Requiem for Relativity

Barbarossa Affects Planetary Axis Tilts?

Predicted geocentric J2000.0 celestial coordinates of the Barbarossa/Frey c.o.m.
for the 2012 solstice, 11:53 UT Dec. 21, 2012:

RA 11:28:44.38, Decl -9:29:19.4

same, heliocentric J2000.0 ecliptic coords.:

ecl. long. 176.36900 deg, ecl. lat. -11.80277 deg


From the 2009 Astronomical Almanac, I got the celestial coords. of the planets' rotation axes (from the 2006 IAU report), then used the free online conversion at www.lambda.gsfc.nasa.gov (tip: it requires decimal RA in hours, not degrees) to get ecliptic coords. The ecliptic longitudes of the planets' N poles are:

Mars 353 (approx. correction to planet's own orbital plane: 355)
Jupiter 248
Saturn 80 (corr. to planet's own orbital plane: 84)
Uranus 258 (corr. to planet's own plane, still 258)
Neptune 319 (corr. to planet's own plane: 316)
Pluto 317 (corr. to NEPTUNE's orbital plane: 317)

Neptune's & Pluto's axes have much different ecliptic latitudes, but the longitudes, if both are expressed in Neptune's orbital plane, differ only 1.0 degree. Maybe Pluto and Neptune were formed together, or at least were together, and therefore had the same spin axis. Torque on the planetary bulge (mainly from the moons, which are nonequatorial; but also considerable from the Sun at this time scale) should continuously change the longitude of the pole. Yet apparently the poles' longitude has changed exactly the same amount, possibly zero, since the planets Neptune & Pluto separated. Their spin seems stuck, and perhaps for this reason, the moons (Neptune's Triton & Nereid, and Pluto's Charon) are in wild orbits.

The big moons of Saturn & Uranus are almost exactly in their equatorial planes, but the Sun should cause these planets' spins to precess in 10^8 or 10^9 yr, resp. Saturn's autumnal equinox is only 2 deg less than Barbarossa's 2012 longitude; Uranus' vernal equinox only 8 deg less. Maybe Saturn & Uranus are stuck there. (If corrected to Jupiter's orbital plane, the longitude of Jupiter's small axis tilt seems unrelated to Barbarossa.)

Mars' spin precession period has been measured at 171,000 yr, near the Newtonian theoretical prediction. Trying to explain Mars' Ice Ages with Milankovitch cycles analogous to Earth's, Barlow, "Mars" (Cambridge, 2008), p. 197, cites calculations that Mars' obliquity (i.e. axis tilt) should range from almost 0, to > 80deg, 42deg most probable. These calculations must be faulty. Mars' present obliquity happens to be almost exactly the same as that of Earth, Saturn and Neptune, all ~25deg. If 42 is "most probable" for Mars, then surely various other numbers are "most probable" for Earth, Saturn and Neptune. So, why are all four, 26+/-3?

What if something happens to Mars too, when Barbarossa reaches its latus rectum? At this 2012 event (whatever that event turns out to be) Barbarossa is only 1deg from Mars' winter solstice. This is analogous to the event one Barbarossa period ago, in ~4300 BC, when Barbarossa was only ~1deg from Earth's summer solstice: the subsequent 6000 years were good for mankind on Earth. Maybe the next 6000 years will have favorable conditions on Mars.

Barbarossa's period, ~6340 yr, differs only 2%, from (1/4)x Earth's precession period, so for a long time, Barbarossa "events" will be at Earth solstices or equinoxes. Earth's Ice Melt period, extending from 10000 to 4000 BC (see my previous short post) started after a Barbarossa "event" when Barbarossa was near Earth's vernal equinox. At 171,000/4 = 43,000 yr ~ 6340*7 = 44,380 yr ago, Mars would have had a Barbarossa event when Barbarossa was near Mars' autumnal equinox.

Maybe this was Mars' last wet period. Kargel, "Mars: a Warmer Wetter Planet" (Springer, 2004), p. 361, says "...the crispest flow and sublimational forms [on Mars]...are probably < 100,000 yr old...".

Ice Age Cycles: Beats of Precession with Barbarossa Period

The Enc. Britannica "Geochronology" article, Macropaedia vol. 19, Fig. 41, p. 861, shows that the last three Ice Age clusters ended at intervals of ~115,000 yr apart, with a trend toward somewhat shorter intervals, for the last few before that (the downward slope's intersection with baseline, at the end of the Ice Age cycle, is most distinctive, so that's what I considered to define those intervals). Fig. 42, p. 863, shows an interval of ~130,000 yr between the last two Ice Age clusters, if one considers the distinctive upslopes of the upper two charts.

Hays, Science 194:1121+, 1976, found four dominant sinusoidal periods in his analysis of Ice Age temperature & isotope data from the last 468,000 yr. These periods are 100,000 yr (50% of variance), 42,000 yr (25% of variance), 23,000 yr (10% of variance), and 19,000 yr. The ~23,000 yr cycle was the first discovered by geologists and has been assumed to be related to Earth's (at present) 25,800 yr precession cycle. Cycles in astronomical parameters (Milankovitch cycles) have been claimed to have the same periods Hays found, though the small amplitude of Earth's astronomical cycles is problematic.

I find today that all four of Hays' periods, are generated by Earth's precession period interacting with Barbarossa's orbital period. I note that Barbarossa's period, 6340 yr by my calculation, is almost 1/4 * Earth's precession period. Let x be Barbarossa's frequency in cycles per millenium, and y Earth's precession frequency. At present, Barbarossa when at its outgoing latus rectum, is always near an Earth solstice or equinox point on the ecliptic. Due to the slight difference between x and 4*y, a beat frequency arises: call the beat frequency z = x - 4*y. The time between these synchronizations, of Barbarossa's outgoing latus rectum (or any other fixed point on its orbit) with Earth's solstices & equinoxes, is 1/z = approx. 100,000 yr.

Thus the main Ice Age periodicity seems to be due to the beat (probably the interaction mechanism is not merely gravitational) of Barbarossa's orbit with Earth's precession. The second harmonic of this process, 2*z, also is likely large, because the process is periodic but not necessarily a pure sinusoid. Let's guess that the other frequencies arise from the product of this beat wave or its second harmonic, with the sine wave describing Earth's precession. One of the harmonics resulting from such a product, is y - 2*z = approx. 1/72 millenia; this harmonic is not mentioned by Hays. Likewise the pure second harmonic 2*z = approx. 1/50 millenia, is not mentioned by Hays. The other harmonics are:

y + z = 1/23
y - z = 1/42
y+ 2*z = 1/19
and the original equation z = 1/100

According to my estimate of Barbarossa's orbit, x = 1/6.34. Given this x, all of the four equations, which, if satisfied, give the periods that Hays observed in Ice Age data, are approximately true with the same value of y. For the four equations, the implied values of 1/y are

27.08, 26.63, 26.26, 27.54 millenia (vs. Newcomb's precession period, 25.785 millenia).

The square root of the variance of these five values (including Newcomb's)(defining variance as: sum of squared deviations, divided by 5) divided by their mean, is 5.1%. Here I have statistical evidence from period analysis, that Barbarossa interacts with Earth's precession and climate. This adds to the likelihood of Barbarossa's reality, and adds to the importance of upcoming special points on Barbarossa's orbit.

Let's find the value of Barbarossa's period, for which the four equations above, for the observed harmonics found by Hays in Ice Age data, give precession periods most consistent with each other and with Newcomb's (for our purpose, Newcomb's value, 25785 yr, will turn out to be practically the same as very current values such as 25771.5). The simplest way, is to choose Barbarossa's period so that the five (including Newcomb's) implied precession frequencies, "y", minimize sqrt(variance) / mean. That period is 6210 yr; it slightly improves the fit, to 4.6%, from the 5.1% implied by my orbital program's period, 6340 yr.

Perhaps the most valid way, is to weight each "y" proportionally to the frequency of its corresponding sinusoid (dividing the observation interval, 500,000 yr, by the sinusoid's period) and also proportionally to the variance in the data explained by that sinusoid, according to Hays (I roughly estimate this as 5% for the 19,000 yr sinusoid). The "y" determined by higher frequency components, effectively samples more values of the precession frequency during the 500,000 yr data set (Hays calls his interval of observation 500,000 yr in the title, 450,000 yr in the conclusion and 468,000 yr in the text). The "y" determined by a component explaining twice as much variance, essentially reflects twice as many data. Both weighting factors are reasonable, they are independent, and both can be applied. Newcomb's value amounts to one sample of the frequency but, in a sense, explaining all variance at that one time; so this value gets a weight factor of 1*1=1.

Weighting both the mean and the sum-of-squared-deviations formulas appropriately, the best fitting Barbarossa period is 6284 yr, if Newcomb's precession 25785 is used, and 6282 yr, if the very modern precession value 25771.5 is used. These are remarkably close to Scaliger's presumed Hermetic value: 6294 yr.

If I assume the observation interval 468,000 yr instead of 500,000, then the very modern precession value 25771.5, gives 6273 yr. If I then change the variance due to the 19,000 year period, to 2.5% (a better guess, I think) instead of 5%, I get 6267 yr.

I can further accurize this by estimating the precession rate that would correspond to the theoretical all-time mean obliquity, 23.497deg according to the 41,000yr sinusoidal formula (Wikipedia; citing Wittman, Astronomy & Astrophysics 73:129-131, 1979). Newcomb's obliquity was 23.452deg, in good agreement with the modern time-dependence polynomial, and the modern obliquity is 23.439. If +0.013deg of obliquity change is associated with 13.5yr longer precession period, then the all-time mean obliquity might be associated with precession period 25771.5 + 0.058/0.013*13.5 = 25831.7yr. This gives a best fitting solar orbital period, for Barbarossa, of 6278yr.

Let us recall that Pope Gregory's calendar reform was, by my estimate of Barbarossa's perihelion, 13yr past perihelion. (Gregory became Pope in 1672 and began his calendar reform initiative right away.) Thus Scaliger's choice of JD 6294yr for 1582AD, makes JD0 occur only 6294-13-6278 = 3 years before Barbarossa's perihelion, if I use the orbital period inferred from climatological data.

(Continued March 23, 2009)

The six periods above, would come from the function

(a + b*sin(2*pi*y*t+phi1)) * (c*sin(2*pi*z*t+phi2)
+ d*sin(2*(2*pi*z*t+phi2)))

where a, b, c, d and phi1, phi2 are unknown coefficients and phases. This is a sinusoid in Earth's precession period, multiplied by a second order Fourier series for a symmetrical periodic function of the angle between Barbarossa's perihelion and the preceding solstice or equinox.

The other two frequencies above, 1/72 & 1/50, which don't appear in Hays' article, do appear in other articles. The standard text, Muller & MacDonald, "Ice Ages & Astronomical Causes" (Springer, 2000), has Sec. 8.12 entitled "The 'Unexplained' 70kyr Peak". Deep sea cores from 20-25 Myr ago (Science 292:274+, 2001, Fig. 2A, p. 276) show these periods of statistical significance p<5% for at least one of the isotopes 13-C or 18-O:

406Kyr, 125, 95, 54, 41, 23, 20, 19.

The 54 is close to the 50 predicted by my model above but not found by Hays. If y=1/25.8 and z = x-4*y = 1/110, then my model, if extended to the fourth order Fourier series, predicts a frequency of y-4*z = 1/417, matching the 406Kyr period. Both the 19 and 20Kyr periods might arise from the y-2*z term, if z, which is a sensitive function of y, changed during the 5Myr interval.

Still needing explanation, is the split of the 100Kyr term into 95 & 125. Also needing explanation is the sudden reappearance of the ~100Kyr period, at ~1Myr BP (Science 277:215+, 1997). Both the split and the intermittence are explained if the constant term "a" in my formula above, is replaced by the augmented term

a*sin(2*pi*u*t+phi3)

where u=1/792Kyr is Barbarossa's presumed spin precession period. This splits the 100Kyr (or rather 110Kyr) period into 95 & 125 Kyr periods, and splits the 55Kyr second harmonic into 51&59 ~ 54. The ~100Kyr periods appear or not, depending on whether Barbarossa is precessing or not. Thus because of some unknown physical interaction, Barbarossa's and Earth's spins appear symmetrically in the first factor of my augmented formula.

[Update March 28, 2009: In an early Icarus article, Oepik rightly complained that it's hard to know whether the match is significant, when a theory like Milankovitch's generates several periods. On the other hand, in making my case I should show every match. The Greenland GISP2 ice cores (Stuiver, Quaternary Research 48:259+, 1997; p. 264) show a 1470yr 18-O cycle approximately corroborated by other studies, and ~10x bigger before the Holocene, than now; using the precession period (25831.7yr) corresponding to the mean obliquity during the 41,000yr Milankovitch cycle, and my presumed Barbarossa anomalistic year (6341.5yr) in the notation above, y+2*(x+4*y)=1/1506yr, matching 1470. (When the frequencies x and 4*y interfere, the beat frequency is x-4*y and the carrier frequency is x+4*y.) Also, y+(x+4*y) & y-2*(x+4*y) are 1/2847 & 1/1705yr, resp., roughly matching the period of Dansgaard-Oeschger events, 2000-3000yr (Bond & Lotti, Science 267:1005+, 1995). If it makes a difference, whether some special timed point on Barbarossa's orbit, is aligned with an Earth solstice or with an equinox, then there should be the period y+(x-2*y)=1/8405yr; this matches the period of Heinrich events, 7000-10000yr (Lott & Bondi). ]

Presumably Barbarossa has a nearby moon, Freya, of ~0.0001 solar mass, at ~0.1 AU. If Barbarossa were just like Earth, Freya would cause Barbarossa's spin to precess in 26Kyr*3.2(Sun causes 1/3.2 of Earth's precession)/0.0001 * 0.1^3 = 800Kyr. The main moon, Frey, has been observed on four sky surveys; its orbit is eccentric, e = 0.6 (and the c.o.m. implies it has 0.0002 solar mass). Likely Freya is eccentric too. Its inclination would vary (Kozai phenomenon) conserving its Tisserand parameter. The Tisserand parameter involves semimajor axis, eccentricity and inclination. The semimajor axis is conserved to second order (progressively conjectured and proved by Lagrange, Poisson & Tisserand) but e and i teeter erratically between big eccentricity with small inclination, and vice versa. When i is small, Barbarossa doesn't precess.

Barbarossa may well be Earth size, but its mass is ~3600x more. If it spins with 60x the frequency, it has the same shape as Earth because 60^2=3600. It would have 60x more angular momentum per unit mass then, so Freya would need to be 60x more massive, or 4x closer (4^3=64) or some of each. If Barbarossa bulges 8% (similar to Jupiter, 6%, or Saturn, 10%) instead of 1/300 like Earth, it needs to spin yet sqrt(8/(1/3))=5x faster (P=24*60/60/5 = 5 min) but, with 25x the bulge, Freya can be 25/5 = 5x less massive (e.g. 0.0012 solar mass at 0.1 AU).

Using Paul Wesson's constancy of J/M^2, an Earth-size Barbarossa with the same "J0" (mass profile) as Jupiter would need to spin with 1000x the frequency, i.e. P=10hr/1000=36sec, which is far beyond any stability limit. Barbarossa, like the Sun, must have given most of its angular momentum to its satellites.

Barbarossa is like the Sun's binary pulsar. Taylor's 1995 pulsar catalog shows that 39/45 binaries have e<0.3 but 6/45 have 0.6<e<0.9, so Barbarossa conforms in eccentricity.

Worley's 1983 visual binary catalog (N=933) shows that (lumping all spectral types) the eccentricity histogram doesn't drop off much until e>0.65 (Barbarossa = 0.61 for its solar orbit, and ~0.6 for its binary orbit with Frey). Aitken, "The Binary Stars", gives for double stars with Type G primaries (N=54) ave. e=0.52, ave. P=84yr. Worley's catalog lists only two double stars with Type G primary and Type M (the closest I can come) secondary: these have e=0.78, P=693yr, and e=0.90, P=2205yr.

(email sent 19:01h UT March 20, 2009)

To: Vice President Albert Gore (ret.), Scheduling Requests, info@carthagegroup.com

cc: editor, "Atlantis Rising"; also posted to messageboard, www.metaresearch.org (Dr. Tom Van Flandern, founder); & interested members of Lowell family

Re: Scheduling Request

Dear sirs:

I wish to schedule one or two of Mr. Gore's scientific advisors to come to my house to visit with me about global warming. In two years of research, I have discovered that imminent climate change will be even more drastic, than the projected change of which Mr. Gore has warned with such dedication.

My recent letter about my discovery was rejected immediately by about a dozen relevant scientific journals, with neither peer review nor any reason. The exception was the editor of "Icarus", who complained that my letter was too short, but was unwilling to correspond further; I supposed he was "giving me the runaround".

A friend warned me not to "lead with my credentials", but otherwise you likely will not read further. I was graduated from Harvard College, B. A., c. l. in (pure) Mathematics, 1977. Recently I worked part-time for a year under an NSF grant, doing the math and Fortran programming for a graduate/faculty Engineering group at Iowa State Univ., whose leader got a statewide award for that project. I mention these achievements only to make it plausible that I might make the discovery of which I am about to tell you:

In 2007 I discovered Percival Lowell's "Planet X".

[ It is perhaps the size of Earth, but there is much indirect evidence that it is very cold, partly "gravitationally collapsed", with about 10x Jupiter's mass. Its orbit is moderately eccentric but never comes near Earth, and is now slightly beyond 200 A. U., slightly south of the constellation Leo. A novel astrophysical theory of mine, had localized this object, Barbarossa, to within a few degrees, so I was able to search the online photographic sky survey plates until I found Barbarossa (named from the prologue to a novel by Berry Fleming) on all four of the red and "optical infrared" band plates. I found fewer than 100 starlike candidate objects in my searching, so it's unlikely that these four would chance to lie so perfectly on an orbit.

[ I find Barbarossa on none of the four relevant blue band sky surveys. In the prospective astrophotographs I have persuaded amateurs and institutions to take (none with telescopes bigger than 17 inch) the longest, clearest exposures with the biggest of these telescopes, show Barbarossa at about the right extrapolated coordinates, but too faint to convince mainstream astronomers, who perhaps expect too much of small telescopes with CCD cameras and data-wasting "stacking" image processing. Details are posted on Dr. Van Flandern's messageboard under my name, Joe Keller.

[ According to current astrophysics, Barbarossa should have practically no direct effect on Earth, but might influence comets. Barbarossa might influence Earth through a new, non-gravitational force, such as the unknown force which causes millisecond pulsar decelerations (as observed from Earth) to cluster near the value of the Hubble parameter. ]

This month, I discovered that Barbarossa's perihelia almost coincide with the promulgation of the Gregorian Calendar, and before that, with "Julian Day Zero". In the 16th century AD, scholars such as Pope Gregory XIII, Christoph Clavius and Joseph Scaliger pursued ancient "Hermetic knowledge". An estimated 90% of Hellenic literature was lost with the fall of Classical civilization. Also one might, like Giordano Bruno, be burned at the stake for saying too much. It seems that nonsensical "cover stories" were provided, both for the urgency of Gregorian calendar reform, and for the choice of JD 0.

The Mayan "long count" calendar begins in almost the same year as Egyptian dynastic chronology. A physically significant point on Barbarossa's orbit will occur within a few days of the Dec. 21, 2012 end of the "13th pik", i. e. "long count" cycle, said on Monument 6 at Tortuguero to be the "descent" of "Bolon".

Ice Age and warming cycles (Hays, Science 194:1121+) have been attributed to low-amplitude astronomical "Milankovitch cycles" of similar periodicities, but incalculable positive-feedback mechanisms must be supposed to account for the magnitude of the Ice Age changes. Alternatively, the Milankovitch cycles themselves might be effects, not causes. This week I found that the "beat" between Barbarossa's orbital period, and Earth's precession quarter-period, or the second harmonic of the beat, when multiplied by a sinusoid in Earth's precession period, yields six frequencies, four of which are the same as the four climate change frequencies found by Hays.

My sky survey "Barbarossa" identifications imply Barbarossa's orbital period is about 6340 yr. The presumed "Hermetic knowledge" placed into the calendar by Pope Gregory XIII and by Joseph Scaliger, as obvious clues, implies a period of 6294 yr. The best simple fit to Hays' climatological periods, occurs for a Barbarossa period of 6320 yr.

Sincerely,
Joseph C. Keller, M. D.

Surprising Accuracy of the Periods

My computer program uses the four sky survey detections to find 6340.0yr for the solar orbital period of the Barbarossa system's c.o.m. The ultimate accuracy limit of this approach, is ~0.5" / 0.1 radian * 6000yr = 2mos.

Another approach is to accept Brauer et al's German lakebed chronology (which the popular press reported in 2008, had been refined to, exactly 12679yr prior to 2008AD) for the sudden onset of the Younger Dryas; and to accept the 2012 Mayan calendar date as "Hermetic knowledge" because, according to remaining historical records, not until 16th century AD Europe (or possibly 12th century AD India which, I deduce from the Wikipedia article, possessed an accurization of the Hellenic measurement of equinox precession) was the tropical year well enough quantified, to admit a calendar which reliably ends 1500 years later on a solstice. In this approach, the disaster interval is (12679+(2012-2008))/2 = 6341.5yr.

A third approach is to accept my computer program's latest Barbarossa perihelion, 1569AD (which should be more accurate, than the program's value, of the period); and to accept as Hermetic knowledge, Joseph Scaliger's placement of JD 0, 6281yr prior to that perihelion, as though secretly basing the astronomical calendar on Barbarossa, much as the Gregorian calendar reform had moved Earth's perihelion to near New Year's. In this approach, Scaliger's 6281yr period is corroborated by climate time series analysis, which in my best effort (see above) gives a period of 6278yr.

These approaches can be reconciled:

1. Keller's sky survey/computer fit period, 6340yr, is Barbarossa's sidereal year.

2. The German "Younger Dryas" / Mayan calendar period, 6341.5yr, is Barbarossa's anomalistic year.

This amounts to perihelion advance of 5 arcmin / period. Adapting the apse precession formula of the last section of Roxburgh, Icarus 3:92+, 1964, I find that a second Barbarossa of comparable mass and major axis to the first, would give the 1/r^4 time-average gravitational force term needed for this. Two Barbarossas would restore the (3::1)::(2::1)::(1::1) outer solar system precession ratio (see above) and if opposite, might cancel the Sun's acceleration in interstellar space vis-a-vis pulsars.

3. The Scaliger / Buoncompagni period, presumed 16th cent. AD Hermetic knowledge, accurized at its latter terminus to Keller's (sky survey based) perihelion date, is Barbarossa's tropical year, 6281yr. It is corroborated within 3yr, by climate time series period analysis.

Time series analysis (see above) suggests that much of the time, Barbarossa's (variable) precession period is 790Kyr. A sidereal period of 6340yr becomes a mean tropical period of 6281yr, when the precession period is 680Kyr; slower precession suffices if the tropical period is with respect to an equinox or solstice on the farther portion of Barbarossa's orbit.

A brightening of Barbarossa, like a cataclysmic variable, at a certain season of Barbarossa's year, would have let ancient astronomers know its tropical year w.r.t. that season. Barbarossa's orbital radius at that season, would change little during civilized history, because of Barbarossa's ~700Kyr precession period. This tropical year would become Hermetic knowledge which somehow influenced Scaliger to set JD 0 appropriately.

On the other hand, drastic Earth climate change seems to correlate with Barbarossa's precise orbital position at some point not far from the outgoing latus rectum. The interval between occurrences of this position, is Barbarossa's anomalistic year.

(March 25, 2009)

On March 6, 2009, the same philanthropist who arranged the February 16 photo, arranged another photo with the same telescope. The March 6 photo is 50 stacked 30sec ( = 25min) clear filter exposures, apparently in quick succession; anyway the start was 05:08 UT & midpoint 05:22:30.

I looked for Frey at the linear extrapolation of Frey's positions on the philanthropist's (midpoint 05:16) 2/16 photo (200+ min, red filter, >16 inch aperture) and Genebriera's ~01h 2/23 photo (20 min, red filter, 16 inch aperture, Tenerife)(see coords. above). The predicted Frey position is

11:26:45.0, -9:18:36

Indeed an object is detected at

11:26:44.7, -9:18:30 pixel coord. (112, 415)

The discrepancy is about the net error of the linear extrapolation (which includes Frey's binary orbital motion).

This photo lacks built-in coordinates but does have built-in pixel "counts". When I use the "histogram equalizer" in the "fv" viewer, the higher the "count" the brighter the pixel, within a given small area. I chose the brightest 3x3 pixel array which contained the brightest pixel in the area (I don't know the "seeing" for this photo, but the U. of Iowa in S. Arizona typically has 2.5" Full Width Half Maximum on a clear night). I compared these 9 pixels to the surrounding 16 pixels with Student's "t" test for unequal variance (Dixon & Massey, Intro. to Statistical Analysis, 2nd ed., Sec. 9-3, bottom half of p. 121 continuing onto p. 122; Table A-5, p. 384. Snedecor, Statistical Methods, 5th ed., Table 2.7.1, p. 46). The t value was 2.6, 23 degrees of freedom; p<1%, 1-tailed.

I used the brightest pixel as the definitive position. I divided the 24 micron pixel size by the focal length, to get the angular pixel size of 1.7", then counted pixels from a nearby reference star on the sky survey. Mainly because the photo is somewhat rotated, over a long oblique distance the error from this sometimes was almost 20%, so for Frey I used a reference star only (30,16) pixels away, i.e, error < 10". For Frey, I used a correction factor to lessen even this small error, by testing true vs. pixel, EW & NS distance, over a long distance in roughly that direction on the photo; for Barbarossa (see below) I skipped this last step because its reference star was only (5,12) pixels away.

The Barbarossa that I found on this photo, is ~1' NW of its predicted position, retrograde along the orbital path. (The 1997 sky survey Barbarossa also was ~1' retrograde of predicted, based on only the 1954 & 1986 positions, according to Kepler's 2nd law.) The predicted c.o.m. position according to my newest program (posted above) is

11:26:24.0, -9:14:32

Frey's position and the 50:1 mass ratio let me predict Barbarossa itself at

11:26:23.6, -9:14:27

The best Barbarossa candidate is found at

11:26:19.8, -9:13:48 pixel coord. (291, 210)

This is 68" retrograde along a 35deg slope (Barbarossa's orbital slope is 30deg). The same t test procedure as for Frey, gives t=5.4, 23 d.o.f.; p<0.05%, 1-tailed, for the significance of the detection.

A catalog star near Barbarossa, had R2 mag +19.33, and was unusually faint (yet B2 mag 20.16, much brighter than I estimate for Barbarossa or Frey, however) on the 1983 Blue sky survey, for a star this bright on the 1987 Red sky survey. On a clear filter CCD photo, such a star might not appear much brighter than Barbarossa or Frey. Its t test, using the procedure above, was 6.5 with 23 d.o.f.

The Barbarossa on this photo is inconsistent with those detected on Riley's March 29, 2007 photo; the philanthropist's Feb. 16, 2009; or the U. of Iowa Feb. 23, 2009. All three of these older detections are consistent with each other, and about 1' S of my latest predictions for their dates.

Update March 26:

The large plutino, Orcus, has been called the "anti-Pluto" because of its similar size and similar, but roughly diametrically opposed, orbit. There might be an "anti-Barbarossa" or second Barbarossa, as I discuss above.

All three recent Frey detections - the philanthropist's 2/16/09 & 3/6 photos, and Genebriera's 2/23 photo - show a light distribution sloped several arcsec NE-SW. I hope to find the statistical axes of these three distributions (corrected for the slight rotation of the photos) to show that they must be the same object. My latest estimate of the Barbarossa::Frey mass ratio, is 0.9791::0.0209. So Frey would have ~0.0002 solar mass, about the same as Saturn's 0.0003.

Saturn's rings (typically chunks of water ice) are said to be not only much brighter, but also fundamentally different qualitatively from the rings of the other giant planets. Frey, like Saturn, might have just the right mass to have such rings.

(email just sent today, March 26, 2009)

To: Prof. Mike Brown, Cal Tech

Dear Prof. Brown:
I challenge you to a public debate! I've discovered Lowell's "Planet X", which I have named Barbarossa. Would you be willing to take the other side, that there is no such planet?

Dr. Neil Tyson already has turned down my offer of debate. I hardly can ask Dr. Phil Plait because I've been censored from his messageboard.

Sincerely,
Joseph C. Keller