Paradoxes Resolved, Origins Illuminated - Requiem for Relativity
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Joe Keller

USA
956 Posts

Posted - 16 Feb 2007 :  16:15:48  Show Profile  Reply with Quote
If this distant orbit is elliptical, its projection on the celestial sphere is nonetheless a great circle, so the extrapolated sky trajectory is the same except for rate of travel. The extrapolation is so small (2.4 degrees) that for an orbital eccentricity of 0.2, the rate of travel would vary at most 0.8% (causing, at most, an error the size of the rms error from rounding the epoch dates). Furthermore, the orbital period, as implied by the orbital resonances of J, S, U & N, is consistent with the present angular speed (1965.1-1976.1), if the orbit is nearly circular.

The dimmer of the two red magnitudes, for each of the four collinear objects I found in the USNO-B catalog, was +20.61, 20.26, 20.68, and 20.68. I plotted all 61 dim red magnitudes obtained when I searched the USNO-B catalog for all objects in the above seven disks, which had proper motions >80mas/yr in both directions (an indicator of bogus combination) and which also had one red magnitude < +18.99 and one > +19.50. Fifty-nine of the dim magnitudes were roughly evenly distributed between the 19.50 cutoff, and about 20.90. The occurrence of the eight pairs of precisely equal magnitudes conformed everywhere to the Poisson distribution. Two of the magnitudes were > 24 which, according to the documentation accompanying the catalog, usually denotes an invalid reading. One of these "invalid readings" occurred for one of the four collinear stars (p=0.125). One of the equal-magnitude pairs also occurred among them (p=0.09).

Furthermore the chance that four points from a uniform distribution of length 1.40, will span a range of 0.43 or less, is small. The chance that any three of the four will span a range of 0.08 or less, also is small. For four numbers chosen randomly in the unit interval, the mean sum of differences squared is one (by a four-dimensional integral). Scaling the observed magnitudes, above, to a unit interval, gives a sum of 0.245. The only a priori distinction of this group of four, from the other 57 high proper motion, discrepant red magnitude stars, in the searched region, is that they formed the straightest line of any four stars that I could find by eye on my handmade plot on Keuffel&Esser graph paper.
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Joe Keller

USA
956 Posts

Posted - 16 Feb 2007 :  22:18:19  Show Profile  Reply with Quote
I found another object resembling USNO-B catalog objects #2-#4 above:

Object #5. USNO-B 0830-0272239

I found it 4.9" from the extrapolated great circle, searching with overlapping disks, of sometimes 1' but usually 2' radius, so that the band halfwidth always was more than 50" and usually was almost 120", along the chord of the previously unsearched extrapolated (to the present time) portion of the great circle made by objects #2 & #3. This time I searched for either Red1 or Red2 magnitude between 20.54 & 20.75. Roughly 30 objects were found for which the other red magnitude was 19.xx, and comparably many such objects also were found searching randomly a fraction of a degree away.

Only two objects along this arc of the great circle, had the other red magnitude < 18.99. Of these, Object #5, had not only an R2 magnitude of +18.59, but also a large proper motion of the order of that given for Objects #1-#4. Its B2 magnitude was +23, hence "invalid", further accentuating that characteristic of these objects.

The epoch was given as 1974.5. Only one pair (#2 & #3) among the five objects has epochs consistent with other orbital period estimates. Maybe the epoch given, usually is determined by the midrange, not of plates showing the object, but of all plates covering that region of sky. The following post will argue that by considering brightness, even the #2 & #3 epochs must be rejected. It's likelier that the object is, as initially estimated, moving with the angular speed of a circular orbit of 355 AU radius, but has an elliptical orbit whose period is that of a circular orbit of radius 270 AU.


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Joe Keller

USA
956 Posts

Posted - 17 Feb 2007 :  17:56:37  Show Profile  Reply with Quote
I discovered and realized the existence of at least one moon, shortly after midnight UT, Friday, Feb. 16, 2007. The distribution of the "moon" magnitudes (not including the fifth "moon" found by searching for such magnitude) is 20.61, 20.26, 20.68, 20.68. This suggests that there is a large moon causing the 20.26 magnitude while a smaller moon causes the others. The closeness of the other three numbers makes an outlying measurement error, or varying albedo, unlikely. Eclipse would be too brief or too rare. My IBM 486 Monte Carlo trial indicated that the chance of any three such close points (sum of squared differences) in a set of four, from a uniform interval from 19.50 to 20.90, is about p=0.02; the closeness of the fourth point (one "Jupiter" & three "Saturn" sightings, but with "Saturn" closer to the "sun" than "Jupiter") reduces this to p=0.01.

The 20.30 Blue magnitude and 20.66 average Red magnitude of the smaller moon give B - R = -0.36. The USNO-B1.0 catalog gives B - R = -0.365 for Capella (a double star, G6 & G2, vs. the sun's G2). For reflection (generally weak in far blue) to achieve this B-R value using sunlight, it would likely appear bluish to the eye, which is sensitive mainly to near blue (maximum human retinal cone sensitivities are red 0.59 micron, green 0.55 micron, & blue 0.45 micron, according to the CRC Handbook of Chemistry & Physics, c. 1960).

The mass-radius relation for a giant planet or brown dwarf is very flat; due to electron degeneracy at high pressure, 0.019 solar mass would give about 10% less area than Jupiter (Burrows et al, Reviews of Modern Physics, 65:301+, 1993; graph reproduced in the above-cited book, "Protostars..."). An albedo of 5.7% (1/10 of Uranus, but close to average for a common kind of Kuiper belt object or asteroid) gives +18.1 magnitude at 360 AU.

I have five red, two blue and two infrared (0.75-1 micron band) magnitudes for the presumed larger body:

Object 1: R 17.41, B 19.80, I 18.78
2: R 18.17, B 18.95
3: R 18.57
4: R 18.03, I 18.36
5: R 18.59

These nine, average +18.07. The absence of any Red magnitudes between 18.60 & 18.99 is significant at roughly p=0.03, based on the distribution of fellow R values found in the above search of all objects whose smaller R value was near 20.6. The distribution of the magnitudes is most consistent with a large red spot covering almost one hemisphere of the large body, and a rotation period of between a day and a decade.

The spectrum, though red, is unusually flat. This suggests reflection instead of Planck curve emission. I searched USNO-B1.0 within a 20 degree radius centered at RA 11h10m Decl -7, for objects with both RA & Decl proper motions > 80mas (as before), R1 within 0.25 mag of the mean R for the presumed large body, and R2 within 0.25 mag of the mean R for the presumed "first moon" (using only Objects #1-4). Only 150 objects were brighter in both I & B; 1415 were dimmer in both I & B.

This flatness is not due to the averaging of four objects: a calculation based on galactic disk thickness at this galactic latitude, and textbook published main-sequence spectral type counts near the sun, implies that half the stars of the larger body's apparent magnitude, would be spectral class K5-K9, half class M, and all main-sequence. My IBM 486 Monte Carlo trial showed that a group of four equally bright stars with temperatures randomly differing over a +/- 10% range, perceived as one object, would have B-R & I-R, averaged over many groups of four, differing < 0.02 magnitude units from a single object at the population mean temperature. (This seems to grow quadratically with the range.) Furthermore, one side of the curve was raised and the other dropped almost the same amount, so what small effect there was, would mostly cancel, in the statistical test in the preceding paragraph.

In the USNO-B catalog, I checked the photometric values of Procyon (F5 IV-V) and Capella (I called it G6; it's G6 III + G2 III). From these, I interpolated by steps in spectral type, to obtain for the sun (G2 V), B - R = -0.46, I - R = +0.20, B - I = -0.66. For the presumed large body, these figures are +1.34, +0.53, +0.81, resp. This suggests sunlight reflected by a reddish object.

Galactic dimensions and main-sequence spectral type distribution, imply that almost all stars in the magnitude range, were Type K5 through late M (about half late K, & half M). For a mid-TypeK to late-TypeM star, B-R is large positive, but also I-R is large negative. Aldebaran (K5 III, somewhat variable) has B-R=+2.13, I-R=-0.85, B-I=+2.97. Gacrux (Gamma Crucis, in the Southern Cross)(Type M3.5 III, & variable like most Type M stars) has B-R=+2.16, I-R=-0.85, B-I=+3.00. If a dimmer second red magnitude for the object, implies that both B-R and I-R should be corrected downward, then I-R is less discrepant but B-R is even more discrepant.

The theoretical predicted surface temperature for this brown dwarf is 430K (interpolation or slight extrapolation, for 0.02 solar masses & 5 billion yr, in Table I, p. 316, Burrows, op. cit.; there was a log-log relation to age and a linear relation to mass). This might make it look more like Jupiter or Venus than like Pluto: its albedo would be too high. Maybe it cooled faster or burned less deuterium than theorized. Maybe it is less massive or accreted gradually.

Theoretically, "late M" dwarfs progressively show a blueward shift in their color temperature (Burrows, op. cit., Fig. 5, p. 309; quoting Allard, 1991). That is, according to Kirchhoff's law (Condon et al, Handbook of Physics, 2nd ed., p. 5-37, 1st partial par.) they emit & absorb blue better, and reflect red better. This trend might continue into brown dwarfs and giant planets. Also, common kinds of Kuiper belt bodies are reddish.

At 0.08 solar masses, one has a red dwarf (Burrows, op. cit.); not only does it begin to emit its own light, but the radius considerably increases. Even before that, one has a "hot" brown dwarf with self-produced IR magnitude. So, the distance can't be much more than 360 AU or the mass needed would be too great. A 440 AU distance likewise makes it too bright, even with the lowest likely albedo.

According to the 2003 AJ article giving information on the USNO-B catalog, it used almost 8000 plates; a plate sometimes included 5 million stars. For a billion stars, this implies that each small region of sky is included in < 40 plates.

Let a moon orbit Planet X; the moon's orbit might lie near the plane of Planet X's orbit around the sun. In a 6600 yr circular orbit, Planet X moves 196"/yr. That's 0.34 AU, at Planet X's orbital radius. Because Planet X has roughly the geometric mean of the sun's and Jupiter's masses, its main satellites might orbit at roughly the geometric mean of the distances, of the main satellites of the sun and Jupiter. A quarter of the time, a moon in a circular orbit, will be within 22.5 deg of its greatest elongation. For a 0.34 AU orbit, that is within 15". A 5deg orbital inclination for the moon, would cause typically only another 12" displacement perpendicular to the first. A somewhat larger orbit would be somewhat less efficient at placing the moon near 0.34 AU before or behind Planet X.

Generally, objects on the plates might be combined, if no more than 30" apart. Maybe half the time, the Red1 & Red2 plates were taken one year apart. Then, a quarter of the time, Planet X's moon would be positioned to impersonate Planet X on the plates. So, such a mysterious object would appear, in one of the 40 plates, 40/2/4 = 5 times. I found five objects in a thorough search of the USNO-B catalog.
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Joe Keller

USA
956 Posts

Posted - 19 Feb 2007 :  12:11:41  Show Profile  Reply with Quote
This new giant planet (or small star as the case may be) shall be named Barbarossa. Its largest moon shall be named Frey and its next-largest moon, Freya. The estimated diameter of Barbarossa is 83,000 miles; of Freya (sighted four times among the above five USNO-B catalog objects) and Frey (sighted once), 18,000 miles and 23,000 miles, respectively. The radius of Freya's orbit is about 1/2 AU and of Frey's orbit, 1 AU. Barbarossa rotates with a period of many days; it is mostly red on one side, dark gray on the other, with a visual albedo of about 6% on both sides. Frey and Freya resemble Neptune: blue, with albedos of 30%.
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Joe Keller

USA
956 Posts

Posted - 19 Feb 2007 :  18:42:35  Show Profile  Reply with Quote
If the proper motion were computed without regard to the dates of the plates on which an object actually appears, but rather the dates of all plates covering that region of sky, it still could be accurate for real stars. The planet and moon, appearing in one position on only one pair of plates a year apart, will have their proper motion underestimated by a factor of roughly (2000-1940)/2=30; that is, the typical 15"/3=5" separation will be reported as 5000/30=170mas/yr proper motion, typically 120 pmRA and 120 pmDec.

Suppose Barbarossa's moons, like Jupiter's moons, orbit in Barbarossa's equatorial plane. Let this plane be tilted 5 degrees from Barbarossa's orbital plane. Typically then we would see the moons describe ellipses tilted 3 degrees, implying 7" vertical error; the horizontal error was estimated at 5" in the previous paragraph. In absolute value, the mean putative PM in Decl then would be 1.4x the mean putative PM in RA; for the five objects, the observed ratio is 1.5.

It's likelier that the moon's orbit is slightly larger than optimal for mutual impersonation, than slightly smaller. So, usually the putative proper motion will be rearward, i.e., positive in RA (because there is reason to believe Barbarossa's orbit is retrograde, like the motion of the CMB dipole). Barbarossa's orbit line is inclined -26 degrees to the RA & Decl axes. The putative PMs would tend to be 5 units down and right along the orbit line, then perpendicularly 7 units up & right (if Barbarossa's equator is so inclined); indeed 4 of the 5 PM's (128,426; 274,394; 308,234; 302,142; but not -120,-502) lie in the first quadrant clustered about this point. The aberrant PM (Object #5) could be accidental; the moon's orbit isn't edge-on. Likewise a second moon accidentally could cause the PM of Object #2.

The earliest epoch of any object is given as 1965. This implies that the plates used for this region span about (2003-1965) x 2 = 76 yrs. The distance between Objects #5 & #4, corresponds theoretically to 69 years of orbit.

When I searched for Object #5, I extrapolated (westward only) one degree from Object #1 (using the line through Objects #2 & #3, because of Object #1's suspiciously different magnitudes). I narrowed the dim red search window 7-fold. There had been 61 candidate objects found in 4 sq degrees, so I expected only 61/4/7 = 2 per sq deg. Yet I found Object #5 within 5" of the predicted orbital great circle (p=0.006).

The RAs of the objects show periodicity analogous to the Saros eclipse cycle. Objects #5, #1 and #3 (all thought to represent the moon Freya) are on even minutes of RA. Object #2 (thought to represent the moon Frey) is near an odd minute of RA. Object #4 (representing Freya, with exactly the same magnitude as one of the other Freya sightings) is on a half minute of RA.

It's mere chance (1 in 3) that Frey's sighting occurred ten seconds away from a minute of RA (as measured from the Freya sightings to either side). The other four Object sightings (Freya) occur at intervals which are approximately multiples (1x, 3x, & 3x) of 115 seconds of RA; this corresponds to 9.8 years, considering the 26 degree slope of Barbarossa's orbital line. Freya displays "beats", because plates of the constellation Leo tend to be made at the same season, if not the same date.

If Barbarossa has period 4400 yr but present angular speed 2/3 of average, that's approximately 270*sqrt(1.5) = 330 AU. To give the gravitational effect I theorize on the CMB dipole, Barbarossa would be 0.016 solar masses. If Freya were in a circular orbit of 0.31 AU radius (just big enough to impersonate Barbarossa, next year or last year) Freya's year would be 1.36 Earth years. Really, Freya's orbit probably is slightly bigger. The period depends strongly (i.e., ^1.5) on radius. Freya might travel 0.5 *(1 + 1/9.8) orbits in one Earth yr., an orbit of 1.82 yrs., which, if circular, would have 0.37 AU radius, but which could have a radius only slightly more than 0.31 AU at greatest elongation on one side or the other, if moderately elliptical. Approximately every 9.8 yr, Freya would be roughly synchronized with Earth so that Freya is near maximum elongation when Leo is high in the night sky.
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Stoat

United Kingdom
964 Posts

Posted - 20 Feb 2007 :  04:47:27  Show Profile  Reply with Quote
And I thought i was being a bit controversial with the "planet stoat." Barbarossa, was a crusader, so that might raise a frown from Islam. Barbarossa was the code name of the Nazi invasion of Russsia, so I think you might be stepping on a few toes there as well.

What happens is that you would get the credit and the first suggestion as to what to call the thing but it will be decided by an international astronomy body. I think it will end up with a name from a mythology other than the Eurocentric.
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nemesis

84 Posts

Posted - 20 Feb 2007 :  12:42:57  Show Profile  Reply with Quote
Joe, how does this possible companion relate, if at all, to the work of Matese et al., who have proposed a companion of up to 5 Jupiter masses at about 8000 AU, or possibly a Neptune-sized body at around 2000 AU?
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Joe Keller

USA
956 Posts

Posted - 20 Feb 2007 :  13:33:19  Show Profile  Reply with Quote
quote:
Originally posted by Stoat

And I thought i was being a bit controversial with the "planet stoat." Barbarossa, was a crusader, so that might raise a frown from Islam. Barbarossa was the code name of the Nazi invasion of Russsia, so I think you might be stepping on a few toes there as well.

What happens is that you would get the credit and the first suggestion as to what to call the thing but it will be decided by an international astronomy body. I think it will end up with a name from a mythology other than the Eurocentric.



Response:

I, the lone and sole predicter and discoverer of the planet and its two largest moons, and my friends, will continue calling the planet Barbarossa, and the two largest moons, Frey and Freya. Those are the names already, and will continue to be the correct names, forever. If anyone ever calls them by any other names, he's incorrect.

- Joseph C. Keller, M. D. (Harvard class of 1977)
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Joe Keller

USA
956 Posts

Posted - 20 Feb 2007 :  13:36:40  Show Profile  Reply with Quote
quote:
Originally posted by nemesis

Joe, how does this possible companion relate, if at all, to the work of Matese et al., who have proposed a companion of up to 5 Jupiter masses at about 8000 AU, or possibly a Neptune-sized body at around 2000 AU?



Thanks for mentioning this interesting work. Of course, that is much farther and much less massive. Was there a search for those bodies?
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Joe Keller

USA
956 Posts

Posted - 20 Feb 2007 :  14:28:24  Show Profile  Reply with Quote
The statement at the top of USNO-B online catalog searches, says the plates are from the last 50yr. This round figure implies they might go back 55yr, or 60yr if the time was counted from the completion of a given survey project. The assumed angular speed implied a range of 69yr for Objects #1-5, but a 10% reduction in orbital radius would reduce this to 59yr.

I've now searched, in the USNO-B catalog with my original criteria, a region 7'-8' to either side of the track, from RA 11h3m to 11h31m. I found no additional objects near enough to the track and similar enough to those already found, to be candidates.
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nemesis

84 Posts

Posted - 20 Feb 2007 :  14:51:39  Show Profile  Reply with Quote
Joe, the paper by Matese, Whitmire, and Lissauer, from 2006, was theoretical and the companion was proposed to explain Sedna-type objects, but they say the object could be present but unrecognized in the IRAS and maybe the 2MASS data. Google "wide binary" with "Sedna" and the paper should come up.
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Joe Keller

USA
956 Posts

Posted - 20 Feb 2007 :  15:03:21  Show Profile  Reply with Quote
quote:
Originally posted by nemesis

Joe, the paper by Matese, Whitmire, and Lissauer, from 2006, was theoretical and the companion was proposed to explain Sedna-type objects, but they say the object could be present but unrecognized in the IRAS and maybe the 2MASS data. Google "wide binary" with "Sedna" and the paper should come up.



from the paper:

"...[RS]Gomes et al. [CeMDA](2005) discuss two resonant mechanisms for converting objects in the scattered disk into high-perihelion (q > 40 AU) scattered disk objects, but they find that they cannot produce these de-tached objects with a > 260 AU. ..."

*******

This correlates with the 270 AU distance, where the circular orbital period, is that implied by the giant planet orbital resonance discrepancies discussed above.
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Joe Keller

USA
956 Posts

Posted - 20 Feb 2007 :  20:52:26  Show Profile  Reply with Quote
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.
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Stoat

United Kingdom
964 Posts

Posted - 21 Feb 2007 :  03:26:54  Show Profile  Reply with Quote
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.
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nemesis

84 Posts

Posted - 21 Feb 2007 :  08:46:20  Show Profile  Reply with Quote
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.
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Joe Keller

USA
956 Posts

Posted - 21 Feb 2007 :  10:29:54  Show Profile  Reply with Quote
quote:
Originally posted by nemesis

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.



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.

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Joe Keller

USA
956 Posts

Posted - 21 Feb 2007 :  20:02:37  Show Profile  Reply with Quote
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 <+18.99 and the other Red magnitude >+19.50, and proper motions allegedly >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)
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Joe Keller

USA
956 Posts

Posted - 21 Feb 2007 :  21:53:07  Show Profile  Reply with Quote
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.
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Joe Keller

USA
956 Posts

Posted - 22 Feb 2007 :  17:27:13  Show Profile  Reply with Quote
The monotonic trend in Red magnitude of the four Freya sightings, has a correlation coefficient of 0.9275. For n=4, tables give p=0.01, two-tailed, for a correlation coefficient of 0.917; by extrapolation the Freya sightings have p=0.008. Freya has uniform albedo.

Barbarossa's semimajor axis, a = 270 A.U., is given precisely by the discrepancies in giant planet resonances (which give Barbarossa's period). To a good approximation for small eccentricity, the angular speed, when r=a, is independent of eccentricity. The distance estimate of 330 A.U., depends, on the accuracy of this approximation, and on the accuracy of the determination of present angular speed. The latter depends on the accuracy of the COBE & WMAP CMB dipole directions, and on the accuracy of my theoretical correction accounting for the gravity of the four known giant planets. Be all this as it may, 330 A.U. implies plausible albedo and mass for Barbarossa.

Computing Freya's distance from Earth, from Freya's magnitude, the best fit line gives an angle arctan(0.36) between Barbarossa's path and the constant circle. Graphical solution of the orbital equation gives eccentricity 0.36, and Barbarossa 60 degrees past aphelion. Aphelion is 420 A.U. and perihelion 200 A.U.

Takeda & Rasio (ArXiv.org, Oct. 10, 2005) state that the median orbital eccentricity for known extrasolar (giant) planets is 0.31, and the third quartile 0.43, but such planets would be much closer to their stars than is Barbarossa. A more appropriate comparison might be to 61CygniB whose eccentricity is 0.40 and period 650 yr.; the pair 61CygniAB has 4/3 the mass, of the pair sun+Barbarossa, but it is almost equally divided.

If my gravitational theory of the CMB is accurate, the 3-yr WMAP dipole temperature should be 33.6 microK warmer than the 4-yr COBE dipole temperature (25.0 microK from Barbarossa's approach and 8.6 microK from the overall improved alignment of J, S, U, and mainly N). It is 5 microK warmer, but the error bar for the difference is 29 microK.
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nemesis

84 Posts

Posted - 23 Feb 2007 :  08:48:02  Show Profile  Reply with Quote
Joe, I hate to ask what may seem a naive question, but when you say Barbarossa is "aliased by moons" exactly what does that mean?
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