Requiem for Relativity

<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote"><i>Originally posted by Maurol</i>
<br /><blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote"><i>Originally posted by nemesis</i>
<br />I'll rephrase my precession question a little differently. Currently, at the winter solstice in late December the Earth is near perigee. In roughly 13,000 years, halfway through the precession cycle, at the winter solstice, still late December by the tropical year, will the Earth be near apogee?
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Hi nemesis,
Short answer: No.
What encompasses the points of perihelion and aphelion is the length of the sidereal year. The tropical year is 20 minutes shorter, to align the calendar with the seasons, that is, to maintain the equinocces(marks of the seasons) in relatively the same days, due to the earth axis precessing, and then changing the occurrence of the equinocces. The tropical year is a convenience.
In 13.000 years, as the difference is cumulative, you'll have a (significant) difference of 13000 * 20 = 26000 minutes, around 18 days, between a calendar based in the sidereal year, and one based in the tropical year.
So in late December, the Earth will still be near perihelion, although in a calendar based in the tropical year perihelion will really occur around December 13.
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This is incorrect! As the seasons depend on the amount and angle of incidence of light on each hemisphere, and as that depends on the direction of the inclination of the Earth axis of rotation, in 13000 years, having the direction of the axis preceded 180 degrees, winter will occur near aphelion, as nemesis says.
That moment will be called December 21, if our calendar is still in use, but the Earth will be then in the opposite side of its orbit.

I was confused by the proclivity to associate closeness to perihelion and occurrence of the summer/winter seasons, common to our time.

All this holds if, as current astronomy says, perihelion is stable and precedes only a small number of arc secs/century.

The above program uses objects A & A2 from 1954, B & B3 from 1986, and C11 & C from 1987. All three are online scans of Red sky survey plates. The coordinates and dates are to be found in the program. The former object of each pair is the one I now identify as Barbarossa, the more massive member of the binary; and the latter is the one I now identify as Frey.

The designation "C11" was chosen for ease of remembering (like "CII"), not because I found so many disappearing dots. The object "C" is the very first "disappearing dot" I ever announced; I thought it was Barbarossa but now realize it is Frey.

USNO-B Blue magnitudes of stars comparable to these, if given at all, usually are near the faintness limit of accuracy, +21. On the other hand, there are many comparison stars with reproducible Red magnitudes (i.e., R1 = R2). Looking almost perpendicularly out of the galaxy, most stars this faint, are red dwarfs (also, many objects this faint are galaxies). According to the Red magnitudes of nearby similar stars, my estimates of these objects' magnitudes range from about +17.5 to +19.5.

The USNO-B Red magnitudes of comparable stars are consistently about 1.5 mag brighter than the photometric magnitudes on the Jan. 20, 2009, U. of Iowa photo. That is, a typical comparable star has USNO-B Red magnitude +18.5 but is said to be +20.0 Visual magnitude on the U. of Iowa photo. This is reasonable for red dwarfs, which most of them must be, at this high galactic latitude.

Objects A2 and B3, both Frey, have one or more dimmer companions (other disappearing dots) within about an arcminute or less. These might be sub-moons of Frey.

One other object I use in my program, is located at RA 11:27:30.17, Decl -9:21:48.6 on the Dec. 22, 2008 U. of Iowa CCD photo, taken with their 15 inch robotic telescope in southern Arizona and median stacked by Professor Mutel. This object has a starlike appearance; it is the most starlike of any candidate image on any CCD photo I have examined. It is similar to the nearby USNO-B 0806-0230017, whose Red magnitudes are +19.4 +/- 0.2. The object is near the west edge of the photo but well outside the obviously affected edge region. It is Frey; the theoretical position of Barbarossa is outside the photo, because I changed my orbital theory.

Other "Barbarossas" and "Freys" identified on this and other prospective CCD photos, are not used in the program, because although such "disappearing dots" are important discoveries, they do not fit my revised, corrected and accurized theory of the orbits. Even with the new predicted coordinates, the other photos are, more or less, of the correct patch of sky, but I have not had time to check them. Someone else might check them using the above program, which gives the center of mass prediction, given the Julian date. The positions of Barbarossa and Frey then can be found from the center of mass. For Frey, subtract the predicted Dec. 22, 2008, c.o.m. coordinates from Frey's actual Dec. 22 position. The binary period is about 22 yr, so this difference still can be used for Frey now. The mass ratio is Barbarossa::Frey = 0.8898::0.1102, so to find Barbarossa, multiply Frey's lever arm by -0.1102/0.8898. The Jan. 20, 2009, U. of Iowa photo, made according to my earlier theory, is too far east to contain either Barbarossa or Frey.

The program has two parts. The first part uses the three sky survey dot pairs, to get the c.o.m. solar orbit. The mass ratio, orbital radius, and first and second derivatives of the orbital radius, are varied to find the trajectory which minimizes the difference between Newtonian gravitation and the theoretical orbit's acceleration. This difference can be made very small for these three dot pairs, but not for any other sets of three pairs tried. The result is the mass ratio Barbarossa::Frey = 0.8898::0.1102, initial 1954 radius 205.2 AU, initial 1954 dr/dt = -1.0 AU per radian of orbit, and d2r/dt2 = -23.3 AU per radian per radian. So, Barbarossa is near aphelion, and its solar orbit has eccentricity e = 0.114. When parameters are varied enough to change predictions by an arcsecond, the unexplained acceleration becomes much larger, so, the prediction might have arcsecond accuracy. However, the path is so short, that the eccentricity cannot be known very accurately.

The program's second part analyzes the Barbarossa/Frey binary orbit. A fourth binary orbital point is achieved by predicting Barbarossa's position, from the Dec. 22, 2008 U. of Iowa Frey observation, and the program's predicted c.o.m. position. Yesterday I graphed all these, noticing that the 1986, 1987, and 2008 Frey positions, relative to Barbarossa, are almost collinear. There is only a narrow range of possible fifth points such that an ellipse can be fitted.

Frey's 2008 position (relative to Barbarossa) is only a little past its 1986 and 1987 positions, on an almost straight line, so by conservation of angular momentum, the speed on this segment must be almost constant, and the time of travel on this segment can be estimated. I also drew a straight line through Frey's 1954 position, and the origin, to get an estimate of the position 1/2 orbit past 1954; this happens to be between the 1987 & 2008 positions. Assuming between one and two orbits during 1954-1987, and again during 1987-2008, and a mass Barbarossa+Frey = 0.01 solar mass (estimated from my theory of outer solar system precession resonances, and in other ways) these two constructions, with straight edge and ruler on graph paper, imply semimajor axes of 1.61 and 1.73 AU, resp. The former figure should be more accurate for a noncircular orbit, because it employs a whole orbit, not an orbit and a half.

If the binary orbital eccentricity is small, then the foci lie near the center, and the tangents to the apparent binary orbit ellipse, near 1987 and near 1954, are parallel because these points lie near the opposite ends of the "diameter" drawn through, the focus, which approximates the center. If these two parallel tangent lines are near eclipse (suggested by the small area of the apparent ellipse) then points on them appear to move perpendicular to the lines, but also to stream along the lines.

The three collinear Freys, slope 54.25deg NW to SE. Early in my research I had noted that Barbarossa's solar orbit slopes 27 deg on average during this time.

(email response sent 5 min. ago)

Hi Prof *********!

The "royal road" to Planet X / Barbarossa, is Paul Wesson's article in Physical Review D, in 1981, on "tax day", April 15. Wesson noticed that (angular momentum)/(mass^2) is roughly constant in astronomical systems of all sizes, and thought this phenomenon might reflect an underlying universal physical constant. I would augment Wesson's article three ways:

1. Some systems should be disregarded because it's fairly certain that their angular momentum value is due to special effects. These systems include Mercury, Venus, and Luna rotation (tidal drag, spin-orbit locking), double planets (Earth-Luna, Pluto-Charon)(capture?) and binary stars (capture?)(undetected distant member?). The most pristine systems are the rotations of the four giant planets. These all have J/M^2 = Wesson "p" factor within a factor of two of each other.

2. I didn't see this mentioned in Wesson's article; maybe I missed it (I looked up the article in the library downstairs the day that I visited the U. of Iowa Astronomy Dept.) but the "p" factor for the giant planets, differs from the "p" factor for a spinning electron, by a factor equal, to within an order of magnitude, to the "electric-to-gravity ratio". Wesson's "p", seems to be the gravitational counterpart of electron spin.

3. It's a good guess that the proto-sun, and hence the solar system, has the same "p" factor as the giant planets. One might ask, does it have enough angular momentum? Is another planet needed to bring the "p" factor up to the norm? How big a planet, how far out? It turns out that the solar system's angular momentum is at least 20x too small, by comparison with the giant planets. Addition of Barbarossa at my estimated mass and distance, makes the angular momentum about right, no more than 2x too large.

This is the "royal road". It's something that can be understood and checked quickly. It doesn't prove that my "dots" are the planet, but it's strong circumstantial evidence for such a planet, somewhere.

&gt;...Peter Goldreich is probably the most respected solar system dynamical theorist in the world. He is not known for making sloppy approximations. ...

I never called him sloppy or said he wasn't respected. Goldreich himself expressed at least some doubt, in his article, of the validity of at least one of his approximations. Making a nonrigorous calculation doesn't damn him; a rigorous calculation was impossible, as far as anyone knows. This is the infamous "many body problem" with at least 1+4+1=6 massive bodies. Someone said that even the wanderings of the Jupiter-Saturn resonance were analytically intractable, and that's only a three-body problem. Also, respected solar system dynamical theorists can disagree. Harrington said on his deathbed that Standish's correction to Neptune's mass, didn't remove the residuals. Eckert found a residual so big that Standish's correction couldn't possibly remove it.

There's a tendency to escape uncomfortable ambiguity by a "rush to judgment". To say, "Whew, Goldreich says I can stop thinking about this, what a relief!" when really "stop thinking about it" is only the "executive summary" of what Goldreich really said, and other respected dynamical theorists, Eckert and Harrington, have made claims which seem to contradict Goldreich and Standish.

The Kimura phenomenon provides a paradigm. Basically, Kimura noticed that accurate determinations of declinations of bright stars near the north ecliptic pole, made from northern observatories, showed systematic seasonal change not explained by any known correction. Soon afterwards Chandler endorsed, not exactly Kimura's conclusion, but at least Kimura's reputation. One would think that the Kimura phenomenon, with at least Chandler's limited endorsement, would be taken seriously, and apparently it was for about a generation.

Then in Astronomische Nachrichten (I accidentally discovered this article at Drake University) someone said, in a short letter, basically, "Kimura didn't know how to average data correctly; it's all just an artifact of that." I, for one, could not decipher, let alone verify, the objection to Kimura's method of averaging data. Furthermore I could not imagine how any erroneous method of averaging data, could cause a seasonal change. I suppose everyone was tired of looking at the unsightly clutter of Kimura's phenomenon, and unconsciously wanted to throw it in the trash so we could all feel better. I think it's good to have a sense of humor about this, but I'm not belittling anyone in particular; these are human failings we all share.

A careful, peer-reviewed theoretical estimate of the albedo of one particular class of cool brown dwarf (indirectly supported by some observations) is, &lt; 1%. I've posted all this material to Dr. Van Flandern's messageboard during the last two years.

Sincerely,
Joe Keller

(previous email, sent last night)

Hi Prof. *********!

I've become something of a specialist in the literature on this!

&gt;...the perturbing effect of such an object on the orbits of the outer planets...

I read Goldreich's article about that, in the Pacific astronomy journal. I counted that Goldreich makes four explicit mathematical simplifying assumptions in his lengthy calculation. It was a nonrigorous calculation. There's a lot that can go wrong with that kind of calculation.

For the distance and mass I propose, the orbital precession rates of Neptune, the plutinos, and the classical Edgeworth-Kuiper belt objects, stand in 3::2::1 resonance. Furthermore the torque at the classical Kuiper belt due to Barbarossa (the outward part of the solar system), equals the torque there due to Jupiter, Saturn, Uranus & Neptune (the inward part of the solar system). That's solving (3-1)+1 = 3 rather fundamental equations with, really, one adjustable parameter (Barbarossa's mass / distance^3). Why should that be, unless there is something happening, dynamically, that Goldreich didn't know?

&gt;...the size and therefore the apparent magnitude of such an object...

Nobody knows what size it would be, or what temperature it would be. I saw a quantum mechanical calculation from Physical Review in the 1990s, concluding that every mass between Jupiter and a hot brown dwarf, gives about that same 120,000 km diameter, and that even a 5 billion year old 0.01 solar mass hyperjovian that never burned deuterium, should be room temperature or so. But that's just a quantum mechanical calculation, and a pretty big extrapolation from the lab! What if there is an unforeseen mechanism of cooling by convection? What if formation is by accretion so that all the gravitational energy is released at the surface where it can radiate away quickly? What if, somehow, it's pulsar-like (nuclear density) material?

There's an article saying that at least some brown dwarfs ("black smokers") have albedo 1% or even less - something about alkali metals at the surface. We know little about very cool brown dwarfs, distant from any star, because there's no way to observe them directly. A recent article estimates that, accounting for observation bias, the cooler known brown dwarf spectral type outnumbers the hotter type, almost 10:1. What if there's an even cooler type that outnumbers it 100:1? Is that our dark matter?

I don't think that surprisingly high density or surprisingly low albedo have been ruled out. There's a tendency to be overconfident in current theory, therefore not to look at contradictory data, and to miss discoveries. Why couldn't dark matter come in big blobs?

Sincerely,
Joe Keller

The four Freys I've identified above (the Dec. 22, 2008, U. of Iowa photo's Frey, referred to the center of mass extrapolated using my program; and the 1954, 1986 & 1987 Red sky survey Freys referred to the centers of mass calculated using their and Barbarossa's positions) do not, in the most straightforward way, fit an orbital ellipse. I investigated this using my program above, and a supplemental program based on formulas appearing in, inter alia, Love's Analytic Geometry, especially ch. VIII, sec. 69.

The satisfaction of Kepler's second law by the adjustment in the program as posted above, is suggestive, but the adjustment made differs from textbook reality in three ways:

1. The sector area is calculated only to quadratic accuracy.
2. Each side of the orbit is given the full displacement, instead of dividing the displacement between the sides according to their foreground or background distance.
3. The component of displacement parallel to the binary orbit is ignored.

The change in aspect of the Barbarossa-Frey orbit, from 1954 to 2008, due to Barbarossa's orbital motion, amounts to a precession of 0.112 radians about an axis at 27deg counterclockwise of North (Barbarossa's orbit slopes about 27deg south and east). To adjust for this, the 1954 and 2008 Freys must be moved parallel to Barbarossa's orbit. The distances to be moved, are unknown because they depend on the size and shape of the binary orbit. However, the 2008 point must be moved westward, because it is almost collinear with 1986 & 1987, so with eastward motion, the orbit quickly becomes hyperbolic and then fails even to be convex (no solution).

I tried many plausible pairs of distances by which to adjust these points. For each pair of distances, I used my program to find the "fifth point" of the ellipse (that is, the western x-intercept) satisfying Kepler's 2nd law best. Because there are 4-1=3 sectors, there are two Kepler's 2nd law equations to satisfy. Generally only one member of the pair of adjustment distances, was independent, and often there was no solution. (I corrected the accuracy of the sector areas to a cubic approximation, which should suffice.)

I found only orbits that are too small or too eccentric (e.g., e = 0.99). None of them implied the parallax displacements assumed.

[Digression about believable eccentricities:

[The six binary pulsars in Taylor's 1995 catalog (VizieR) with e&gt;0.3, have 0.61&lt;e&lt;0.87, median 0.74. (The binary orbit part of the catalog has 45 entries; eccentricities are given for 30.) So, Frey's eccentricity is typical of the eccentric 20% of binary pulsars. Worley's 1983 visual binary catalog (N=933) contains 79 systems with 0.3&lt;e&lt;0.35; this drops off smoothly to 49 with 0.85&lt;e&lt;0.9, then drops faster to 31 with 0.9&lt;e&lt;0.95 and 11 with 0.95&lt;e&lt;0.99999. Neptune's moon Nereid has eccentricity almost 0.8.

[Digression about method:

[Following the basic methods in Love's Analytic Geometry, and using a short supplemental computer program, I found the real orbit from the apparent one, by searching (with an IBM 486 desktop computer) all axes and angles by which to rotate the apparent orbit: first I transformed the axes by theta, to the trial axis of rotation, and in the same stroke transformed one axis to expand the orbit perpendicular to the trial axis, by sec(alpha). I then put the transformed orbital equation into standard form (using another axis rotation to eliminate the cross term) and saw whether or not the center of mass (origin) equalled a focus. (For the correct real orbit, this will be so. The process amounts to solving two equations - that (0,0) is a focus - by varying two parameters - the direction of the unit normal to the real orbit.)

Hi Prof. *********!

&gt;...tidal effect of a 0.01 solar mass body at 200 AU on the Sun...

Goldreich and I refer to the tide on the outer solar system (e.g., Planet X acceleration of Neptune, minus Planet X acceleration of Sun) which Goldreich and I agree would not be negligible in its effect on solar system structure. This effect is difficult if not impossible to calculate rigorously in a many-body system. It might express itself most obviously as a small-integer resonance between precession periods.

&gt;The Sun's spin angular momentum...

Paul Wesson and I refer to the solar system's angular momentum (i.e., proto-sun's angular momentum), not the small part retained by the sun today.

&gt;...darker than every other known solar system object...

Stranger things have happened. Also, we don't know its albedo because we really don't know its size. Anyway, the true object might be brighter but undetected (the binary orbit could fool detection algorithms).

&gt;...extraordinary claims require extraordinary evidence.

Extraordinary evidence will not be found without looking (sometimes looking quite a bit). To motivate the photographic effort, I make the case for finding something.

&gt;I looked at your 'detection' in the Dec 22 image - it was so faint that I could not determine a point-spread function...

The third, latest and best detection (11:27:30.17, -9:21:48.6 on the Dec. 22, 2008 U. of Iowa photo) closely resembles a nearby cataloged USNO-B object, with R1=19.6, R2=19.2. It conforms to my revised, corrected and accurized orbital theory (see computer program posted to Dr. Van Flandern's messageboard).

Sincerely,
Joe Keller