Requiem for Relativity

Hi Dr Joe, You are saying the calculated mass is ~28 Jupiter mass-right? In my studies(as nutty as yours no doubt) I have become a mass that big would radiate lots of infrared and since you say no IR is observed at the calculated location on anywhere nearby would that indicate the model is wrong? I don't know if your calculations are right but I assume they are for this exercise.

Barbarossa's Aphelion Direction is Within a Fraction of a Degree of the Galactic Center

I found these disappearing "Barbarossa" dots on the sky surveys three years ago, then calculated (by a best fit method using a computer program) a precise solar orbit for them one year ago. I noticed two days ago, that the aphelion coincides with the galactic center. I couldn't have planned this, and it hardly can be chance.

I returned to my notes from a year ago, and used the numbers there to find Barbarossa's remaining orbital elements, i.e. the ascending node and longitude of perihelion, as accurately as possible (three years ago I estimated the ascending node as 288, a year ago re-estimated that as 293, but never had tried an accurate calculation).

(A year ago, I assumed that Barbarossa has 0.01 solar mass. A new reduced-mass correction assuming 0.028 solar mass, would change the aphelion position only slightly. In effect, the Sun's gravity would become stronger. For a given r and dr/dt fitting the observations, Barbarossa would reach aphelion about 1.8% sooner, but would have, near aphelion, about 1.8/2=0.9% smaller distance, so by conservation of angular momentum would have 1.8% greater angular speed; thus the longitude of aphelion happens to be about the same.)

Assuming 0.01 solar mass:

a=343.84 AU (semimajor axis)
e=0.610596 (eccentricity)
i=12.93 (inclination)
Omega=290.84 (ascending node)
omega tilde = 86.46 (longitude of perihelion)

The true anomaly (i.e. angle theta along the orbit from perihelion) at 12h GMT Dec. 21, 2012, is 91.018deg.

The J2000.0 ecliptic coords of Barbarossa's aphelion are:
(266.46, -5.41)

The ecliptic coords of the galactic center, as defined by the origin of modern galactic coords, are, according to F. Walter's course webpage at astro.sunysb.edu, and NASA's online "Lambda" coordinate conversion service:
(266.13, -5.54) (per F. Walter)
(266.84, -5.54) (per NASA online converter)

The ecliptic coords of Sagittarius A* (A-star), according to Wikipedia, are:
(266.85, -5.61)

Proxima Centauri's major axis also aligns with the galactic center. Simulations by Wertheimer & Laughlin, Astronomical Journal 132:1995+, 2006, imply a 45% probability that Proxima Centauri is gravitationally bound to (i.e., in closed orbit around) Alpha Centauri AB. These authors explain that if P. Cen is bound, it probably is near apastron in a very eccentric orbit (near the limit of Hill stability vis a vis galactic tide). So, P. Cen's position approximates its major axis.

According to the coordinates and parallaxes in Wertheimer's Table 1, the vector from P. Cen, to Alpha Cen AB, has celestial coordinates (242, -21). Within the 2-sigma error of the parallaxes, I can move the vector a few degrees closer to the galactic center. I recall that this vector is not the major axis, but probably is a fair approximation of it.

More about the alignment of Proxima Centauri with the galactic center

I slightly changed three of the Proxima Centauri data in Table 1 of the Wertheimer & Laughlin article (AJ, 2006):

1. Following Segransan et al, A&A 397:L5+, 2003, I adopt 0.123 +/- 0.006 solar masses for P. Cen, instead of Wertheimer's (from a 1999 source) 0.107 +/- 0.0214. Apparently 0.123 is implied by Morel's stellar model, and this model has been corroborated by new, more accurate stellar radii measurements (Morel et al, A&ASupp 124:597,1997; Thevenin et al, A&A 392:L9,2002; Kervella & Thevenin, ESO release,2003).

2. I adopt the Hubble telescope value (AJ 118:1086+, 1999) of 768.7 +/- 0.3 mas, for P. Cen's parallax, instead of Wertheimer's (1997 Hipparcos) 772.33 +/- 2.42.

3. I made a weighted average of Wertheimer's (2004 private communication source) P. Cen RV of -21.8 +/- 0.2 km/sec, and the value -22.4 +/- 0.5 given in A&A 460:695+, 2006. My result is -21.88 +/- 0.33.

All three of the new values above, also are the ones given by Wikipedia. I changed none of Wertheimer's Alpha Cen AB data (based on the 1997 Hipparcos catalog and on Pourbaix et al, 2002), because I found nothing convincingly better.

These data imply that P. Cen has positive energy, i.e. is unbound. The consensus of recent astronomy journal articles, is that P. Cen is so close to Alpha Cen, that it almost certainly is part of the same physical system, not a random interloper, and yet that P. Cen's orbit probably is hyperboloidal, carrying it away in ~10^6 yr. This contradiction disappears, if the Alpha Cen system has dark mass, far enough from the primaries, that its effect on the AB orbit is negligible.

The error in P. Cen's relative velocity is much greater than the error in its relative position. The velocity (of P. Cen relative to Alpha Cen AB's center of mass) uncertainty, in absolute terms, in the skyplane is almost as big as that radially, apparently because of uncertainty in the Hipparcos catalog's proper motion of Alpha Cen B. The 1-sigma uncertainty in the relative velocity vector is roughly 30%. The relative velocity vector is almost perpendicular to the relative position line. The orbital plane, of P. Cen about the primaries, misses the galactic center by 19.5deg, but this is within the usually accepted error.

I added hypothetical mass near Alpha Cen AB, to give P. Cen negative total energy and a closed orbit. At least a 37% increase in the total system mass is needed. For this smallest possible mass, the axis of P. Cen's (parabolic) orbit, is toward celestial coords (249, -16). For very large mass, P. Cen would have to be at its apastron, therefore the axis is the same as the separation vector, namely (242, -21).

For intermediate masses, the calculated eccentricity decreases from 1, to a minimum of 0.054, then increases again to 1. Assuming that the actual gravitating mass is twice the mass of the three stars, then P. Cen's e=0.378 and it is now 11deg retrograde of periastron. Assuming four times the mass, then e=0.317 and it is now 7deg prograde of apastron. The eccentricity minimum occurs, at near three times the visible mass.

If P. Cen's e > 0.35, or the total mass (visible + dark) is < 2x or > 4x the system's visible mass, then P. Cen's position is within about 10deg of its major axis, therefore the major axis is within about 30deg of the galactic center.

Detecting an "Ummo" hoax

The "Ummo" letter, alleged to be an extraterrestrial communication dating from 1965 or according to some authors maybe as late as 1969, says that Wolf 424 is 3.68502 light year from the Sun as of Jan. 4, 1955. This seems to be grossly incorrect, but, given access to the astronomical literature of 1971 or later, and a slight misunderstanding of terminology, it would have been a good guess to say either that Wolf 424 is 3.68502 parsec distant, or that it is 13.68502 light year distant.

The 13.68502 light year figure, nearly equals the smallest, and arguably the most authoritative (at least, done with the biggest telescope, and by the most famous parallax specialist) estimate, extant in 1965, of the distance to Wolf 424. The 3.68502 parsec figure, nearly equals the smallest estimate that it would be possible to make, by mistakenly applying the Pythagorean formula to published parallax estimates in two different directions, extant by 1971. The "Ummo" letter could be emended to either 3.68502 parsec, or 13.68502 light year, thereby agreeing with either, of what the author of that letter thought, were the two smallest estimates of the distance to Wolf 424.

If it had happened that the smallest estimate (van Maanen, 1944) of the distance to Wolf 424 were correct, then the "Ummo" letter could have been emended to 13.68502 lt yr, very near van Maanen's 13.6467 lt yr. If it had happened that 271.0609 mas were correct (the misinterpretation of Kerridge's 1971 figures) then Ummo could have been emended to 3.68502 pc, very near 1/271.0609 = 3.6892 pc. The midpoint of Kerridge's data, is 1954.4, so Ummo gives the very next date of Earth perihelion, Jan. 4, 1955, as the epoch.

Nearly complete list of the most accurate estimates of parallax of Wolf 424, published before 1955:

239 mas (my error estimate, +/- 21), van Maanen, Astrophysical Journal 100:55+, 1944, Contributions from the Mt. Wilson Observatory #692, "19th series" (no error bars given, but these 16 exposures with the Hale 100 inch telescope usually would give sqrt(12/16) the error of 12 similar observations; see below)

213 +/- 24, van Maanen, PASP 51:358, 1939 ("preliminary" parallax, 12 exposures; with 60 or 100 inch telescope?)

213 +/- 17, van Maanen, Astronomical Journal 50:41, 1942 (also 12 exposures; maybe a statistical reworking of the 1939 PASP report, apparently both are cited as one, by van M. as "17th series" in the 1944 ApJ article above)

217 +/- 10, Reuyl, PASP 53:336, 1941 (McCormack telescope; earliest relevant observations with this telescope were 1925-1926)

220 +/- 30; preliminary McCormack telescope result quoted by van Maanen in his 1939 PASP article

206 +/- 10 (combined by me, from quoted RA 140 +/- 40 & Decl 210 +/- 10 figures for preliminary Sproul telescope result quoted by van M. in his 1939 PASP article)


Partial list published after 1955:

227.9 +/- 4.6, Altena, 1995; value adopted by Torres et al, AJ 117:562+, 1999

233.5 +/- 0.9; Altena's value modified by me according to Torres' stellar model; according to my calculation today, this is the value implied by Torres' Fig. 5, which shows that both of Wolf424AB are too red and 0.25 +/- approx 0.04 mag (2*3=6 values with +/-0.1mag scatter) too faint in IJK; using W = M^3.8, this implies 97.6% of the assumed distance, 1/227.9mas, if I accept Torres' a^3/P^2 value.

233 +/- 4; value adopted by Heintz in his 1989 article, according to Torres (see above)

205 +/- 11, Kerridge et al, AJ 76:77+, p. 79, 1971 (44 plates 1938.4 - 1970.4; combined by the original authors, from pi x = 207 +/- 11 & pi y = 175 +/- 37; #74, at the top of the list)(mistaken application of Pythagorean formula gives pi = 271 mas)

233 +/- 6, Lippincott, AJ 63:314+, p. 322, last par., 1958 ( >100 plates with 24 inch Sproul refractor)

223 (Lippincott mentions this as the 1958 Yale catalog value)

To: Patrick Gross, ufologie.com, France

Dear Sir:

I liked your article on the Ummo hoax. I found additional evidence, exposing the hoax. The Jan. 4, 1955 epoch of the alleged distance to Ummo, is approximately the epoch of a parallax determination of Wolf 424's distance, published in 1971 by Kerridge et al. Wolf 424 was at the top of the page of its part of this study, so it would be hard to miss. The astronomers published two separate parallax determinations side by side. If the Ummoists combined these mistakenly by the Pythagorean theorem, the result would be 3.6892 parsec, close to the Ummoists' 3.68502 ("light year") figure.

More information and evidence about the parallax of Wolf 424, is posted under my name, "Joe Keller" on the messageboard of the late Dr. Tom Van Flandern, at www.metaresearch.org .

I am a cumlaude graduate of Harvard, B. A. in Mathematics. Three years ago, on online sky surveys, I discovered a planet (it is on all three relevant Red photographic surveys and on the only relevant Optical Infrared photographic survey) at approx. 200 AU on a great circle orbit. A year ago, I determined the orbit. It has eccentricity 0.61, major axis 344 AU, orbital period 6340yr, mass 0.02 +/- 0.01 solar, magnitude on sky surveys (Red or Optical IR) ~ +19. Its major axis lies within less than a degree of the galactic center, and its latus rectum lies within a few degrees of the cosmic microwave background dipole.

For three years, my unpaid part-time job has been to try to persuade the establishment to investigate this adequately (such as, by looking at this place in the sky). I can and have refuted all the usual dismissals. Maybe someday someone will write a book analyzing the psychology and sociology of the establishment's failure. This is typical: when I wrote (by paper mail) to dozens of U. S. Congressmen, who sit on relevant committees, only one responded. The response was a postcard saying, "We can't help you, because you are not from our district."

Much more information about this has been posted by me to Dr. Van Flandern's messageboard. My development of Prof. Eduard Meyer's "Sothic dating" idea, has revealed that a heliacal rising of Arcturus occurred on "1 Thoth" at Elephantine Island at 4329 or 4328 BC, and in the same year, both Arcturus and Canopus rose heliacally at Giza (30N) on the summer solstice. Therefore the Egyptian calendar likely began, Dec. 2012AD minus June 4328BC = 6339.5 yr before the end of the Mayan "Long Count". This is the orbital period of the planet I discovered.

The Mayan "Long Count" was cleverly expressed as a convenient multiplication of days, so that it would be used and remembered, but its deep import is as an astronomical resonance (for example, it is a multiple of the orbital period of Uranus).

Sincerely,
Joseph C. Keller, M. D.

Barbarossa system mass = 0.010026 +/- 0.000290 solar

The orbit I fit to the sky survey positions, assuming exactly 0.01 solar mass, implies orbital period 6339.93 Julian yr +/- about 0.1% (see recent discussion of error, above). During the last year, I've considered not only the Egyptian/Mayan calendar, but also various solar system resonances. These considerations imply that Barbarossa's period is closer to 6339.362 Julian yr (figure determined by consideration of resonance with hypothetical proto-Jupiter).

At the epoch of observation, r = a/1.6 for Barbarossa. According to the reduced mass formula in mechanics, a 1% decrease in Barbarossa's mass, has the same effect on its heliocentric orbit, as a 1% increase in "k", which would increase the magnitude of the potential energy at the epoch of observation, by 1%, and the difference in magnitude, potential - kinetic = 1.6 - 1.1 = 0.5, by 1.6/0.5 = 3%. So "a" decreases 3-1 = 2%, and P, which varies according to a^1.5/k^0.5, decreases by 3+0.5 = 3.5%.

So, if Barbarossa's true period is 6339.362yr, and my orbit is perfectly accurate, then the Barbarossa system's mass must be 0.01 + 1*(6339.93/6339.362)^(1/3.5) = 0.010026. My round figure guess for Barbarossa's mass, has turned out to be in error by only one part in 400. The uncertainty in orbital details, which is equivalent to 0.1% uncertainty in period, also must be equivalent, to 0.1/3.5 = .029% solar mass, uncertainty in mass (one part in 35).

Recently (see above) I rechecked my calculation that the torque of all the other planets on Neptune (per degree of inclination), is 3x the torque of Barbarossa on Neptune, assuming that Barbarossa has either a circular orbit at 198 AU with 0.0107 solar mass, or else eccentricity 0.6106 & a=343.8 with 0.0280 solar mass. (Substituting plutinos, or classical KBOs, for Neptune, gives 2x, or 1x, resp.) Without knowing anything about Barbarossa, I can say that for a distant object of any mass, in any orbit, if its torque (per degree of inclination) on the classical Kuiper Belt is to the torque of the planets on the classical Kuiper Belt, in the ratio X::1, then its torques (per degree inclination) on the plutinos and on Neptune, will be to the torques of the planets on them, in the ratios X::2 and X:, resp.

If X=1, then Barbarossa's mass, estimated from this "precession resonance", is almost three times too great. On the other hand, if 1/X = "e" = 1 + 1 + 1/2 + 1/6 + 1/24 +... = 2.718..., then Barbarossa's mass is 0.01030.