Requiem for Relativity

The following is an edited transcript of the workshop held in the Physics and Astronomy Building at The University of Western Ontario on Monday, November 25, 2002, from 1:00 to 5:00 pm.

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IM  My name is Ian McDiarmid. ÉI was more or less pushed into [space research] by Don Rose, who was doing cosmic ray research at NRC. Don arrived there in 1948 and I joined him as a PDF in 1954. Walter Heikkila at DRTE knew Don was interested in cosmic rays, and he was planning a couple of Aerobee rockets to be flown from Fort Churchill. In 1958 he came and talked to Don and myself and he offered us some space in the nosecones, to do some cosmic ray work. Don was really keen, because he was interested in rockets and of course he was interested in cosmic rays, he'd like to measure them above the atmosphere. I was doing high-energy particle physics at the timeÉ

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GS  He worked in photogrammetry, and he found these streaks in photographic plates taken from aircraft.

IM  Really? I'd never heard that. É

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[Ian McDiarmid] And they probably weren't streaks from cosmic rays at all, they were probably something else [laughter]. Because it would be very hard to get cosmic ray streaks in ordinary photographic plates at that altitude. É

Roland, Iowa March 16, 2007


Open letter to the Director of the Lowell Observatory

Dear Sir:

Like Prof. Lowell, I studied Mathematics at Harvard College (B. A., cumlaude, Mathematics, 1977). The essential details of my recent work on Prof. Lowell's Planet X are posted, to Dr. Tom Van Flandern's " www.metaresearch.org " messageboard, under the name, "Joe Keller", in the thread "Requiem for Relativity". (I use Dr. Van Flandern's messageboard as an alternative to "ArXiv.org".)

Planet X, which I have named Barbarossa, appears at

RA 11h 18m 03.2s Decl -7deg 58' 46" on the La Silla sky survey Red plate SERC.ER.DSS2.713 dated January 31, 1987. Possibly there is a second appearance of Barbarossa at

RA 11h 14m 36.0s -7deg 32' 17.5" on the Blue plate SERC.J.DSS1.713 dated May 8, 1983.

Assuming a circular orbit and making first order approximations to correct for Earth parallax, Barbarossa has period 2640 yr. and is 191 AU from the sun. Accordingly, the resonances of the orbital periods of the outer planets have discrepancies which advance prograde with periods

Jupiter:Saturn 5:2 2780 yr
Saturn:Neptune 6:1 2180 yr
Jupiter:Uranus 7:1 -5970 = -2985 * 2 yr (retrograde)
Uranus:Neptune 2:1 4380 = 2190 * 2 yr
Saturn:Uranus 3:1 1190 = 2380 / 2 yr.

I discovered Barbarossa on February 15, 2007 as a sequence of statistical artifacts in the USNO-B1.0 catalog. I informed the U. S. Naval Observatory on February 21.

I first saw the La Silla Red image of Barbarossa on March 4, and realized on March 5 that it is Barbarossa. By comparison with the four nearest cataloged stars, Barbarossa's Red magnitude is about +17.3. A 6% Red albedo would imply 46,000 mi diameter. Barbarossa might be either a giant planet or a cold brown dwarf.

I realized yesterday, March 15, that the above La Silla Blue image is Barbarossa, which is dim in Blue. The pattern seen on this Univ. of Strasbourg "Aladin" image depends on one's monitor setting. At its best, it shows Barbarossa as a lean-to adjoining a nearby star with a separate USNO-B catalog number. It shows a moon of Barbarossa's (I've named the largest & next-largest moons, Frey & Freya) as a disjoint dark pixel 3" toward azimuth 245. From my drawing of the best image obtained (Prof. Lowell drew lines on Mars; I draw pixel boxes), I estimate this moon to be 1.7 magnitudes dimmer than Barbarossa.

The Red La Silla image shows no disjoint moon, nor any star near enough to confuse. Thorough computer search found the best fit for three points of light, was to have a moon 1.2 magnitudes dimmer than Barbarossa, 2.5" away at azimuth 275; and another moon 1.6 magnitudes dimmer 2" away at azimuth 75. Thus the Barbarossa system consistently appears parallel to the ecliptic. Furthermore the best fit for one point of light, lay outside the darkest pixel box, indicating either multiple sources or quickly varying magnitude. As a gravitationally bound body subject to Poincare instability, Barbarossa hardly can rotate appreciably during these 1 hr exposures.

In 2002 at a Physics and Astronomy conference, cosmic ray expert Ian McDiarmid disparaged the statement that cosmic rays would be readily detected by ordinary photographic materials onboard airplanes [let alone at 7800 ft at La Silla]. A Kuiper Belt Object would leave a streak of this length, but even then, the magnitude would suggest another Pluto or Sedna.

By great-circle extrapolation, with a rough correction for Earth parallax, Barbarossa's March 10, 2007 position is

RA 11h 27m 10s Decl -9deg 18' 58".

Alternatively, my statistically-derived greatest-likelihood great circle, estimates the Declination at this RA as

Decl -9deg 05' 46" (for RA 11h 27m 10s)

The greatest-likelihood great circle goes through this point with slope -7.35 arcminutes Decl per minute of RA.

Sincerely,
Joseph C. Keller, M. D.

Barbarossa and "the Triad"

Obtaining more recent estimates of the orbital periods of Jupiter and Saturn, I found that the discrepancy in the 5:2 resonance, progresses one cycle in 2696 yr. This is practically equal to the approximate 2643 yr period calculated above for Barbarossa, from its sightings as Object #7 & Object #3, assuming a circular orbit. Barbarossa shepherds one point of the Triad (equilateral triangle) formed by the three recurring conjunctions of Jupiter and Saturn around the ecliptic.

On April 17.5, 1981, such a conjunction occurred at 187.15deg heliocentric ecliptic longitude. (If the alternate criterion, closest three-dimensional approach, is used, this becomes 186.65.) By extrapolating the Barbarossa positions associated with Object #7 and Object #3, I found that Barbarossa was at heliocentric ecliptic longitude 172.5 then.

The difference, 187.15-172.5=14.65deg (14.15deg by the alternate criterion), is explained by the orbital eccentricities of Jupiter and Saturn. Roughly, Jupiter is 180deg from perihelion & Saturn 90deg from it. A somewhat more precise first-order calculation shows Saturn a net 8.0deg ahead of Jupiter, when a "mean Saturn" and "mean Jupiter" reach heliocentric ecliptic longitude 172.5. Jupiter has extra catching-up to do.

On the average, with 5:2 resonance, this would occur over 5/3 of the catch-up angle, but Jupiter also is about 9% slow here, Saturn 1% fast, and Jupiter's average speed really is 0.7% too low for 5:2 resonance anyway. So, Jupiter needs 14.3deg to catch up.

Averaging Jupiter & Saturn (their ascending nodes and orbital inclinations are similar), gives 1.9deg inclination to the ecliptic, with ascending node at 107deg ecliptic longitude. Therefore Jupiter's & Saturn's tracks are nearly parallel to the ecliptic here. Barbarossa's projection onto this Jupiter-Saturn average ecliptic, would change the above 14.65, to 14.85. (The difference between true Jupiter-Saturn conjunction, and mere equality of ecliptic longitude, is negligible in either ecliptic system.)

So, Barbarossa's position, extrapolated from its sightings as Object #7 and Object #3, is only 0.55 deg (or 0.05deg by the alternate criterion) west of a mean shepherd position for the 5:2 Jupiter:Saturn resonance. Because there are three such positions, p=0.55*2/(360/3)=0.009 (p=0.0009 for the alternate criterion). More precise calculations might enhance this agreement.

According to Jewitt et al, "...Varuna", Nature, a canonical albedo for Kuiper Belt Objects is 0.04 [also the albedo of small comet nuclei, and the darkest albedo known for solar system bodies - JK]. This albedo would give Barbarossa a diameter of 57,000 mi.

According to Hainaut et al, Astronomy & Astrophysics 389:641+ (graph), Mars has Blue-Red magnitude = 2.2; Varuna is typical of the reddish type of Kuiper Belt Object, with B-R = 1.6. The only one of the Object #1-#8 catalog magnitudes of Barbarossa, which equals its photographic Red magnitude on the SERC Red plate for Object #3 (+17.3 by comparison with neighboring stars), is the catalog magnitude of Object #1, +17.4. The catalog Blue magnitude of Object #1 is +19.8, for B-R = 2.4.

On the SERC Blue plate for Object #7, two catalog numbers (USNO-B 0824-0279078 & USNO-B 0824-0279077) are given, seemingly for Barbarossa and for a star 2" away, resp. The two objects barely can be separated by looking at pixels. With catalog Red magnitude +17.8 and Blue +19.6, the star, USNO-B ...-77, resembles the "true" Barbarossa's magnitude. Barbarossa, USNO-B ...-78, resembles the typical catalog Barbarossa magnitudes for Objects #1-8.

Barbarossa & Nemesis: wheels within wheels?

Above, I show how to calculate that the presumed sightings of Barbarossa follow the mean position of one of the three resonance points of Jupiter & Saturn. According to what seem to be the most accurate available periods for Jupiter and Saturn (11.6821 & 29.458 yr, resp.), this resonance point recurs after 91.0092 ( = 2*45 + 1 + 0.0092) revolutions of Saturn (2680.95 yr)(p=0.009).

Maybe just as Barbarossa shepherds the third resonance of Jupiter & Saturn, Nemesis shepherds the 45th resonance of Barbarossa with that third resonance. In this Pythagorean astronomy, the period of Nemesis would be 2680.95/0.0092 = 290,000 yr. If more accurate periods were known for Jupiter & Saturn, this might become the 26 million yr speculated for Nemesis.