Requiem for Relativity

Oh yeah, gravitational acceleration
Little m here is the same as the the mass mentioned in my previous post.
Big M here does not appear in my previous post.

Big M creates a gravitational force field around itself by absorbing and scattering some of the graviton flux that is continuously passing through it. It also creates a gravitational potential field.

Little m experiences the force field as a force in the direction of M. It experiences the potential field as very small speed and altitude dependent variations in the force field. These small variations are what we mean when we talk about relativistic phenomena such as clock slowing.

This is not the entire story, but it covers many of the major points. If anyone else is interested in taking a shot at this, be my guest.

Regards,
LB

Pulsar "Pdoubledot" Confirms Barbarossa Mass

My foregoing study essentially repeats that of Zakamska & Tremaine, but using only the eight Taylor (1995 catalog) millisecond pulsars (P < 30 ms) whose Pdot/P ranges from 0.23 to 0.36 (/10^17 per sec). Not only is this the densest and most distinct cluster of Pdot/P values, but the endpoints happen to equal 1.0 or 1.5 * 72km/s/Mpc, the most accepted value of the Hubble parameter. The reciprocal of what would be Earth's precession period, if subject only to the torque of the outer planets, lies at the midpoint of this interval.

The direction correlating best with -Pdot/P, for these eight, differs only 25 deg (p = 5%, one-tailed) from the (+) CMB dipole (i.e., the predicted position of Barbarossa). Narrowly limiting Pdot/P to get a pristine subject group, limits the mass estimate to an inaccurate lower bound, about 1/8 of expected.

Yesterday I used the "Topic Search" of "Web of Science" (online Science Citation Index) to find (and at least glance at, online or in print) almost all the ~100 articles about these eight pulsars. When I found secondhand data, I traced it when possible. The two explicit "Pdoubledot" determinations I found, are for J1012+5307 (Lange et al, MNRAS 326:274+, 2001; Webb et al, A&A 419:269, 2004). This is a "field" millisecond pulsar; i.e., not in a globular cluster. Webb's table misprints Pdot as 0.7...; it should be 1.7... .

Note that Pdot^2 << Pdoubledot*P. Lange, and Webb, analyzed their long strings of data on this pulsar, to find Pdoubledot values giving (d/dt)(Pdot/P) = 0.97, and 4.74/10^28 per sec^2, resp. The derivative of the apparent acceleration toward the pulsar, is (d/dt)(-Pdot/P * c). The derivative of the sun's acceleration due to Barbarossa is 3.78/10^28 per sec^2 * c. The angle, between Barbarossa's orbital velocity vector (i.e., between the derivative of the sun's acceleration vector toward Barbarossa), and the radius to this pulsar, is 180 - 55.75 deg. So, the expected value of (d/dt)(Pdot/P), is 2.13/10^28. The measurements of Lange, and Webb, confirm the mass and direction of Barbarossa within a factor of two.

For two more of these pulsars, I found significant, consistent data from which to calculate Pdoubledot myself. J0613-0200 (Bell et al, MNRAS 286:463, 1997, Table 1; Hotan, Bailes & Ord, MNRAS 369:1502, 2006, Table 3) lacks sufficiently precise Pdot at the earlier epoch reported, but P is precise enough for quadratic interpolation. The two reports are by the same research group. I estimate Pdot at the midpoint, from delta(P)/delta(t), then estimate Pdoubledot by differencing with the later epoch's Pdot. Observed (d/dt)(Pdot/P) is thus 10.88/10^28 per sec^2. The angle between Barbarossa's orbital velocity, and this pulsar, is 180 - 30.36 deg, so expected is 3.27/10^28.

B1855+09 (a.k.a. J1857+0943)(Kaspi, Taylor & Ryba, ApJ 428:713, 1994, Table 2; Hotan et al, op. cit.) has sufficiently precise Pdot at both epochs reported. The two reports are by different research groups. Differencing Pdot, gives observed (d/dt)(Pdot/P) as -0.48/10^28. The angle is 41.53 deg, so expected is -2.83/10^28.

Summary: observed vs. expected, for (d/dt)(Pdot/P), is

J1012+5307: obs +0.97 or +4.74, exp +2.13 (/10^28 per sec^2)
J0613-0200: obs +10.88, exp +3.27
B1855+09: obs -0.48, exp -2.83

Averaging the two observed values for J1012+5307, gives a correlation of +0.836, p = 8%, one-tailed. The best-fitting line corresponds to a time derivative of acceleration, only 50% bigger than that expected from Barbarossa.

This corroborates the theoretical time rate of change of the sun's acceleration due to Barbarossa. Factors corroborated include Barbarossa's mass, distance, angular speed and sense, and ecliptic longitude.

From these journal articles, I found some proper motions, and if not there, some in Hobbs' 2004 (online, VizieR) pulsar catalog. Only two PMDecl and one PMRA value now are missing, for these eight pulsars. The pulsar with no PM information is J2129+1209H, which lies in a globular cluster, M15. Shklovskii transverse motion correction, and correction for differential galactic acceleration (assuming our sun lies at a maximum of v(r)), separately or together, greatly worsen the correlation of -Pdot/P, with the direction to Barbarossa.

The derivative of acceleration includes a Shklovskii-like term with factors (PM)^2 and (RV)^1, a galactic acceleration term, and cross-terms. Insofar as due to galactic-size motions, all these are negligible because Barbarossa's period is 1/100,000 that of the galaxy.

Though Hobbs' 2004 catalog lists Nudoubledot (the second time derivative of 1/P) for most of these eight pulsars, only one (J0613-0200) was significantly nonzero, and that was of opposite sign to my finding above. More accurate determinations of Pdoubledot likely will reveal Barbarossa's mass and orbit.

Yesterday a moderate-size remote-control college telescope photographed Barbarossa and Frey in one frame. (This is not the Bradford telescope, which has had my job "waiting" for a week. Nor is it the Slooh pay-per-reservation telescope, from which I also have been unable to get any photos during the same period. Both these are on Tenerife; bad weather is part of the explanation.)

Here is my letter to the full professor who supervises the telescope:


Dear Prof. *********:

Our one and only photo, #350 (which you helped me take at my coordinates, and courteously emailed to me immediately) does seem to show the bodies I seek. I assume that the epoch of this photo (or rather, median of stacked photos) is approx. 13:00 GMT Dec. 22, 2008 (the meridian, and still astronomically dark in *******).

The best candidate image for "Barbarossa", the more massive body, is at RA 11:28:22.079 Decl -9:16:6.42. Barbarossa lies at some especially dark pixels of the (FITS version) ESO POSS2 Red sky survey. This region is not available in the ESO POSS2 Blue survey; and due to "issues" downloading Java, I can't get Aladin. The extremely bright nearby star is USNO-B 0807-0228814 (USNO-B Red2 magnitude +15.40). Barbarossa is much dimmer in our photo than USNO-B 0807-0228808 (Red2 mag +18.15), and slightly dimmer than USNO-B 0807-0228824 (R2 mag +19.07). So, I estimate its magnitude as +19.4.

The best candidate for "Frey", the main moon of Barbarossa, is at RA 11:29:4.656 Decl -9:07:2.28. Frey likewise lies at some especially dark pixels of the (FITS version) ESO POSS2 Red sky survey. Frey is much dimmer in our photo than the very bright nearby star, USNO-B 0808-0228849 (USNO-B Red2 mag +18.14). On the ESO POSS2 Red, USNO-B 0808-0228845 (R2 mag +19.18) is bright; yet it is hardly if at all detected on our photo. USNO-B 0808-0228852 (R2 mag +19.05) is only slightly brighter than Frey on our photo. So, though our photo was not red filtered, I estimate Frey's magnitude as +19.1. This is consistent with the magnitudes of Frey and Barbarossa found on sky surveys.

I found the center of mass (c.o.m.) using the ratio 0.877::0.123 I determined in early 2007 from online sky surveys and amateur photos (Joan Genebriera of Barcelona working in the Canary Is., the first to photograph Barbarossa, except for sky surveys; Steve Riley of southern California, the first to photograph Frey, except for sky surveys; and Robert Turner of England working with the Bradford College remote telescope on Tenerife, who has photographed Frey). Mathematically, linear extrapolation of 1986 & 2007 heliocentric celestial coordinates is precise enough. These coordinates as I gave them, really are centered at the barycenter of the known solar system. Today I made the small correction for the movement of Jupiter and Saturn, and estimated expected geocentric coords., accounting for Barbarossa's inclination, Earth's eccentricity, and to first order the curvature of the celestial sphere. The c.o.m. of Barbarossa & Frey is within 1" of predicted in RA, and only 4" too far North in Declination. On about half the previous photos, the presumed c.o.m. ecliptic latitude was too far N or S; the longitude has been much more consistent.

On several photos, Barbarossa or Frey have seemed to have rings roughly parallel to Barbarossa's orbital plane around the sun. It was Robert Turner who first explicitly advocated to me the idea of rings around Barbarossa.

Sincerely,
Joseph C. Keller, M. D.

Hi Joe, this is sounding good. Is there any chance of sending the fits to Marsrocks to let him do his photoshop magic on the image?

(Edited) Hi Joe, I would think that your letter to this astronomer will have piqued his curiosity, has he got back to you yet for a time for your next image shot? I suppose it depends on where Frey is in its orbit. Hopefully it's not moving towards or away from us, as that will make blink comparison difficult.

Changing the subject, I was going to suggest that you gave a brief description of dot notation and the question of pulsars. There are a number of people following your thread, who I think would have to agree, that maths is not their strong point.

<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote"><i>Originally posted by Stoat</i>
<br />...a brief description of dot notation and the question of pulsars...
<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">

My best recommendation is VM Kaspi, "High-Precision Timing of Millisecond Pulsars and Precision Astrometry", at citeseerx.ist.psu.edu

This article is especially good for five reasons:

1. It can be downloaded free from the internet, at least if one has Acrobat Reader. It's only 132 kB because it has no graphs.

2. It's by one author, a founder of pulsar investigation (primary author of one of the articles I relied on for B1855+09's Pdot, i.e., time derivative of P; a collaborator of Taylor, author of the most famous pulsar catalog).

3. It doesn't sweep crucial details under the rug. I haven't seen any article on millisecond pulsars, that better covers the practical issues. Someone who reads this, would be ready to help with the work.

4. It's in the plainest English possible without sweeping crucial details under the rug.

5. It's modular, so usually one can understand a section or paragraph or sentence, without reading the others. It's good for a person who doesn't have time to read it all.

email title: "Overwhelming Confirmation of Double Planet Orbit"

Dear Prof. *********,

Thanks for letting me know. I was excitedly checking the ******* [U.S. remote telescope] site and my email every morning...(the weather's been too bad to go to town and I don't have the internet at home). "Slooh" and "Bradford" have failed to get any photos this season, from Tenerife, due, I think, to bad weather, and to the backlog at Bradford, and to an equipment failure at Slooh.

I now have another overwhelming confirmation of the double planet. Though I only have four Barbarossa/Frey sightings that have near-perfect center of mass position (1954 & 1986 sky surveys, 2007 Genebriera/Riley/Turner photos, and the ******* Dec. 2008 photo) I can assume a fifth ellipse point as an adjustable parameter. When I do this, I find that the 4 - 1 = 3 areal rates, become equal (0.13% relative standard deviation, assuming 2+ orbits 1954-1986 & 1+ orbit 1986-2007) using the same adjustable fifth point, which also is about right for the period and implied mass.

I haven't posted this to Dr. Van Flandern's messageboard yet, though I will soon. You are the first astronomer I've told.

Sincerely,
Joe Keller