed of light [16, 288, 233, 51, 234]. Intuitively, if one is working to only first order in v/c, then all that counts is the uniform motion of the planet, Jupiter (its acceleration about the Sun contributes a higher-order, unmeasurably small effect). But if that is the case, then the principle of relativity says that one can view things from the rest frame of Jupiter. In this frame, Jupiter’s gravitational field is static, and the speed of propagation of gravity is irrelevant. A detailed post-Newtonian calculation of the effect was done using a variant of the PPN framework, in a class of theories in which the speed of gravity could be different from that of light [288], and found explicitly that, at first order in v/c, the effect depends on the speed of light, not the speed of gravity, in line with intuition. …

There are many arXiv articles on the debate. With no less than four fairly entertaining “comment on” articles. At this time it appears that the “no measurement was made” side has the upper hand.

**Gamma Ray Bursts and Gravity Waves**

In 1987, the supernova SN1987A was detected in our local galactic neighborhood. Supernovas are expected to produce vast quantities of neutrinos, and it was very satisfying to see that neutrinos from this explosion were detected at roughly the same time as photons. These sorts of experiments, where the same event is observed with instruments that detect different particles, are some of the most useful for verifying models of physics. In the case of SN1987A, observations showed that the massive neutrinos arrived a few hours before the massless photons. The delay is due to the fact that neutrinos interact only weakly with matter and so can escape from the center of the supernova faster than photons.

If an astronomical event produces both photons and gravity waves, and these two waves travel at the same speed, then we may be able to detect them approximately simultaneously on the earth. So the gravity wave experimenters have set up a system whereby whenever there is something interesting is observed by the photon astronomers, the data from the world’s various gravity wave experiments are compared to see if there is a coincident signal. If the gravity wave arrives early or late, this would be a good test of many theories of gravity.

Gravity wave detectors have rather high noise levels compared to the size of the signal that they are looking for. If one were to leave a gravity wave detector running for a few years, one would undoubtedly find many apparent signals even in the absence of true detection of a gravity wave.

The expected value of the peak noise (i.e. the best fake gravity wave that noise can put together)scales as the square root of the time one observes. To reduce the chance that a signal is just noise, one can look for coincidences between different detectors and for coincidences between gravity wave detectors and telescopes or neutrino detectors. Since these coincidences greatly reduce the time that the gravity wave detector is on, they also greatly the expected value of the peak noise (signal) expected, and this increases the sensitivity of the detectors.

Kea (Marni Sheppeard), is blogging the General Relativity & Gravitation #18 conference. A few days ago she posted the following report:

The new, preliminary S5 result of most interest is for GRB 070201 in the galaxy M31. Images show the source region overlapping the spiral arms of M31. This burst duration was around 0.15 sec with a secondary pulse of 0.08 sec, and it was observed using two Hanford LIGO detectors. No GWs detected. The conclusion is that it is quite unlikely the source can be associated to M31 at all, and an upcoming paper will include minimum distance estimates for the source (based on the assumption that gravitational waves exist).

This is interesting in that it may be the first evidence that the speed of gravity waves is not the same as that of light. The next few years could see an interesting debate between the gravity wave observers and the observers of photons and neutrinos. [edit]The paper is now out: Implications for the Origin of GRB 070201 from LIGO Observations. Interestingly, they write “*We also implicitly assume that the propagation speed of the gravitational waves is the speed of light.*”

**The Heretical View**

My own (heretical) opinion on this is that aether is halfway between perfectly compressible and perfectly incompressible, and has a Poisson’s ratio of 0.25. For comparison, the Poisson’s ratio for glass is 0.24. This gives , which matches the superluminal speed implied by the 3-dimensional analog to Feynman’s checkerboard model of the electron. But discussing this would take us too far from the subject at hand.

[edit]From a classical point of view, hidden dimensions will give an incompressible aether a Poisson’s ratio smaller than 0.5. For instance, if there are a total of 5 dimensions, compressing one will lead to expansion in four others, and Poisson’s ratio will naturally be 0.25. Examined from a physics that uses only 3 dimensions, the result will look like a compressible aether.[/edit]

Suffice it to say that I expect that the gravity wave people will eventually detect gravity waves, but that these will not correlate to any simultaneous astronomical events. Given the astronomical distances, any significant difference between the speed of gravity and the speed of light will separate the signals by such a long time that we on earth will have great difficulty correlating them. I believe that the gravity waves will arrive first, so if it were possible to accurately determine the arrival direction of the wave (it is not with present technology), then those directions will point toward astronomical objects that seem likely to someday produce gamma ray bursts or neutrinos.

[edit]If gravity waves from a pulsar are detected, and gravity waves are slower than c, then it will be possible to get a good estimate of the speed of gravity by taking into account the rate of spin-down of the pulsar. So an interesting search would be to look for pulsar like signals in the gravity wave data, but with frequencies other than those observed in pulsars nowadays.[/edit]

Cool post, and I’m impressed by the latex in comments. Let me try: $\chi$, $\psi$. Back in NZ.

Kea, you need to put a “latex” after the first dollar sign. More complete explanstions are here.

I’m really tired about having to carefully read WordPress comments. They need to get a preview working. I’ll look around and see if there is a fix already available…

Very nice post. I am interested in this topic and I will have some comments when I read it more carefully. But, let me ask, why not write your eqn. 1 as

PHI = 2GM/(the stuff on the denominator)

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Hello Carl:

As you know, I have a 4D wave equation to unify gravity and light, . It is the c’s in this equation that dictates that EM travels at c, and since this is a unified field theory, gravity does too. It may be natural to think a longitudinal wave should travel faster, sound as you say being a great example. The problem with that is link is sound is governed by Newtonian physics, not relativistic physics where non-intuitive things happens. A great example is the speed of light being the same for all inertial observers! I accept that as true, but it is still odd. So it could be true and odd that a longitudinal gravity wave travels at the speed c. If that is the case, it would remove the need for the aether. We can disagree on this one :-)

doug

I always need to edit my LaTeX! The two c’s are in the wrong spots, but you get the point.

String theory plays catch-up: Gravitational waves propagate faster than the light velocity in the brane universe.

The speed of gravity is defined in general relativity as a speed entering the partial time derivatives of the metric tensor in the gravity field equations. Though the conventional notation for this speed is “c” (the same as the speed of light in vacuum) it is a matter of experiment to confirm that “c” is indeed equal to the speed of light in vacuum. The VLBI experiment of 2002 with Jupiter was designed to measure the numerical value of the fundamental speed “c” entering the Einstein equations. Einstein’s theory predicts that a moving massive body must deflect light from its retarded-time (as opposed to present-time) position on its orbit because gravity interacts with light on the null cone of the Minkowski space-time as predicted by the Lienard-Wiechert solution of the gravity field equations. This prediction of general relativity was confirmed and the experiment has proved that the fundamantalspeed entering the Einstein equations is indeed equal to the speed of light. The opposition to the experiment is because the opponents believe that gravitational field of a moving body interacts with light only in the form of gravitational waves. This is not true because the gravity is a tensor field, which is decomposed in several various multipolar components, from which only one has a character of a static field while others (not only the gravitational waves) propagate on the null cone. Various components of the gravity field are known as Petrov’s type components. Light-ray deflection experiment measured one of the propagating components in the near zone of the solar system. It propagates with the speed of light, as the experiment shows, but it does not mean that the speed of light was measured. Increasing precision of the experiment will allow us to measure the speed of other components in Petrov’s decomposition of the gravity field of moving bodies, including the speed of gravitational waves. Any critics of the Jupiter’s experiment should learn Petrov’s classification of gravitational field and the Lienard-Wiechert solution of the gravity field equations before making any statement about the physical interpretation of the experiment.

[added by Carl: Sergei Kopeikin is the author of The Measurement of Light Deflection from Jupiter: Theoretical Interpretation which gives more information on the above argument. Of course this is not the last of the argument.]

More references interpreting the Jupiter measurement as not giving the speed of gravity. The reader is invited to decide for himself:

“In recent, Kopeikin and Fomalont claimed the first measurement of the gravity speed by VLBI. However, the measurement has no relevance with the speed of gravity as I had shown before the observation was done. It seems that our conclusion has been established well by re-examining recent papers with great care.”Comments on “Measuring the Gravity Speed by VLBI”Hideki, Asada, Proc. of “Physical Cosmology”, the XVth Rencontres de Blois, 15-20 June 2003.

“… it is impossible that the speed of gravity was extracted from the data, and I explain what when wrong with the data analysis. Finally, mistakes are shown in papers by Fomalont and Kopeikin intended to rebut my work and the work of others.”

On the Speed of Gravity and the Jupiter/Quasar Measurement, Stuart Samuel, Int.J.Mod.Phys. D13 (2004) 1753-1770. Also see On the Speed … by the same author, Phys.Rev.Lett. 90 (2003) 231101.

“… within this class [of models], observations are thus not yet accurate enough to measure the speed of gravity.”

Model-Dependence of Shapiro Time Delay and the “Speed of Gravity/Speed of Light” Controversy, S. Carlip, Class.Quant.Grav. 21 (2004) 3803-3812.

“The main purpose of this Essay is to show an altogether new approach which, in our opinion, completely invalidates the claim made in [Kopeikin S M, Kopeikin S M and Fomalont E B].”

Speed of Gravity and Gravitomagnetism, J.-F. Pascual-Sánchez, Int.J.Mod.Phys. D13 (2004) 2345-2350.

The basic sociological problem of physics is that very few people actually understand a given subject at its deepest level. The rest of the crowd just follows the lead of the leaders. In the case where there is a disagreement such as the above, those who are specialists can pursue their own opinions, but the majority of physicists do not have sufficient time to understand the details and will be reduced to measuring the weight of the figures arguing on either side.

In the case of measruements of the speed of light, recent gravitation reviews agree with me that the weight of the “evidence” is in favor of those who say Kopeikin is wrong. Clifford Will’s review article from 2006 is still the latest word on the speed of gravity.

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gravity energy transfer is immediate

the speed of gravity seen to be faster than speed of light at least several milions times due to some calculations , i would like to discuss this in future.

This “gravity” is a product of the Universe, therefore

there is no Velocity or Time . involved in the acquisition

of this force.

It is yet another demonstration of a Phenomena of the Universe,

which I name ….“A Simultaneous Transition.”

Brian, your claim might be valid but to advance that argument you’ll need to demonstrate–either theoretically or obsrvationally–that gravity is some kind of emergent property, that gravity (and inerita too?) is somehow lonlocal and entangled with other matter, or that matter itself is inherently non-local (and thereforre we have an answer to the action-at-a-distance problem, and no signal need pass.)

In other words, it’s an interesting theory and I hope you get the opportunity to grow some legs on it.

Meanwhile, thanks and congratulations to all of you who are insisting on actual observations to deal with this. As Galileo said, “It moves.” :-)

A`simultaneous tansition simply means ;

The transition requires NO TIME and has NO VELOCITY.

irrespective of the distance involved.

Further more, is the basis of telephathy, and communications between most living entities in the Universe.

Unfortunately not common in humans.

Kopeikin: If you’re wondering why your recent comments didn’t get past moderation here, you should consider the possibility that you’ve already stated your positions and I don’t care to read the same thing over and over again, and I’m too busy to debate you.

Your argument is exquisitely complicated because you’re trying to use only light to measure the speed of gravity. To do that you have to make assumptions that depend on special and general relativity.

P.S. Do you really think it’s worth your time to try to post a comment on the blog of an amateur who doesn’t believe in special relativity, much less general relativity?

Carl, I was indeed wondering what’s the hell is going on with your site, who you are in this life, and what exactly you want to reach. It became crystal clear after you posted your promt reply. I have nothing to say any longer besides wishing good luck to you. Cheers!

Carl: before I shall leave you in piece one more remark — to measure any property of gravity (including its speed of propagation) one has to measure motion of a test particle in the gravitational field. The nature of the particle (light) is irrelevant. Gravitational perturbation of the particle (light) motion characterizes gravity, not the particle.

Good buy!

We Can Find Out

Let me propose two experiments. The first should be able to determine the speed of the propagation of gravitational information, or whether information/ gravitation is nonlocal (instantaneous) and do so without resort to any tensor analysis, any kind of relativity, and possibly with observations already made. The second experiment should be able to determine if gravity waves exist at all. It might not be possible and wouldn’t be sensible without results from the first indicating that some kind of information propagation exists.

*** First Experiment

Several planets orbit the the reduced center of mass of the sun-planet system. If the sun were to suddenly lose some significant mass, then a planet’s orbit would wobble or change in some small way in response to the new lower mass of the sun and the changed position of the reduced center of mass. Every planet is several light minutes away from the sun. It should be straightforward to measure a speed of propagation of gravitational information if such speed is anywhere near the speed of light.

The sun obliges us. It periodically fires off massive solar flares and coronal mass ejections. These can contain millions of tons of material. When these occur they cause the sun to positionally respond (Newton’s third law,) and lose mass. This event is inevitably noticed by the planets, whose orbits perturb by some small amount.

Someone (if I were a grad student I’d propose this for a thesis, but I’m not; I have a family to feed.) could go through the decades of observations we’ve already made of planets–particularly Jupiter for orbital perturbations. We have done this primarily looking for inbound asteroids, but the observations are good. Note each perturbation and carefully note the time. Then go through the records we have of solar activity, noting the time of mass ejections. Normalize the two time stamps. Compare the results. When we have solar events, does Jupiter respond immediately, soon thereafter, or fifteen minutes later as we’d expect if V(g) = V(c)?

We could repeat the perturbation measurements for as many planets as we have time and data. With luck we could even see the gravity “wave” speed out from the sun to each planet.

A logic proof of the observations would be to see if it’s possible to more accurately predict orbits based on each orbiting where the reduced center of mass of the system was X minutes (or seconds) ago. (Heck you could do this to demonstrate that Jupiter’s orbit is probably unstable if it orbits where it thinks the sun was 15 minutes ago.)

*** Second experiment

If we could find a very-closely-spaced pair of gravitational lenses–for example an orbiting pair of back holes or massive white dwarfs–and we could observe some gravitational event through them, then would we see a single-slit diffraction pattern of gravity? (I’m not sure yet how to determine this, variable lensing?) If we did, then we’d know gravity has a wave (and possibly a particle) aspect. If we don’t, (and / or depending on the results of the first experiment) then we need to rethink some basic premises such “action at a distance.”

I invite comments

—

Richard Johnson

great blog …well written for hard hat. ;)

especially enjoyed the lesson on LONGITUDINAL wave speed calculation….and the historical perspective.

What really concerns me is how to determine the degradation in the amplitude of a longitudinal wave as a function of density, elasticity, etc. …how do you calculate if it actually “spreads out” only 1/r or even possibly less.??

I’ve seen ancillary evidence that (if they exist) a longitudinal GW wave may be be very ‘narrow’ (“laser like”).

Any idea?

thx,

gip

I have obtained the NASA planetary ephemerides, and will be installing them on my machine shortly. From them I will attempt to determine the speed of gravity from existing measurements of perturbations and solar activity. I will post occasionally as work progresses (and concludes.) Hopefully you can collectively keep all the math honest.

No attempts here to validate or falsify any particular theory, but just to see what the data says. If I had to predict an outcome at this point, it would be that the signals are the same size as noise. Haven’t actually -looked- at the data yet, but that would be first guess. :-)

—

Richard

another interested amateur

Sooner or later the academic world is going to have to face up to the notion, that with in the Universe there exists a small number of vitally important true constants. These constants are perfect, and require no energy to function, distance is irrelevant.

They will be powerful and immutable and are required to maintain stability with in the Universe.

Gravity is one of these constants.

This phenomena is distributed via a

“Simultaneous Transition”

I would suggest that the solar energies are delivered to the Sun’s corona in the same way.

Brian

I read all the way down, and it seemed to me that Richard Johnson was on the right track. So I was hopeful that he would have posted some result since Feb of 2010. Not so. What happened to Richard??

Hi all. I’m still here. No results yet.

What has happened so far is that I have grabbed a whole bunch of data and some public-domain code from a university in Paris and NASA. NASA has a sizable quantity of data about planetary position and motion. The wonderful French added a normalized time stamp to the data, making it easy to compare one planet’s information to another’s. The data consists of sets of numbers that are coefficients to Chebychev polynomials that actually express position, rate, etc.

The program is a set a library routines to convert the data (a small bit at a time) from coefficients to data. The code is written in C, and requires a C or fortran progam to exercise. Unfortunately, my primary language is Java.

So right now I’m (still way too slowly) porting the conversion code from C to Java. This offers some advantages (no more need to worry about internal representation of numbers, floating-point numbers that are more accurate, greater readability (for some of us anyway.) However my day job has been interfering, so I’ve only managed to port the routines that load data and none of the routines that actually exercise the data.

Thanks a lot for the good word. I (honestly!) thought no one cared. :-)

The long-term plan is to run a bunch of data for Jupiter to find bumps and wiggles. Then run data within an hour or so of that event on other major bodies (like Mars, Venus, Earth, moon, etc.) I’ve given no thought at all to how to present the data or findings. I’ll probably just make the raw stuff available for everyone here to look at.

That being the plan, it’s occurred to me I *might* be able to short-cut the process. Given that the data are coefficients to very long polynomial expansions, can we detect perturbations or other sudden short term changes in position or speed –just by looking at the coeffiecients themselves?– IOW, do we actually need to process them first? I’m not enough of a mathematician to make that kind of call.

Thanks, Richard, for the update. Unfortunately for you and for me, I am neither a Java programmer nor a mathematician. So I posted a call for same on Fb with a link to this page. Ditto for Twitter.

Thanks for putting the word out. I’m currently trying to recruit a C programmer to help write an app. That too would bypass the Java rewrite of the Calceph code and speed things up a bit.

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Last night I generated meaningful output for the orbit of Mars. The code is sort of like Linux … intuitively obvious, once you know it. :-) Still have some representational issues (how numbers appear in the output) but cleared a major hurdle.

Once I get a sensible representation I’ll generate a few thousand data points for Mars (It has a very wriggly orbit) and make sure we can detect changes and events.

When that works, I’ll generate a few million data points for (probably) Venus. Then look for events. Finally when we have some events noted, then I can generate data for other bodies near the same time (reducing the workload.)

It’s time: Let’s discuss what a “signal” would be.

If some gravitational event caused a planet’s orbit to adjust, what would that adjustment look like? For instance, when Mars passes an asteroid, it speeds up, pulls outward, slows down, and returns to “normal.” That’s probably not what we’re looking for. So I throw this out to the community–what kind of behavior should we look for?

Asking the right question is useful. :-)

Update:

We’re starting a search.

Methodology — I have chosen seven CME’s whose dates were clearly documented in reliable literature (NASA, New Scientist, etc.) These CME’s occurred between 1997 and 2010. Earlier CME’s represent possibly poor data collection, and later ones (maybe even the 2010 ones) might not actually be represented in the ephemeris.

I am generating position and motion information for the sun and planets, with one minute precision, starting a full day before and ending a full day after the recorded event, using the solar system barycenter as the centroid (not the center of the sun.) If the data is reliable (we’re counting on it!) we should see the sun accelerate during the CME, and then see planets adjust to the moving barycenter within some to-be-seen length of time following the event.

Next update in a few days.

http://users.elo.com.br/~deaquino/ requires time to read; but it has the answer to all of these questions.

Thisgoodriddle … that looks really interesting. For the time being I’m trying to avoid literature and theory that might inadvertently bias the questions I ask and how I ask them. If he really does have a way to unify gravity and QM, more power to him! I hope he has successfully predicted whatever it is we find. :-)

Last night I did several runs of the motion of the sun, using the barycenter as frame of reference, about the time of the earliest CME. There is indeed a large excursion of the sun/barycenter shorlty

beforethe CME was observed. I want to try it again the other way just to see which gives more workable results, and redo the run with more precision too.UPDATE: —

I have been probing NASA’s ephemerides now for some time and routinely see sudden movement of the solar system barycenter. Invariably it turns out to be computational issues associated with internal representation of tiny floating-point numbers. They always occur at midnight GMT. If only CME’s were so obliging. :-)

In short, I haven’t seen any clear signal of barycenter shift. Now I have three choices and would like your opinions as to which to pursue first.

1. I can keep searching for CME-related barycenter shifts. (If the one I’ve been looking for is too small, we might get lucky with another CME.)

2. I can search for simultaneous sudden shifts in planetary motion. (Much harder since planets are always wiggling, and it’s not clear what simultaneous sudden shifts would mean without a clear barycenter signal.)

2. I can try to find some actual observational data. (The ephemerides are coefficients to a polynomial approximation that describes an orbital section. This might mean garbage-in, garbage-out and so no amount of probing this way will tell us anything useful.)

Thoughts or contributions, anyone?