Paradoxes Resolved, Origins Illuminated - Requiem for Relativity
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Joe Keller

USA
957 Posts

Posted - 21 Jul 2007 :  19:01:27  Show Profile  Reply with Quote
Suggestion for small-telescope observation:

The eleven stars which, it seems from my above review of the literature, might be in, or might recently have entered, or might recently have exited, Maunder minimum, are:

HD 3651 (54 Pisces)
HD 10700 (Tau Ceti)
HD 12051
HD 43587
HD 56972
HD 57901
HD 140538 (Psi Serpentis Aa)
HD 164922
HD 179699
HD 221354
HD 233641.

Some of these are visible with the naked eye, under good conditions; all of them are visible with binoculars, under good conditions. All are sunlike, G or "early K" spectral type. All are "dwarf" stars (i.e., on the "main sequence"). According to my theory, four of these stars lie near an envelope, where that envelope is tangent to our line of sight:

HD 43587
HD 57901
HD 221354
HD 233641.

Generally, I expect the envelope to be tangent to our line of sight when we look in one of these three directions:

Cassiopeia A
66.63deg away from Cassiopeia A
90deg away from Cassiopeia A.

My suggestion is to look for anything at all unusual about the appearance (e.g., magnitude, color) or apparent location (angular distance from nearby stars) of these eleven stars, with special attention to the four stars theoretically near the envelope. Also one might observe any and all stars near the envelope (i.e., near Cas A or near the two circles around it, at ~66.63 and ~90deg).

This program is ideal year-round for northern hemisphere amateur astronomers with small telescopes. All these stars are included in robust professional observing programs (Mt. Wilson, Lowell and/or Phoenix projects) but observations are only intermittent. Transient nonatmospheric phenomena, involving either the stars themselves or the intervening space, could be missed.
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Joe Keller

USA
957 Posts

Posted - 25 Jul 2007 :  22:55:13  Show Profile  Reply with Quote
Rho Cassiopeiae and NGC 7789 both lie 1/2 or 2/3 of the way from us to Cassiopeia A, within 5 deg of the line to Cas A. Several different indirect estimates have been made of all these distances; probably rho Cas is farther than NGC 7789. Cas A, rho Cas, NGC 7789 and ourselves are almost collinear.

Rho Cas is the nearest yellow (type recently given as G2Ia0e, but varies from F8Ia, probably its normal status, to K and sometimes even M) hypergiant star; as of 1999 only 12 hypergiants of whatever color were known in our galaxy (ApJ 523:L145, 1999). Usually, roughly every 50 years (1893?, 1946, 1986, 2000) rho Cas seems to eject a shell of gas, causing its apparent surface to dim and cool, with typically -25 km/s (blue)shifted emission lines (not absorption lines as with ordinary photospheric pulsations - PASP 98:914 & 99:272), complete with molecular TiO bands (Sargent, ApJ 134:142, 1961; Beardsley, ApJSupp 5:381, 1961; Lobel et al, ApJ 583:923, 2003). It also varies with sometimes a 300 day and sometimes an 800 day period, but only by 0.2 or 0.3 mag (A&A 325:714, 1997; PASP 112:363, 2000, Fig. 1).

The approximate dates on which rho Cas reached major magnitude bottoms are:

December 1893, 0.6 mag drop (Beardsley, op. cit., Table 2, p. 500)
July 1946, 1.3 mag drop (Beardsley, op. cit.)
March 1986, 0.4 mag drop (Lobel, op. cit., Fig. 13)
September 2000, 0.8 mag drop (Ibid.)

(The last three bottoms were accompanied by spectral changes consistent with an ejected shell; such data might exist for the first bottom also.)

The dates of eruption of Cas A are:

August 1680 (Flamsteed records 6th mag star)(likely peak, +2, likely in April)
1667 (Dreschhoff & Laird, ice cores 1 mo. after Tarumi volcano; so far I haven't found the date, of this volcanic eruption in Japan)

If the 1680 Cas A eruption initialized a 53.4 yr cycle, the 1893 minimum would be four cycles later; the next cycle lengths (to 1946 & 2000) would be 52.6 & 54.2, which average to 53.4. If the 1667 supraluminal early event, initialized a 40 yr cycle, 1986 would be eight cycles later; the two cycles could coincide in 1946, giving a summed effect, and the observed longer bottom. (There was an Astronomische Nachricten article in 1934, available to me only by interlibrary loan or photocopy service, which would reveal whether the 40-yr cycle manifested in 1906.)

Nova 1592C (FR Stephenson, Quarterly Journal of the Royal Astronomical Society London 12:10-38, 1971, Sec. 4, pp. 21, 34) was noted in Korean annals, stationary near beta Cas (Caph) from Nov. 30, 1592 until March 4, 1593. Probably the nova had peak mag +2 or +3, as it "escaped the vigilance of...the West, ...[and of] the Chinese & Japanese..." (Stephenson, op. cit.). Probably Cas A is too far from Caph (Stephenson, op. cit.) but the nova might have been a flareup of rho Cas, only 2.5deg away from Caph. No other easily visible star is nearer to Caph than is rho Cas; this might be the meaning of the oft-used oriental description translated as "within" the reference star. Such a flareup of rho Cas happened in Nov. 1950, though only 0.6 mag (Beardsley, op. cit.).

Burnham, vol. 1, p. 495, says, "Trigonometric parallaxes have been measured [with the large refractors] at Allegheny, McCormick, & Mt. Wilson, and agree in giving a distance of about 200 lt yrs [ = 16mas][to rho Cas]." Allegheny parallaxes c. 1950 (resp. c. 1920) had probable errors of 4.9 (resp. 8.6) mas (AJ 55:185). A McCormick parallax for rho Cas was 8+/-6 mas (AJ 62:276, 1957). Not only the absolute magnitude as estimated from the spectrum, but also the small Hipparcos parallax (0.3+/-0.6 mas), the small proper motion (near zero after correction for galactic rotation), the large radial velocity (Oort's law) and the distances of objects in the presumably equidistant "Cas IV association", suggest a true distance 35x larger than Burnham's parallax figure, or 17x larger than the 1957 McCormick parallax figure: namely, 7000 lt yr. (ApJ 134:142). With a 200 lt yr distance, the detour from Cas A to rho Cas to us is negligible, but a 2kpc distance foils the rho Cas cycle convergences at 1680 & 1667.

Increasing the interstellar speed of light about 270x, rescues the cycle convergence for rho Cas. It also harmonizes the cycles of P Cygni (34 Cygni) and eta Carinae.

Using typical recent distance estimates, P Cygni is the peak of an isosceles triangle. The base angle is 30deg, the sides are 2kpc and the base is 3.4kpc. The other vertices are the sun & Cas A. Extending the base 2.3kpc beyond the sun, reaches eta Carinae. The extra lightpath for P Cygni is 2*2*(sec(30) - 1) = 0.62 kpc. The extra lightpath for eta Car is 2*2.3 = 4.6kpc, 7.4 times more than for P Cyg. The actual observed delays are 56 yr & 7.7 yr (56/7.7=7.3) for eta Car & P Cyg, resp. The ratio is as expected but it is as if the interstellar speed of light is 270x (maybe 137*2; the "fine structure constant" is 1/137) times greater.

Eta Car's outburst peaked 1843 = 1680 + 2*53.4 + 56. If the 53.4 & 40 yr cycles, seen with rho Cas, are initialized in 1680 & 1667, resp., for eta Car also, then their 1843 coincidence (2 & 3 cycles, resp.) would make an unusually big event, analogous to the 1946 event for rho Cas. Because eta Car & P Cyg are "luminous blue variables" (i.e., blue hypergiants) whereas rho Cas is a yellow hypergiant, the former have an outburst where the latter has a dimming. Indeed P Cyg (type B2Ia) is an "S Doradus variable" having blueshifted absorption lines, not blueshifted emission lines as does rho Cas. At 270x lightspeed, the 2.3kpc roundtrip to eta Car requires only 56 yr.

P Cygni suddenly reached +3, then was discovered by Blaeu on August 18, 1600 (Israelian & DeGroot, Space Science Reviews 90:493, 1999). Presumably under the influence of an earlier initialization by Cas A, rho Cas (Nova 1592C) had burst out 7.7 yrs earlier and was discovered in Korea. P Cygni reappeared in 1654, 54 yrs later: the same cycle length as rho Cas.

Cas A also might somehow affect the location of the "blue stragglers", the main-sequence blue stars found within clusters of much yellower stars. NGC 7789 usually is called an open cluster though some call it a transitional object between open and globular cluster; its color-magnitude array resembles that of a globular cluster (MNRAS 114:583). It includes a delta Scuti variable (A&A 366:178) and probably a Mira variable, WY Cas (PASP 72:48).

NGC 7789 is "very rich in blue stragglers", still counted as ~25 in 1995 (A&A 366:490). Already in 1980 (McNamara, 92:682, 1980; Fig. 3, p. 686) 29 were plotted. On the average, the blue stragglers are displaced a few arcminutes toward Cas A. The positional angle of the center of the blue stragglers, relative to the center of the cluster, is 50+/-10deg depending on the weighting used. The position angle of Cas A relative to the cluster center is 53deg.

Blue straggler catalogs of the other, smaller, open clusters near Cas A (NGC 7380, 7419, 7510, 7654=M52, and the overlapping 7788 & 7790) seem to be absent from the literature. "In general, the blue stragglers show a remarkable degree of central concentration [i.e., they tend to be well within the cluster]." (A&ASuppl, 109:375, 1995, Abstract). Blue stragglers have spectral type late B or early A (A&A 366:490, 2001). One could follow the precedent of professional astronomers, who identified stars appearing to be within the cluster and which had "B minus V" magnitude typical of spectral types bluer ("earlier") than about A5. Then those not having proper motion (or radial velocity or light polarization) typical of the cluster would be eliminated, because presumably they are accidentally superposed on the cluster.
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Joe Keller

USA
957 Posts

Posted - 29 Jul 2007 :  17:34:01  Show Profile  Reply with Quote
Luminous blue variable (hypergiant) HD 160529 (V905 Sco)(assigned spectral types range from B8 to A4 Iae, sometimes even to F0)(Stahl et al, ArXiv.org 20 Dec 2002)(Sterken et al, A&A 247:383, 1991)(also online article by AW Fullerton & F Najarro) erupted in 1992 with a blueshifted ejected shell and a magnitude peak (Gaeng, Leitherer et al, display #80.02, 1995 - see internet). Maybe this is analogous to the rho Cassiopeiae eruption of 1946. The 1992-1946=46 yr delay is due to a signal traveling the extra distance from Cas A to V905 Sco & thence to us. For eta Carinae, 2*2.3kpc apparently caused a 56 yr delay (see above). The galactic longitudes of V905 Sco & Cas A are about 0 & 110, resp., so the law of cosines gives 2.4kpc for the distance from us to V905 Sco. Stahl (op. cit.) adopts Sterken's (op. cit., p. 390) estimate of 2.5kpc; Stahl notes upper and lower bounds of 1.9 & 3.5kpc.

In Huygens' construction for light propagation, let the small wavelet circles be 1/137 the radius of the large wavefront circle, or in general 1/137 the radius of curvature, R, of the wavefront. Let r = R/137. If photons move perpendicular to the wavefront, they advance by a distance r. If photons move tangent to the wavefront, they advance by sqrt(R^2+r^2)-R, which is smaller by a factor 2*137=274. The latter might be the usual speed of light; and the former, the faster signal which operates in interstellar space.

The seemingly fairly accurate ground-based parallax of rho Cas, cited by Burnham (see above) is 35x (maybe 17x) too large. The difference between ground- and space-based parallax might be due to different modes of light propagation in matter & vacuum.
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Joe Keller

USA
957 Posts

Posted - 29 Jul 2007 :  20:48:39  Show Profile  Reply with Quote
I found another star with, like rho Cas, Yale parallax catalog ground-based parallax ~20mas with error 8mas, yet Hipparcos parallax much less. This star is Antares. For Betelgeuse the two catalogs are in good agreement. Yet for rho Cas & Antares, the Hipparcos parallaxes are 70x and 4x less, resp., both more than two standard errors lower.

Through Strasbourg's "VizieR", I searched the (ground-based) Yale parallax catalog (4th ed., 1995)(9000 stars) for stars with visual mag < 6.00, 15 < ground-based parallax < 30mas, and given error "sigma" of ground-based parallax < 10.6mas. Then I considered 2 or 2.5 sigma difference from Hipparcos parallax (also requiring Hipparcos parallax < 7.5mas as a labor-saving screen). For convenience I considered only the 375 (3/4 of the Yale stars) for which Bayer or Flamsteed designations were given.

The expected number with Hipparcos, 2.5 sigma or more, less than Yale, is a little less than 375*0.6% = 2.2. Instead I found 4 stars:

rho Cas
55 Cam
beta Sct
36 Aql

The 7.5mas Hipparcos cutoff is about two sigma less than Yale, for the median Yale parallax (21.7mas) and Yale error (7.3mas) of the nine stars eventually found (see below). So here in the tail of the bell curve, almost half of stars for which Hipparcos is 2 sigma or more less than Yale, would have Hipparcos parallax >7.5mas and be excluded. Thus here the expected number of stars with Hipparcos 2 sigma or more less than Yale, is a little more than 375*2.3%*0.5 = 4.3. Instead I found 9:

rho Cas
55 Cam
theta UMi
nu1 Boo
52 Ori
beta Sct
36 Aql
alpha Sco (Antares)
chi Sco

Their positions correlate with the positions of the five SN remant - like radio/X-ray nebulae:

Sgr A
Cas A
M1 (Crab nebula)
Tycho's supernova
Kepler's supernova

Five of the nine stars are within about 15deg of one of these nebulae. Rho Cas has the most extreme parallax discrepancy (2.8 sigma) and is closest of the nine stars, to any of these nebulae (Cas A is 4.3 deg away); 55 Cam has the third most extreme parallax discrepancy (2.5 sigma) and is second closest (~20deg) to Cas A. Also 55 Cas and chi Sco are about 10deg from Tycho's SN and Sgr A, resp.; 52 Ori and Antares are about 15deg from M1 and Sgr A, resp.

Because stars with parallax 4.7mas (median Hipparcos value for the nine above) are 695 lt yr away, comparable to the galactic disk "scale height in the solar neighborhood" of 800 lt yr (ApJ 596:204, 2003), Hipparcos stars with <7.5mas parallax are almost twice as likely as random, to lie within 10 deg of the galactic equator. Even so, the binomial test for 5 or more of 9 stars to lie within 15deg of one of the five nebulae, gives p < 0.5% (the 15deg radius disks for Tycho's SN and for Cas A considerably overlap).

Summarizing this thesis so far: Huygens' construction, together with the ubiquity of the fine structure constant, suggests an alternative lightspeed of 274*c. This lightspeed synchronizes almost all hypergiant star eruptions in this quadrant of the galaxy, on a 53.4 yr cycle initialized by Flamsteed's supernova (Cas A). The "blue stragglers" of Caroline Herschel's cluster NGC 7789 are displaced toward the line of sight to Cas A. Discrepancies between ground- and space-based parallaxes occur for giant stars near lines of sight to SN-like nebulae, especially Cas A. Also, the distribution of sunlike Maunder minimum candidate stars, is consistent with a lightspeed, or slightly greater than lightspeed, initiating signal from Cas A. In particular, the sun's two Maunder minima (c. 1500 & c. 1680) correspond to the two main recent reverse calculations of Cas A's explosion date(s).
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Joe Keller

USA
957 Posts

Posted - 06 Aug 2007 :  17:21:49  Show Profile  Reply with Quote
Thesis: the Milky Way (and other large spiral galaxies, including Andromeda) aren't breaking up other spiral galaxies; they're building additional spiral galaxies, which at first are sparse, though often large in extent. These new spirals are at large angles to the parent galaxy, but their nuclei often lie near the plane of the parent. By forming such additional spirals, spiral galaxies eventually become elliptical galaxies.

Cassiopeia A is the main satellite galactic nucleus in this quadrant. Matter flows from Cassiopeia A and forms open clusters. This flow is almost along geometric lines. Once deposited, the open clusters limit the distance of subsequent flows along these lines. Multiple clusters along the same flow line usually aren't obvious because distances are uncertain and they lie near the galactic plane.

Double clusters might offer evidence for this thesis. If NGC 884 were slightly older, slightly farther from the galactic plane, and slightly nearer to us, all of which it might really be because none of those determinations are very accurate (position must be corrected for differential proper motion since formation), then the other member of the astronomer Hipparcos' famous Perseus double open cluster, NGC 869, would lie on a line segment between Cas A & NGC 884.

Other evidence for this thesis comes from clusters near our line of sight to Cas A. Even if subsequent deposits fall slightly short, of the original cluster at the end of the flow line, clusters on the same line from Cas A, and near our line of sight to Cas A, would look like one asymmetrical cluster. The younger generation of stars ("blue stragglers") will lie nearer Cas A, and the older generation of stars from the earlier deposit, i.e., the red giants and other "turnoff stars", farther from Cas A. This is so. Let's consider seven clusters near our line of sight to Cas A:


NGC 7789:

(See above for preliminary discussion.) McNamara's (PASP 92:682, 1980; Fig. 3, p. 686) plot of 29 blue stragglers in NGC 7789 is displaced from the cluster center, by a distance equal to 2.3 standard errors of the blue straggler mean position (p=0.07). (I subjectively judged the cluster center four times, from NSE&W, then averaging; found the median horiz. & vert. position of the 29 stragglers; and used 16th-84th %ile distances to get the standard error.) The direction of displacement is position angle (clockwise from north) 75 +/- 25; the direction to Cas A is position angle 53. Gim et al, PASP 110:1318, 1998, Table 5, grade McNamara's blue stragglers as Members, Nonmembers, or Uncertain members of the cluster. If Uncertain is weighted 2/3 and Nonmember zero, then Gim's revision (excluding stars included by Gim but not by McNamara) scarcely changes the magnitude of the displacement but rotates the direction ~30deg counterclockwise to about 45deg, i.e., even closer to the direction to Cas A.


NGC 7380:

Besides magnitude (among the brightest in the cluster), spectral type (B6-A5, III-V according to A&A 366:490, 2001, Table 7, & 356:517, 2000, Table 1)(and the communal cluster PM, RV, and polarization) the intrinsic properties of abnormally slow rotation, and very weak magnesium lines, also characterize blue stragglers (A&A 366:490). NGC 7788 & 7790 overlap; NGC 7654(M52) & NGC 7510 have variable extinction (Janes & Adler, ApJS 49:425, 1982, Table 1); and NGC 7419 is relatively unstudied. So although NGC 7380 is associated with nebulosity, I chose it as the best open cluster, besides NGC 7789, to examine near Cas A, for blue straggler displacement.

Janes & Adler give NGC 7380's main-sequence turnoff as B-V=-0.35 (approx. spectral type B2 per the "FBS blue stellar object" online catalog), and its relative B & V extinctions as E(B-V)=0.59. Vega, type A0, is the standard at which B=V=R. Roughly estimating V=5500Angstrom, B=0.8*5500A, R=1.25*5500A, one sees from the Planck curve that R is about 1/3 of the way to the inflection point, so if B-V=-0.35 then V-R=-0.35*0.25/0.2*2/3=-0.29. Also E(V-R), according to the omega^4 law, should be 0.59*(1-(1/1.25)^3)/((1/0.80)^3-1)=0.29. So the apparent B-R at the turnoff should be about -0.35-0.29+0.59+0.29=0.24 (the same as the apparent B-V, because the dimmer Red absolute magnitude approximately cancels the reduced Red extinction, thus helping this rough estimate to be accurate).

I searched the USNO-B catalog for all stars within 8.33' of the center (22h 47m 21s +58deg 07' 54") of NGC 7380, with R2 magnitude < +13.5 (Dreyer says the [bright, i.e., main sequence blue, or red giant] cluster stars have V = +8.5 to +13.5, and above I estimated that near the turnoff this is also the Red mag), which are within 5, or 10, mas/yr of both the cluster RA PM (-2.77mas/yr) & the cluster Decl PM (-3.55mas/yr). (That's 50 or 100 km/s at the cluster distance of 2220pc, good enough to eliminate nearby stars.) Whether I used 5, or 10, mas/yr, the main sequence turnoff seemed to be between apparent B-R 0.23 and 0.28, with subgiant star(s) near 0.27, and bunching of stars between 0.22 and 0.29. This matches the 0.24 estimated from Janes & Adler.

In NGC 7380 there seems to be one blue straggler: USNO-B 1482-0442104, with B2-R2=0.12 (usually these "2" mags, which I normally used here, are from LaSilla) and B1-R1=0.18 (usually these "1" mags are the older and somewhat less accurate Palomar). This star is 3' E and 7' N of the cluster center. This is near the edge of the disk considered, near the limit of PM discrepancy tolerated, and at position angle 335, vs. position angle 280 to Cas A. In ApJ 454:151, 1995, Table 4, the B-V extinction for 10 stars in NGC 7380 ranged from 0.52 to 0.86mag; so this blue straggler candidate easily might be actually less blue than several other stars in the cluster, if it happens to have relatively weak B-R extinction.

So after trying with modest success to do this at home, I went to the Iowa State University library and consulted Moffatt, A&A 13:30, 1971, Table 2 & Fig. 5. The WEBDA star cluster website lists Moffatt's star #21 as the lone blue straggler in NGC 7789. Though #21 is the bluest in B-V, it's far from the bluest in Moffat's "extinction-free" (B-V)0. Moffatt's six stars (#8,13,7,6,16,10) bluest, of his 55 total, in extinction-corrected (B-V)0, ranging from -0.39 to -0.31, also are the six bluest in (U-B)0. All six were among the 45/55 getting Moffatt's highest, "p", cluster membership probability rating. Beginning at -0.30, the histogram becomes much more crowded: two each at -0.30 & -0.29, one at -0.28, three at -0.27, etc. The bluest six have extinction-corrected visual magnitude, V0, ranging from +7.8 to 9.6, consistent with the main sequence at type B, but the two stars at -0.30 have subgiant (main sequence turn-off) V0's of +6.6 & 6.7. Moffatt (p. 35) gives his mean error in B-V as 0.08mag. The position angles of the six are, resp., 250, 340, 235, 330, 270, 360 (ave. 300 +/- 20 , vs. 280 for Cas A), and their distances from the center, 6', 6', 11', 3', 5', and 1'. The "bulk of cluster stars lies within 6' " (Moffatt, p. 32).


NGC 7510:

WEBDA says NGC 7510 (which has variable extinction, according to Janes & Adler and to Barbon) has two blue stragglers, Barbon's #21 and (correcting the misprint in WEBDA) #104 (Barbon et al, A&ASupp 115:325, 1996; Fig. 1 & Table 1). As for the previous cluster, I rely on extinction-corrected blueness instead, finding #17 & #29 in Barbon's Table 2, both with (B-V)0 = -0.28, Mv = -3.8, type B0.5V. (Barbon gives his B & V errors as 0.03mag.) These seem to be the real blue stragglers; the next bluest (corrected) is #55, a turnoff giant with (B-V)0=-0.23, Mv=-4.7, type B1.5II. Their position angles are about 105 & 155 (both only about 1' displaced) vs. 225 for Cas A. NGC 7510 is elongated NE-SW; the two blue stragglers are near the SW corner.


NGC 7790:

Gupta, with B & V errors of only 0.01mag for V < 16.0 (Gupta et al, A&ASupp 145:365, 2000, Table 2, Fig. 7) and employing extinction correction, finds two definite blue stragglers but doesn't name or locate them. Maybe these are the same two blue stragglers WEBDA lists as identical with Pedreros' A & B (ApJ 286:563, 1984) and with Romeo's #25 & #89 (MNRAS 240:459, 1989, Table 1, Fig. 1). Pedrero's chart is tilted but Romeo's agrees with Gupta's and gives position angles of 110 & 140, vs. 120 for Cas A. This open cluster is unique because it has three Cepheid variables.


NGC 7788:

This doesn't seriously overlap the previous cluster. Lacking blue straggler information (WEBDA says there is one, but lists only somewhat inaccessible references) I used Pandey's finding that in NGC 7654 the bright stars (which seem to be those at least slightly turned off the main sequence and V < ~11.5; see NGC 7654 discussion) lie to one side (it happens to be the side opposite Cas A). The position angle of Cas A for NGC 7788 is 120deg.

The distance modulus for NGC 7788 is 12.75, vs. 12.50 (Pandey et al, op. cit., p. 513) for NGC 7654; the reddening is 0.28 vs. 0.57 (Pandey). So I looked in NGC 7788 for magnitude R2 < 11.50 + (12.75-12.50) - 0.5*(0.28-0.57) = 11.90 (rounded to +12.00) within 2' of the center. Four of the five (not counting one star disqualified by large proper motion) stars found had B2-R2 = +0.3 or 0.4 and this wasn't contradicted by their B1-R1. Using E(B-R)=1.5*0.28=0.42, these four would be spectral type mid to late B. 3/4 of these were S, and 3/4 W, of center, that is, these bright and blue stars were displaced toward Cas A. Searching to R2 < 15.00, I found that the stars generally became moderately redder. Never were they really significantly more blue than the bright four, if all listed magnitudes were considered. So I think the bright four, which mostly lie toward Cas A, are from the blue end of the main sequence, i.e. the youngest stars, rather than a turnoff branch of older stars.


NGC 7654 (M52):

The basic charts and photometry seem to be in journals ordinarily inaccessible to me: Lundby, Upsala Astr. Obs. Ann. 1(10), 1946; Pub. USNO 17(VII):349, 1961; Ebbinghausen, Astronomical Journal v. 50 (missing from our library). Pandey (A&A 374:504, 2001, Fig. 20) notes that 13.5/16 of the brightest stars lie north of the midline, (i.e., away from Cas A, whose position angle is 175 here). Pandey's Fig. 12 shows that these bright stars correspond to about V < 11.50 and are just starting to turn off the main sequence, with B-V = +0.55, i.e., -0.02 with dereddening correction; that is, they are near spectral type A0. The presence of more turnoff stars on the side away from Cas A implies that the stars on this side generally are older.

This cluster's reddening (B-V extinction) increases moderately from center (0.57) to edge (0.66) but is radially symmetric and without significant NS or EW variation (Pandey, op. cit., Figs. 8 & 20). This cluster is relatively nearby (1380pc) and has 1100 solar masses.


NGC 7419:

Caron (AJ 126:1415, 2003) notes that this cluster is unique because it has five red supergiants (not mere giants - supergiants!). Another strange trait, is that it has no blue supergiants, but instead has seventeen Be stars (A&ASupp 146:465, 2000); its seven brightest blue stars are B2IIIe giants or thereabouts (Caron, op. cit., Fig. 1 & 2). For this cluster, I found the effect of Cas A on both the young and evolved stars:

Some say this cluster's diameter is 2'. Dias' online catalog gives 5', so I drew a four-leaf clover of 1'-radius circles each tangent to a coordinate axis at the cluster center. My USNO-B1 catalog online search, for R2 < +14.00, found 9 bright stars within each circle near Cas A (position angle 235)(ave. for the two circles, 5.5 non-blue, i.e. [non-blue] giants; 2.5 blue; 1 unknown) and 16 or 17 bright stars in each circle away from Cas A (ave. for the two circles, 10 non-blue; 4 blue; 2.5 unknown). By "non-blue", I mean that the average of listed B-R mags was > 1.5*1.8 = 2.7 , i.e., > 0.00 (equivalent to spectral type later than A0) corrected for E(B-R). This indicates that these bright stars are, mostly, evolved stars. They prefer the side opposite Cas A.

The distance modulus of NGC 7419 is given as 16.37 vs. 12.75 for NGC 7788; the reddening E(B-V) is 1.83 vs. 0.28. So, R2 < 14.00 for NGC 7419 corresponds to about R2 < 14.00 - (16.37-12.75) + 0.50*(1.83-0.28) = 11.16 for NGC 7788.

Beauchamp et al (ApJSupp 93:187, 1994, Table 1, Fig. 8) plotted (B-V)0 for this cluster; extinction correction is essential because this cluster is so reddened that Caron had to use R-I instead of B-V for his fainter stars! E(B-V) averages 2.0, but varies by 0.4 within the cluster (A&A op. cit.). The (corrected) bluest star Beauchamp found was his #689, apparently a blue subdwarf. The stars most resembling blue stragglers were #869, #1156, and #724; these three had V = +15, absolute magnitudes consistent with early BV, were a few tenths of a magnitude bluer than the main blue group which hinted at main sequence turnoff, and were not so blue that was impossible for them to be main sequence. These three and the bluest star all lay in the SE quadrant, the same quadrant as Cas A.
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Joe Keller

USA
957 Posts

Posted - 09 Aug 2007 :  20:51:55  Show Profile  Reply with Quote
There is a simpler way to prove the thesis that Cassiopeia A is a satellite galactic nucleus: open clusters might be concentrated in a shell centered on Cas A. Around a star, a planetary ring nebula really is a spherical shell of gas which looks like a ring where the shell is pierced at a slant. Likewise there seems to be ring of open clusters around Cas A:

Dias' open cluster catalog (online Strasbourg "VizieR") is the successor to Lynga's. Dias' catalog lists 48 o.c.'s within 7deg of Cas A. Twelve of these lie 4.76 to 5.11 deg away from Cas A. Let's "clean" the list: some of Dias' clusters are noted "not found" [on DSS plate inspection] or are noted to have been called "nonexistent" by authorities; let's omit these. Clusters Dias calls "dubious" on DSS will be counted as 1/2.

This "cleaned" cluster list includes 19 closer than 4.76 deg, 6 of which have NGC numbers. Between 5.12 & 7.00 deg, are only 11 clusters, only 2 of which have NGC numbers. Between 4.76 & 5.11 deg are 9.5 clusters, 4 of which have NGC numbers.

The galactic latitude of Cas A is only b = -2.1 deg, so the sparseness of clusters between 5.12 & 7.00 deg, might be due to greater distance from the galactic plane. However this doesn't explain the concentration of clusters near 5 deg. This concentration is analogous to a planetary nebula. The density is even greater than would be expected from the geometry of a spherical shell. Maybe clusters tend to be elongated with axes perpendicular to the radius to Cas A. If so, clusters near the apparent edge of the shell, could appear more spherical and would be likelier to be recognized.

Seven of the 9.5 "cleaned" clusters that lie on the ring, are in a ~25 deg sector including NGC 7788 & 7790. The most important five of these seven, lie at position angles, from Cas A, of 295 to 320 deg, at distances varying smoothly from 5.08 down to 4.81 and then up to 5.05 deg. If the cluster Harvard 21 is included (it's in the Millenium atlas but "not found" in the DSS by Dias) the five clusters King 21 & 12, Harvard 21, NGC 7788 & 7790, lie on a curve whose curvature varies only +/- 15%.

NGC 7789 & 7380 lie well away from that sector, but a "dubious" cluster, Berkeley 100, is the only one lying more than 1 deg above the galactic plane. If the sun is (to give a typical reported value) 20pc below the galactic plane (determination from OB stars by BC Reed, Alma College, internet, c. 2006) an object in the galactic plane and 2000pc distant would appear to have galactic latitude +0.5deg. There might be only a half-shell, which lies in the same galactic hemisphere as Cas A.
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Joe Keller

USA
957 Posts

Posted - 12 Aug 2007 :  21:44:34  Show Profile  Reply with Quote
One of the NGC clusters in Dias' catalog, NGC 7423 (= Berkeley 57) appears near Cas A (~4deg) and has a bibliographic reference in WEBDA, but I haven't considered it above. Fig. 3 in PASJapan 56:295, 2004, seems to me to show that the brightest and bluest stars in this old ( > 10^9 yr) open cluster are above the main sequence turnoff, and thus are blue stragglers. (I think I disagree with the authors, who suggest that the real blue stragglers in this cluster are to the left of the cleft below the main sequence turnoff.) Be this as it may, the brightest & bluest stars seem to be mostly on the side toward Cas A:

I drew two 30"-radius circles tangent to the origin (i.e., cluster center) NW and SE of the center. In the USNO-B catalog I listed stars, within the circles, which had "0" PMs in both directions. Of stars with both B2 & R2 mags available, 18 in the NW circle but only 13 in the SE circle had B2 < R2 + 2. This itself amounts to only 0.9 sigma, but adds to the collective evidence.

Finding the location of Cas A with binoculars, I see that it lies near the center of a dark "hole" in the Milky Way roughly one degree in radius. (Through binoculars this "hole" looks like several other nearby holes that are as big or bigger.) Further investigation of this region of increased extinction, might reveal some kind of symmetry about Cas A.
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Joe Keller

USA
957 Posts

Posted - 28 Aug 2007 :  00:55:12  Show Profile  Reply with Quote
The curvature of the above-mentioned string of open clusters 5deg E of Cas A, is away from Cas A, not toward it. Cas A (l=112), if at distance 3.4kpc, is at the far edge of the Perseus Arm (see plots in, inter alia, Kuehn, The Milky Way, 1982, Fig. VI.14, p. 86; or Inglis, Planets Stars & Galaxies, 1972, Fig. 16-14, p. 428). These open clusters might mark the end of the "bar" of a spiral mini-galaxy formed around Cas A.

The orientation of the Milky Way's galactic bar might be 16 +/-2 deg forward of the radius from the sun to the galactic center at Sag A (Binney et al, "Kinematics of Galactic Center Gas", MNRAS 252:210, 1991). If it is 15deg, that's straight toward Cas A, if Cas A is 3.4kpc away and Sag A 8.5kpc away (the radius preferred by Bok & Bok, The Milky Way, 5th ed., 1981).

The Orion-Cygnus (i.e., Local) Arm is thought to be aberrant and not a true spiral arm: "Observations indicate that we are [within a galactic arm], but theoretical studies say there shouldn't be a major spiral feature where the Sun is." (Branley's Astronomy, 1975, p. 228). The Local Arm might be part of the mini-galaxy around Cas A.

There is a net average Cepheid blueshift ("systematic deviation") of 3 +/- 1 km/sec (Kraft & Schmidt, ApJ 137:249, 1963, Table 8, p. 263). The intrinsic redshift concept of Tifft and Arp suggests therefore that the sun is in a different, younger, galaxy from most of the rest of the Milky Way.
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Joe Keller

USA
957 Posts

Posted - 30 Aug 2007 :  00:12:42  Show Profile  Reply with Quote
Open letter to the Lowell family re: Barbarossa (Planet X)


To: Mr. ******* Lowell

Dear Sir:

I went to the Lowell page of *******.com; you were the first person I found who recently had posted a message about a Massachusetts Lowell and who was named Lowell himself. Perhaps you will forward this email to appropriate members of the Lowell family.

The Charlie Rose (with David Rockefeller) program about the late widow Brooke Astor informed us that although her philanthropy was sound, some Astors sued her because they thought she was giving away the Astor foundation too fast. Indeed a decade ago she announced that she gave away almost all of it.

Sometimes family foundations are taken over by people who care little for the hopes and dreams of the founding family. I think that the Lowell Observatory might be a case in point.

Like Percival Lowell, I studied mathematics as an undergraduate at Harvard (B.A., Mathematics, cumlaude, 1977). Unlike Percival, I'm a retired Midwestern medical doctor, but I have compiled information indicating that Percival was correct about the direction of Planet X though he underestimated the distance. Everything I've published on this, is on Dr. Tom Van Flandern's free-speech scientific messageboard at www.metaresearch.org, under the name "Joe Keller". There I've published all my fruitful ideas, and in enough detail that a trained astronomer can retrace my work to his own satisfaction.

I told the director and the appropriate department head at the Lowell Observatory about this in an email in March, but received zero response from them (now that Pluto has been downgraded from planet status, it is believed widely that Lowell was mistaken). I emailed over 100 relevant professional astronomers about my Planet X findings, again with zero response. I post-mailed the Sec. of the Navy, the commander and several other offices at the US Naval Observatory, and dozens of Senators & Congressmen who sit on relevant committees, again with zero response except for one postcard saying approximately "the Congressman can't help you because you don't vote in his district".

As the discoverer of the true Planet X, I've named it Barbarossa, and its largest satellites, Frey & Freya. I've had to call them something during the last year during which the professional astronomy establishment has been refusing to talk to me. I've been talking about this so long that if the pack decides they don't like the name Barbarossa, they'll need millions of dollars in counter-publicity to make their own name stick. As the world economic situation deteriorates, we move toward political change, and the malfeasance of the astronomy bureaus becomes apparent (e.g., I've been silenced on every Association of Lunar and Planetary Observers messageboard, for daring to say there, less than I say in this letter) the professional astronomers will be too busy wondering how to pay their mortgages, to successfully publicize their own name for this planet.

A summary of my work on Barbarossa (Planet X) follows (#1 is new material)(also see especially #4)(I haven't had time to check all these calculations, so there might be minor errors):

1. Lowell's final statement (WG Hoyt, "Planets X & Pluto", 1980, Ch. 6, pp. 140-141) about Planet X gives two almost diametrically opposite possible positions for epoch 1914.5 (a common mathematical phenomenon known as "dual solution"). For best accuracy, one of these positions should be reflected and averaged with the other. Lowell's comment no. 14 says "precise prediction of place" was possible but not of distance [nor mass]. Though Hoyt reports that Lowell relied heavily on one of Flamsteed's observations of Uranus, in the year 1715, Lowell would have given much less weight to Flamsteed's relatively inaccurate (~1 arcminute) observation. The observations after the discovery of Neptune, i.e. the 1846-1910 observations, should dominate Lowell's calculations because not only were observations of Uranus more frequent and accurate during this era, but also Neptune's position did not have to be extrapolated. According to Lowell's estimate, Planet X was, to a first approximation, roughly 45 degrees from perihelion, and roughly at conjunction with Uranus, at the likely effective midpoint of the 1846-1910 era. Such an approximation makes it easy to estimate the mass, for any "Barbarossa" lying in that same direction, necessary to give the same tidal gravitational work on Uranus as would Lowell's Planet X. The effective average distance of Lowell's Planet X from the sun would be between 43.85 AU (the semimajor axis) and 35.2 AU (perihelion). This puts Barbarossa, assuming it is 198 AU distant, in the range 0.008 - 0.018 solar masses.

2. The 5:2 Jupiter:Saturn resonance isn't exact; it advances with period about 2800 yr. Thus any of the three recurrent conjunction points could be shepherded by a distant planet in a circular orbit at 198 AU. The position of the shepherding planet must be adjusted for the lead or lag of the conjuction point due to Jupiter's & Saturn's eccentricities; thus, I found that one of the three possible circular shepherding orbits, differs only a few degrees, in ecliptic longitude, from Lowell's effective average Planet X position in the interval 1846-1910.

3. The dipole and higher moments of the distribution of apparent Cosmic Microwave Background (CMB) temperature are correlated with the plane of the ecliptic. This implies that at least the anisotropy of the CMB, is due to a solar system influence such as planetary gravity. The constancy of the CMB dipole rules out the known planets as major causes of the dipole, but a planet at 198 AU is acceptable, to the accuracy to which the CMB dipole is known from the COBE and WMAP satellites. The ecliptic longitude of the CMB dipole lags the theoretical shepherd planet (see #2) by four degrees.

4. My search of online scanned sky survey plates, combined with an electronic photo taken in March from Tenerife by amateur astronomer Joan Genebriera of Spain with her 16" telescope (similar photos were obtained soon thereafter with smaller telescopes by Steve Riley of California; and possibly by Robert Turner of England using a robotic telescope also on Tenerife) discovered a recurrent pair of starlike objects consistent, for an appropriate mass ratio, with a center of gravity that is in a circular orbit differing 0.5 degree from the ecliptic longitude predicted by #2 above, and 0.2 degree below the ecliptic latitude predicted by #3. Published Kuiper belt density surveys suggest that some of the starlike objects I found on the photos, especially those noticeably elongated on those one-hour sky survey exposures, are Kuiper belt objects; also, some objects might be novas or glitches. Dr. Ian McDiarmid states that cosmic ray artifacts do not appear on photographic plates (e.g., the sky surveys) at moderate altitude. Despite the many possible combinations of objects for an orbit, I estimated that the closeness to a perfect constant-speed great circle was statistically significant. Genebriera and Riley were recruited by me through a mass emailing to ~100 amateur astronomers; Turner contacted me through Dr. Van Flandern's messageboard.

5. The origin of the CMB and its dipole can be explained by a simple theory which likens the solar system's Maxwellian ether to a drop of boiling water. According to this theory, the CMB dipole could be caused by the gravitational field and potential, of a planet of 0.0116 solar masses at distance 198 AU. This agrees well with what Lowell's last work implies should be the mass of Planet X at this distance (see #1 above).

6. I found that if Barbarossa (together with, of course, its satellites Frey, Freya, etc.) possess 0.0104 solar masses, then Barbarossa produces a torque (per degree of orbital inclination) on a typical member of the main (i.e., non-resonant) Kuiper belt, equal to the torque of all the known planets, moons, asteroids, etc., combined. The agreement, with #5 above, would be perfect if a little more planetary mass were discovered at the distance of Neptune.

7. If the tidal force of Barbarossa et al, is subtracted from the observed sunward "anomalous acceleration" of Pioneer 10/11, there remains a simpler, monotonically decreasing anomalous acceleration, whose graph is roughly a normal distribution with the sun at the origin.

8. More and more colder, less massive brown dwarfs are being discovered. Often they are binary. A close pair of brown dwarfs lies in distant orbit around a sunlike star, 12 light years from us. The median distance from brown dwarf to sunlike star, seems to be a few hundred AU, typically in nearly circular orbit. Indeed it might be atypical for a star like the sun not to have one or a pair of smallish cold brown dwarfs in an orbit like that which I claim for Barbarossa & Frey.

9. If Barbarossa is at equilibrium temperature with solar radiation, it should indeed not be seen by the IRAS satellite. Highly theoretical articles estimate that Barbarossa should be much warmer and therefore easily seen by IRAS, but the assumptions of such theory are suspect: indeed if heat were generated, during the accretion process, only at the surface, not within the interior, of his superdense core, then Barbarossa could have cooled rapidly by convection.

10. The objects in #4 above, have comparison Red magnitudes of +18 or +19. This requires moderately smaller-than-theoretical size, and/or very dark albedo comparable to the darkest albedo theorized for "roaster" brown dwarfs.

11. Steve Riley's photos pushed the limits of performance for a telescope his size: sometimes stars of the same magnitude as Barbarossa and Frey, appeared normal; sometimes fragmentary; and sometimes absent, all on the same photo. Though Joan Genebriera's larger telescope fared better (the president of the Des Moines, Iowa, astronomical society concurred with me, that her Barbarossa image hardly could be "artifact"), there seems little chance that amateur astronomers soon will be able to compile the traditional number of photographs. The only way to resolve the existence or non-existence of Barbarossa is to look with bigger telescopes available to tax-funded or tax-exempt foundation-funded professionals. I have investigated the protocols for applying for observation time myself at major observatories, but so far have been discouraged by blatant bureaucracy (e.g., pointedly requiring that applications be on an online form which is not accessible, or requiring excessive and unprecedented numbers of hardcopies of the application - indications that the observatory is so uncooperative that application is a waste of time).

Sincerely,
Joseph C. Keller, M. D.
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Stoat

United Kingdom
964 Posts

Posted - 30 Aug 2007 :  04:15:17  Show Profile  Reply with Quote
Hi Joe, I think that you are letting your, quite understandable, frustrations make for a counter productive introductory letter. I believe that any first approach has to be short and hopefully tantalizing.

First paragraph, along the lines of, "I have been advised by Dr ****, that you may be of assistance in gaining two photographic telescope plates, for the purpose of blink comparison of stars."

Second paragraph, is one where you can ask your "hook" question, and pique their interest. Something along the lines of, "could our sun be one member of a failed binary star system?" Explain how binaries are very common, so that failed binaries also have to be common.

Third paragraph, state that you believe that this is the case, and give the proposed position of the companion. I personally wouldn't mention its satellites. It's always best not give too much information about specifics at this early stage.

Fourth paragraph, ask for time on the size of telescope you want and pencil in the best times for the plate exposures you want.

Fifth paragraph, offer to fax/e mail further information, and ask if it would be okay to write/phone later in the month to enquire about progress. Then a thank you for reading the letter and sign off.

This approach lets the first reader of the letter make a decision, without having to pass it on for comments. I think your long letter is being passed on by the boss, and then no one in the pecking order wants to have to explain it to that same boss. That's human nature, they'll opt for, "just ignore it and it will go away." Your letter intimates that there is some huge fight going on, people, even those in ultimate resposibility, will often decide that they'll not get involved in it. The quite reasonable request, to take two photographic plates gets lost in the shuffle.

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Joe Keller

USA
957 Posts

Posted - 30 Aug 2007 :  19:51:51  Show Profile  Reply with Quote
[quote]Originally posted by Stoat

Hi Joe, I think that you are letting your, quite understandable, frustrations make for a counter-productive introductory letter. ...


You may well be right. Some of my friends here in the US say what you're saying. Thanks for your input!


Notice:

$100 reward! I, Joseph C. Keller of Roland, Iowa, USA, will pay $100 to whomever is the first, to get someone with a 40 inch (1 meter) or larger optical telescope, to look for Barbarossa. The reward is for getting someone to look, not for looking yourself. With a telescope this size, it's professionals who will look, and they're unlikely to be swayed by $100. So the contest is, somehow to get professionals to look, and see whether Barbarossa is there, or not there.

Whether the search finds Barbarossa, or shows that Barbarossa isn't there, is not important. It is important that it be a bona fide attempt.

To prevent complications, I'm the sole judge of what is a bona fide attempt to look for Barbarossa (with an optical telescope at least 1 meter in size) and of who is first. Many disputes can arise in a deal like this, so to save everyone grief, I'm the judge of who, if anyone, wins, and there's no appeal. I don't promise fairness. I don't promise any particular standard of judgment. I'm the arbitrary judge.

Sincerely,
Joseph C. Keller, M. D.
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Stoat

United Kingdom
964 Posts

Posted - 31 Aug 2007 :  02:59:00  Show Profile  Reply with Quote
Hi Joe, somewhere in this thread I mentioned a post by cosmicsurfer, which links to the site of this very rich man who believes we have a brown dwarf companion. Now the down side with this guy is that he appears to have an ego as large as a brown dwarf. Having said that, perhaps he's worth a try. I wouldn't argue with him too much. I'd just say I believe that I've found something and that it's at such and such co-ordinates. Say that I have some photographic evidence but that it needs verifying with the use of a larger telescope.

My draft introductory letter, I'd send by pm here to Tom Van Flandern, for comment. I believe that he once did some work for this chap but that they had to part company, because as I've said this guy makes King Canute look like a modest man. This guy will probably try to save face by claiming that it was his idea all along but people are going to see through that hubris.

(Edited) Perhaps now would be a good time to put together a pdf that explained, in layman's terms, the idea of a "failed" binary system. Lots of diagrams and pictures. Probably written in a Carl Sagan like style.

Then approach your local radio/t.v station and also get a lecture set up for school sixth formers. Tape or video the whole thing, and burn that onto a cd to send to science reporters of the larger national newspapers. Do expect that newspapers will garble your argument but don't fret about that, the object is to get the thing into the public domain.
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thebobgy

USA
94 Posts

Posted - 31 Aug 2007 :  05:05:32  Show Profile  Reply with Quote
Hey Joe, check this place out for publishing your work, it is Cornell U. http://arxiv.org/. They print papers on many subjects daily. I have been reading your work for quite some time and your efforts are deserve a chance. Good luck.
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nemesis

84 Posts

Posted - 31 Aug 2007 :  08:26:46  Show Profile  Reply with Quote
Stoat et al, the "very rich man" must be the guy who believes the phenomenon of precession of the equinoxes is due to the solar system orbiting an unseen companion. That idea was critiqued pretty thoroughly on another thread on this board, and in any case, the required period of 23,000 years or so would be far to long for Barbarossa at 198 AU. But still, he could well be interested, there's nothing to lose.
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Joe Keller

USA
957 Posts

Posted - 01 Sep 2007 :  14:06:52  Show Profile  Reply with Quote
quote:
Originally posted by Stoat

Hi Joe, somewhere in this thread I mentioned a post by cosmicsurfer, which links to the site of this very rich man who believes we have a brown dwarf companion...


I think these are good ideas. I won't be offended if somebody else does these before I do.

An analogy might be to Charles Darwin & Thomas Huxley. Huxley did more than Darwin, to gain acceptance for Darwin's evolution theory. Either Huxley was a better persuader, or Darwin was beat up from the Beagle voyage and the tropical diseases, maybe including Chagas disease.

Reply to "thebobgy": when Cornell took ArXiv.org over from Los Alamos, they made it a closed club. Last time I checked, you can't post unless someone already in the club, and in that subject area, "endorses" you for membership. A few years ago, when I was a graduate student in Math at Iowa State Univ., I asked several physics/astronomy faculty at ISU to "endorse" me for membership, but they refused.

Reply to "nemesis": a year or so ago a magazine I saw (in the Borders bookstore) had an article about solar system precession vs. Newton's sun/moon-on-Earth's-equatorial-bulge torque-on-Earth-rotation precession. I tried to email the authors but never heard back. They said there was a discrepancy between Earth's observed polar motion, and that predicted by Newton's equatorial-bulge theory. Although my own calculation (and surely the calculations of many astronomers before me) shows that Newton's theory does give roughly the right answer, it may well be that there is, due to some unknown cause, a discrepancy, perhaps revealed only by modern measurements of Earth's mass distribution and polar motion. However, even another sun, at 200 AU, would cause only 1/200^3 = 1/8,000,000 the precession that the sun does, according to Newton's equatorial-bulge theory.
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Joe Keller

USA
957 Posts

Posted - 21 Nov 2007 :  17:08:30  Show Profile  Reply with Quote
Barbarossa, and Lescarbault/LeVerrier's Vulcan

Lescarbault's data didn't determine "Vulcan" 's eccentricity. So, the near equality, of Vulcan's and Barbarossa's inclinations (to the principal plane of the known solar system) suggests that Vulcan is a tail-less long-period comet related to Barbarossa dynamically. Though the sky surveys came close, I don't know of any astrophotographic record on which such a body should be visible, even with the most optimistic diameter and albedo estimates.

Barbarossa's and Vulcan's inclinations to the principal plane, differ almost two degrees, but their inclinations to (Earth's) ecliptic (by LeVerrier's calculation) are equal, to the nearest arcminute. Torques from distant objects precess Earth's orbit 12 times slower than Jupiter's, so the ecliptic might better indicate initial solar system conditions. Also, LeVerrier's calculation of Vulcan's ascending node, is only 25.5' less than 90 degrees ahead of Barbarossa's.

Because Vulcan grazed the sun's disk, not crossing the center, a parabolic orbit for Vulcan (instead of LeVerrier's circular assumption) lessens by parallax, Vulcan's calculated inclination by about 1/250 radian = 15'. This advances its calculated node, by 1/2500 radian = 1.5'. So the nodes (modulo 90) and inclinations of Barbarossa and Vulcan are each only ~20' different.

Alternatively, Lescarbault's estimate of Vulcan's apparent diameter as less than 2.7" (1/4 Mercury's) is consistent with a 1:1 or 2:1 mirage image of Barbarossa. From a compromise, between the brown dwarf diameter estimated from theoretical physics, and the somewhat smaller diameter inferred for Barbarossa from its apparent magnitude combined with theoretical chemistry's estimates of brown dwarf albedo, a 60,000 mile diameter for Barbarossa, gives 1.5". With "one arcsecond [atmospheric] seeing" (i.e., each point of light becomes a two-dimensional normal distribution with half-maximum 0.5" from the center) if Barbarossa's black image somehow were superimposed on the sun, the half-maximum brightness circle would have diameter 1.2".

Two special correlations with Earth, suggest that Vulcan was a mirror image of Barbarossa. Barbarossa and Vulcan (assuming circular orbits) have, as discussed above, exactly the same inclination to (Earth's) ecliptic, within an arcminute (this accuracy isn't impossible with the sky survey, or with Lescarbault's data). Also, Vulcan was observed when about 70' S of the celestial equator. At the time, correcting for equinox precession, the center of gravity of the Barbarossa/Frey system, was about 40' S; and with 2 A.U. (roughly Frey's maximum distance from the center of gravity) subtending 30', Frey might have been 70' S.

There is a correlation with Dayton Miller's annually varying "ether drift vector". The equatorial component of that vector, is roughly proportional to a 90-degree rotation of the vector, between Earth, and the center of gravity of the solar system including Barbarossa.
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Joe Keller

USA
957 Posts

Posted - 15 Feb 2008 :  16:58:48  Show Profile  Reply with Quote
Additional Solar System Features Suggesting the Cold Brown Dwarf Companion, Barbarossa

Earlier on this messageboard I mentioned that if my mass and distance estimates for Barbarossa are accurate, then the classical Kuiper Belt (a.k.a. "cubewanos") occurs at that distance, at which the torque on an orbit, per degree of tilt, due to Barbarossa, equals the torque per degree of tilt due to the entire known solar system combined. That is, for cubewanos, precessions about Barbarossa's orbital plane, and about the principal plane of the known solar system, occur at equal rates.

Yesterday I confirmed that calculation and went further. Including only the known giant planets, JSUN, I found that if Barbarossa is in a circular orbit at 197 AU, then 0.0102 solar masses for Barbarossa and its satellites, gives a ratio for Neptune, torque per unit tilt due to Barbarossa & satellites : torque per unit tilt due to JSU = 1:3. Then the 1:2 ratio (Neptune now included) occurs at 40.2 AU, for a body in a circular orbit; the mode of the semimajor-axis histogram for plutinos is about 39.4 (the semimajor axis of Pluto). The 1:1 ratio occurs at 43.8 AU, vs. the mode of the cubewano histogram, 44.2 AU (the mean and median appear to be slightly less). The fundamental trans-Uranian spacing process might be the torque due to Barbarossa and the resonance of orbital precession rates. The 3:2 Pluto:Neptune orbital period resonance might be a bonus possible because both processes, orbital period and Barbarossa-caused orbital precession rate, go as r^1.5, while the orbital precession rate of Neptune due to JSU equals that of plutinos due to JSUN.

Following Brauer & Nohel, Qualitative Theory of Ordinary Differential Eqns (Dover, 1989), pp. 51-53, I solved the nonhomogeneous system of linear differential equations describing Neptune precessing about the orbital plane of Barbarossa and simultaneously about the presumed fixed principal plane of the known solar system, with exactly 3x the torque, per degree of tilt, as Barbarossa. The result is precession along a small closed curve amounting to a circle superposed on a larger cardiod, or equivalently to a slender ellipse superposed on a hypocycloid of three cusps (see, inter alia, CRC Standard Mathematical Tables, 26th ed., ch. VII - Analytic Geometry, pp. 264,267,269; ES Smith et al, Analytic Geometry, sec. 100, prob. 15; and the Wikipedia article on Lissajous figures). The predicted rms deviation for Neptune resembles that currently observed, and Neptune lies near a point on the predicted curve.

The same equations also predict that Uranus would have an rms deviation resembling that observed. The deviation would be due to the sum of comparable contributions from Neptune and from Barbarossa.

The deviation of Saturn is not explained by the above, but might be related to the Jupiter:Saturn:Barbarossa resonance discussed by me earlier. Suppose that the energies related to this resonance, are proportional to the gravitational forces, and minimized when the resonance is perfectly aligned. Suppose further that there is equipartition of energy between the two degrees of freedom, which correspond to the imperfect alignment, due to Barbarossa's inclination and to Saturn's. I calculate that this equipartition occurs when Saturn's orbit is inclined 1.01 degrees to Jupiter's, vs. 1.25 deg observed.
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Joe Keller

USA
957 Posts

Posted - 15 Feb 2008 :  22:46:24  Show Profile  Reply with Quote
Assuming, as above, circular orbits, with Barbarossa at 197 AU with 0.0102 solar masses, Saturn's rate (i.e., frequency) of orbital precession, due to J,U & N, and Saturn's hypothetical rate of orbital precession due to Barbarossa, are in the ratio 1:0.00206. Jupiter's rate of orbital precession due to S, U & N, and Jupiter's hypothetical rate due to Barbarossa, are in almost exactly the same ratio, 1:0.00205. Here U and N are almost negligible, so basically, Jupiter and Saturn happen to have the mass ratio needed for them to have the same ratio, of orbital influence by Barbarossa to orbital influence by each other.

The orbital influence (i.e., precession rate) hypothetically caused by Barbarossa goes as r^1.5, like the orbital period. But why should Saturn's 2.5x longer orbital period imply that its orbit precess 2.5x faster than Jupiter's? A distant massive solar companion, such as Barbarossa, seems a likelier reason why the masses of Jupiter and Saturn happen to be just right to conform to this r^1.5 law for their orbital precession rate. If Barbarossa precesses Saturn at 2.5x the frequency it does Jupiter, but Saturn's orbital angular momentum vector's precession cycles around Jupiter's are 2.5x quicker than Jupiter's around Saturn's, then the displacement of Saturn's vector, by Barbarossa, during a quarter cycle of Saturn's precession around Jupiter, equals the displacement of Jupiter's, by Barbarossa, during Jupiter's quarter cycle around Saturn. Regarding the absolute value of the difference between the J & S orbital angular momentum vectors, the discrepancy induced by Barbarossa, thereby amounts to the sum of two sinusoids of different frequency but equal amplitude.
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Stoat

United Kingdom
964 Posts

Posted - 16 Feb 2008 :  05:49:27  Show Profile  Reply with Quote
Hi Joe, time maybe for another try at a telescope shot.Here's a screen shot of the ones on the Bradford robotic, Pick out the best position one and I'll put it up again as a job. Though veiwing is not too good at the moment.

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Joe Keller

USA
957 Posts

Posted - 16 Feb 2008 :  23:35:53  Show Profile  Reply with Quote
Originally posted by Stoat:
"Hi Joe, time maybe for another try at a telescope shot.Here's a screen shot of the ones on the Bradford robotic, Pick out the best position one and I'll put it up again as a job. Though viewing is not too good at the moment. ..."

Great! My notes aren't with me now but I can do it tomorrow.
- Joe Keller
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