Requiem for Relativity

Because Frey's magnitude (Red 20.26) is significantly brighter than Freya's (Red 20.61, 20.68, 20.68), it may be distinguished and Object #2 excluded from the test of periodicity. Observations do not always occur exactly at Freya's maximum elongation. Even with this large source of statistical noise, the periodicity is significant:

For these small increments, multiplying the RA by the cosine of the midlatitude of the chord, then using the Pythagorean theorem, gives accurate arclength. Let's neglect eccentricity (variable angular speed) and assume that the true period is the gap between Object #5 & #1. Even after three more cycles, the gap between Object #1 & #3 is only 0.037 of one period off; the gap between Object #3 & #4 is 0.24 period off. Including the possibility of positive or negative error, this is still significant at p=0.036.

Joe, you now need to have telescope time, and a check through with a blink comparitor of old plates. Time is money and you have to convince the guys that hold the purse strings to do this.

Freyja and Freyr will raise no eyebrows but naming a planet after a total psycho (Frederick I ) will. You do know that Ceres was once going to be called George? There was uproar over that.

We simply cannot name a planet after a real historical personage. I suggest you stick to the Norse gods and call it Wotan or Odin. I can't see any astronomer, with an ounce of political savvy, calling this planet Barbarossa. Seriously, I believe that it would lead to deaths.

Joe, naming my be secondary to the more pressing issue of protecting your claim of discovery. You have given out information in a public forum that those "who hold the purse strings" could use and take the credit if the object is confirmed.

<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 />Joe, naming my be secondary to the more pressing issue of protecting your claim of discovery. You have given out information in a public forum that those "who hold the purse strings" could use and take the credit if the object is confirmed.
<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">

Thanks, both to you and to Stoat, for your information (and Stoat's humor!).

A few years ago, ArXiv.org began requiring "endorsement" of authors. That is, one couldn't post unless someone else in the club admitted one to the club. A few years ago, I asked a few faculty members here at Iowa State Univ., to endorse me to ArXiv.org, but none would. So, I use Dr. Van Flandern's messageboard as my ArXiv.org. Dr. Van Flandern is for me, what the ArXiv.org editors are for regular academics.

During the last week, I've reposted (sometimes only minutes later) some abridged versions to several astronomy messageboards. I hope they will look and see Barbarossa. A magnitude +18.1 +/- 0.3 planet will be difficult; the USNO-B plates only go down to about +20.9.

The Discovery of the Planet Barbarossa with Moons Frey and Freya: Report to United States Naval Observatory

(by FAX, Feb. 21, 2007)

Author: Joseph C. Keller, M. D. (B. A., Harvard, cumlaude 1977)

Copies: Capt. Edwin C. Keller, U. S. Army, ret.
Prof. Roger Rydin, Physics Dept., Univ. of Virginia, ret.
Dr. Tom Van Flandern, formerly of U. S. Naval Observatory
Prof. Steve Willson, Mathematics Dept., Iowa State Univ.


Abstract. This author’s physical theory implies a distant massive planet in the direction of the cosmic microwave background dipole. The planet, Barbarossa, appears five times in the U. S. Naval Observatory B1.0 catalog:

Object #5. USNO-B 0830-0272239
Object #1. USNO-B 0827-0286487
Object #2. USNO-B 0824-0279170
Object #3. USNO-B 0820-0274026
Object #4. USNO-B 0813-0233607

Barbarossa is aliased by moons.


The Physical Theory. I do not remember who wrote that the sun’s gravitational field is the only known object big enough and symmetrical enough to cause the “cosmic” microwave background (CMB). In 2001 (Aircraft Engineering and Aerospace Technology, 2002) this author discovered that the internal gravitational field of a Heisenberg-uncertain proton (Gaussian radius hbar/(2mc) ) equals solar gravity, at 52.6 A.U. In 2007 (archived on the metaresearch.org messageboard, Dr. Tom Van Flandern, editor) this author discovered that this same distance, 52.6 A.U., is where the 1.5-root-mean-1.5power speed of electrons at the “cosmic” background temperature, equals escape speed. These two equations give the “cosmic” temperature as a function of the gravitational field and potential.

This author noted in 2001 (published; op. cit., 2002) that two kinds of anomaly in the Pioneer 10 probe signal occur, or begin, at about 53 A.U. In 2007 this author found two 2001 reports in the Astrophysical Journal, that the end, or minimum, of the Kuiper belt is at 52 or 53 +/- 1 A.U.

The small-scale statistical distribution of CMB anisotropy is quantitatively consistent, near the ecliptic, with the gravitational effects of Kuiper belt objects. The large-scale anisotropy discovered by Davies at Madeira, is consistent with an Earth-mass planet at 62 A.U., far from the ecliptic, near the edge of Tombaugh’s search region; such a planet would move the CMB dipole a fraction of a degree. Known planets, especially Neptune, also would move the CMB dipole a fraction of a degree. The difference between the 4-yr COBE DMR probe and 3-yr Wilkinson WMAP probe, shows a significantly, retrogradely, revolving dipole, if the true error bars are smaller than published. From these estimates and uncertainties I defined a 1x3 degree search region, backward in time 80 yr, for the hypothetical distant planet mainly causing the CMB dipole. For its circular orbit I estimated 355 A.U. and 6830 yr. For its mass I estimated 0.019 solar masses.

Most stars are detectably double or triple; presumably the sun has a faint companion, a brown dwarf or giant planet. Like the CMB dipole, Percival Lowell’s predicted major axis for Planet X was near 180 degrees ecliptic longitude; a much farther planet’s radius vector almost constantly in this direction, could have similar effect. The solar system origin of the CMB explains the correlations of its multipoles with the plane of the ecliptic.

The Trans-Neptunian Objects (those known in 1998) and long-period comets have aphelia clustered toward 180 ecliptic longitude. Such displacement could neutralize, the CMB quadrupole induced by the distant planet which causes the dipole.

The discrepancies in the orbital resonances of the giant planets (as known c. 1980) sometimes equal simple multiples of Pluto’s period, but mostly equal simple multiples of 4430 yr., corresponding to 266 A.U. for circular orbit. (Gomes et al (2005) calculate that planetary resonances cannot propel small bodies into orbits above 260 A.U.)

An elliptical orbit of this period would give the predicted angular speed, not at 355 but at about 330 A.U., reducing the mass of Barbarossa to 0.016 solar mass. This makes Barbarossa, in present astrophysical theory, a small, cool brown dwarf of surface temperature 378K assuming age 4.6*10^9 yr (slightly extrapolated from Burrows & Liebert, Reviews of Modern Physics, 1993). At 83,500 miles diameter, it would have magnitude +18.1 if its albedo is 7% (slightly more reflective than many asteroids and reddish Kuiper belt objects). If Frey and Freya are bluish gas giant moons with Neptune’s albedo of 30% (and Neptune-like internal heat production), magnitude +20.26 and +20.66, resp., then their diameters are 22,000 miles and 18,000 miles.


The Search. On Feb. 15, I realized that other bodies (later that night, after 00:00 Universal Time on Friday, I realized from the consistency of the magnitudes that they were moons; subsequently I learned that asteroids would be unlikely - textbooks c. 1970 estimated only 40,000 asteroids of adequate size) could impersonate or “alias” Barbarossa, causing two presumed detections near one point on plates made one year apart: thereby inclusion in the USNO-B1.0 catalog. Without further ado I searched the online U. S. Naval Observatory B1.0 catalog, from “Computer #1” in the Nevada, Iowa, public library, throughout the overlapping disks comprising the above 1x3 degree region, for objects with one recorded Red magnitude &lt;+18.99 and the other Red magnitude &gt;+19.50, and proper motions allegedly &gt;80 mas/yr in both directions. I found 61 objects, four of which lay very near a line. I briefly thought it was five objects, but one was a transcription error. Heartened by this mistake, on Feb. 16 I searched for Red magnitudes in Freya’s magnitude range, one degree farther along the line in the retrograde direction, and found Object #5. On Feb. 17 I calculated that Object #5 was only 4.9” from the great circle through Objects #2 & #3 (p = 0.006)(I was suspicious of Object #1 because of its differing magnitude). On Feb. 20 (yesterday) I searched with my original criteria, along that great circle, from RA 11h 3m to 11h 31m, 9 degrees total, finding no others.

The 61 fainter Red magnitudes for each original object, had a uniform Poisson distribution. This indicates that the clustered four faint Red magnitudes of the objects are due to Freya, and the less faint one, of Object #2, due to Frey. The four objects associated with Freya show periodicity of position.

Of the five brighter magnitudes of the objects, none lie between +18.60 and +18.99. Object #1 is brighter in Red than the other objects, and very dim in Blue though not bright in Infrared (“I”, 1.2 micron). An IBM 486 Monte Carlo trial showed that averaging four or five objects does not vitiate the result, that Barbarossa has a spectrum too flat, and too dim in Infrared, to be a Type M or late K star with a Planck spectrum. (Galactic dimensions and star type counts imply that half the stars in my brighter Red magnitude range, would be K5-K9, & half M.) Almost ten times as many stars found within 20 degrees, in the same parameter range, had B & I both fainter than for Barbarossa, than had both brighter. Barbarossa’s color magnitudes suggest a large red spot covering almost one hemisphere of the rotating planet.


Object #5. USNO-B 0830-0272239
Object #1. USNO-B 0827-0286487
Object #2. USNO-B 0824-0279170
Object #3. USNO-B 0820-0274026
Object #4. USNO-B 0813-0233607


Object #5. USNO-B 0830-0272239 RA 11h10m08.44s Decl -6d59'37.2"

Object #1. USNO-B 0827-0286487 11h12m05.59s -7d14'27.8"

Object #2. USNO-B 0824-0279170 11h14m54.41s -7d35'13.7"

Object #3. USNO-B 0820-0274026 11h18m03.53s -7d58'41.0"

Object #4. USNO-B 0813-0233607 11h23m30.03s -8d38'37.8"



Analysis. If the typical orbital radii of large satellites follow a power law for parents of between Jupiter’s and solar mass, then the angular distance at greatest elongation, for at least one of the moons, would approximately equal Barbarossa’s travel between one photographic plate of the constellation Leo, made in northern hemisphere Earth early springtime, and the next. Assuming 30 plates covering the region of sky over 60 yrs, about four close aliasings would be expected for a nearly optimal moon. From the Astronomical Journal (2003) article explaining the USNO-B catalog, I guess that these usually would be combined into one star, with its motion attributed to the entire 60 year time interval, hence underestimated 60-fold. The fiction is the assumption, valid for stars, that the object is present with equal likelihood on all plates of that region, so that dates of individual plates are inessential.

One pair of “epoch” dates (Objects #2 & #3) corresponds, to the above 4400 yr period, if the orbit is circular at 270 A.U. This would seem to require Barbarossa to have either 3% albedo and 0.011 solar mass, or else less than 0.001 solar mass (abandoning my theory of the CMB dipole) and thereby smaller diameter (theoretically the diameter is almost constant above Jupiter mass, until red dwarf mass). On the other hand, the track would be 44 yrs instead of 69 years long (“50 years” of Schmidt plates are specified, in the heading of USNO-B searches). The other pairs of “epoch” dates variously imply large speed or small, pro- or retrograde. The explanation is, that epoch dates usually are for the region, not actual detections of the object.

As expected, observed Objects are more and more frequent in the retrograde direction, as astronomy facilities improved and sky surveys intensified. Then they suddenly end, at least for the next three degrees.

For aliasing, the moons’ orbit can be bigger than the minimum, but not smaller. The apparent proper motion usually will be positive in RA, and consistently of one sign or the other in Decl, depending on Barbarossa’s (est. 5 degree) axial tilt (hence the orbital tilt of the moons). The Frey observation, and three of four Freya observations, have proper motions lying on part of a rough ellipse in the first quadrant. The other proper motion lies on the same ellipse in the third quadrant, suggesting accidental position on a centripetal part of the apparent tilted orbital ellipse.

Freya makes slightly more than half an orbit in one year. After perhaps ten years, alignment is good again: Objects again may be found on the plates. Due to Freya’s moderate orbital eccentricity, the period between observations alternates longer and shorter. The first (easternmost) Freya interval was shorter (short + long + short) than the middle interval (long + short + long); the last interval should be “short”: it’s not shorter than the average for the first interval, but it is shorter than the average for the middle interval.

Barbarossa’s orbit crosses the celestial equator near RA 10h 15m. The curvature of the track on RA/Decl coordinate paper, is of the correct sign, and roughly the correct magnitude. Barbarossa’s orbit is inclined 27.5 degrees to the celestial equator and 16 degrees to the ecliptic plane.


Naming the Planet and Moons. That myth originates in fact, is often speculated. Hellenic and Roman literature is a continuous spectrum, from myth to fact. Some hold that the myth or legend of Wotan, originally was the story of a prehistoric king. That the myth or legend of the returning king, Barbarossa, is associated ambiguously with both Holy Roman Emperors Frederick I and Frederick II, adds to its mythological validity. Furthermore there is a Mohammedan corsair named Barbarossa, for our Mohammedan friends.

The two largest moons, Frey and Freya, are named for brother and sister Teutonic Divinities. All three mythological entities are associated with peace.


Further reading. As I did it, I posted verbal synopses my work on Dr. Tom Van Flandern’s internet messageboard (for me, it served as a substitute for ArXiv.org, to which I am not allowed to contribute). Details and references will be found there which, from length or time constraints, I omit here. Beginning Jan. 21, 2007, I posted messages there about the physics directly leading to Barbarossa’s discovery, and then later about the discovery of Barbarossa. My earlier posts there are about more distantly related topics in physics and astronomy.

During the last six days, I have posted abridged messages about this discovery to several astronomy internet messageboards including but not limited to those of England’s Hanwell Observatory, NKIAC (one of my earlier posts had evoked a handwritten response from a member of the local Ames, Iowa, Astronomy Club), and the Association of Lunar and Planetary Observers’ Remote Planets group. None of those messages contain any relevant information that is not on Dr. Van Flandern’s messageboard.



Sincerely,
Joseph C. Keller, M. D. (B. A., cumlaude, Mathematics, Harvard University, 1977)

The five Objects span four degrees. Open clusters such as the Hyades and (some of the stars in) the Big Dipper, can be this big, but their proper motions tend to be radiant rather than unidirectional.

The Hipparcos probe showed that the sun's apparent apex motion is roughly the same, even when determined relative to stars farther than 300 parsecs (over 900 light years). At 100 light years and 90 degrees away from the apex, the average proper motion associated with apex motion, is roughly 100mas/yr; at 2000 light years (likely about the farthest distance of any of the five Objects, if they're stars) the motion is likely still roughly 5 mas/yr. At Leo, the direction of star proper motion bias due to presumed solar apex motion, is negative in both RA and Declination.

Yet 10 of 16 presumed proper motions (RA or Decl) of Objects #1-#8 (see Feb. 26 post below) were positive. Though star counts indicate that maybe none of the (now eight)"stars" would have been close enough for solar apex motion to be important, that bias could produce statistical significance.