Requiem for Relativity

A planet in a SN event would have an altered orbit at least because some of the mass of the star going SN is ejected from the system. How can the ejected mass from a SN event be estimated? It seems to me all SN events originate in a mass range of 5 to 20 solar mass stars but maybe all the mass is ejected at some of the events and not other events. The total energy of the event can be reasonably estimated but how would the ejected mass be estimated?

<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote"><i>Originally posted by Jim</i>
<br /> ...The total energy of the [supernova] event can be reasonably estimated but how would the ejected mass be estimated?
<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">

I don't know offhand, but it seems to me that maybe there would be articles about that in the mainstream literature. If you have a college library (2 or 4 yr) in your town, the reference librarian might be willing to set you up on "Web of Science", basically an online paperless Science Citation Index. Even if you're not a student, they might do this as a community service; I've had things like that done for me before. Often, these articles are quite technical, but the abstract or, at the end, conclusion or discussion often are surprisingly non-technical. Let me know what you find out, perhaps post it to this thread.

In Defense of Cruttenden, Part II

Suppose that the "physical, dynamical, or Machian" frame isn't the same as the "extragalactic, stellar" frame. That is, our physical laws hold in a local frame ("ether island" or sphere; "big jello ball") that's rotating vis a vis the frame established by distant galaxies (or, for practical purposes, stars in our own galaxy).

Then, in the "stellar" frame, there's Coriolis acceleration. Suppose the principal angular momentum vector of the solar system is near the axis of rotation of the big jello ball, which counter-rotates. I've mentioned several reasons to think 52.6 AU (a function of the sun's mass and fundamental physical constants) is special; for one thing, the Edgeworth-Kuiper belt seems to end basically about there. Maybe it's the radius of the big jello ball ("ether island").

Let's suppose there's a centripetal "extra sunward acceleration" proportional to 1/sqrt(r), and taking the value 0.5*H*c, at 52.6 AU, where H is Hubble's parameter & c the speed of light. For now, I'll use H = 74.43 km/s/Mpc, because it will be shown below to correlate with 1/3 of Mercury's General Relativistic apse precession, neglecting the eccentricity correction. This H value is near the result of a meta-analysis of H determinations, which was published in the 1990s.

(The NASA website lambda.gsfc.nasa.gov, as of July 18, 2008, lists determinations of H, which they call "H0", via 15 different theories, all based on 5-yr WMAP data. Determination of H from CMB data is now thought by many to be the most accurate. Sometimes upper & lower error bars were slightly unequal; then, I averaged them. I made two meta-analyses of these 15 determinations of H, using elementary parametric statistics. For the first meta-analysis, I found the arithmetic mean of the 15, weighted by 1/sigma^2; the result is 71.42 km/s/Mpc. For the second meta-analysis, I used the CRC normal curve table to find the log of the product of the 15 one-tailed p values, at 66, again at 68 & again at 70 km/s/Mpc. Quadratic extrapolation to the max log gave 71.25 km/s/Mpc.)

The median "millisecond pulsar" deceleration Pdot/P, is about H per sec, according to my count of the pulsar catalog. If everything in our part of the universe (except millisecond pulsars) is accelerating that fast, then Hubble's redshift law is explained simply: things were slower in the past. We might wonder why millisecond pulsars here in our own galaxy are decelerating by H relative to us, i.e., not really changing; but, let's proceed.

If the "extra sunward acceleration" just cancels the Coriolis acceleration on a prograde circular planetary orbit (so we think the "stellar" frame is alright), then the big jello ball's retrograde rotation is 28.65"/century (exactly 2/3 Mercury's General Relativistic apse advancement!) corresponding to period 4.52 million yrs (thus maybe in 1:1 spin orbit resonance with something less massive than the sun, in circular orbit 27,350 AU = 0.432 light yr distant).

The ratio of the jello ball radius to Mercury's major axis, is 52.6/0.387 = 135.9, and the ratio of the major axis of this presumed very distant companion, to my best estimate of Barbarossa's major axis, is 27,350/184.52 = 148.2 (if I use my best estimate of Barbarossa's present distance assuming circular orbit, 198.4 AU, as a possibly better indication of the true major axis, the ratio becomes 137.85). So, both these distance ratios approximate the fine structure constant, 1/137.036.

Axial misalignment of 13deg (Barbarossa's inclination to the principal plane) would alter the longitude of Neptune cumulatively no more than

0.287"*(1-cos(13))*164.79/(2*pi) = +/- 0.19" (& Uranus, half that)

and would alter the change in obliquity of Mars no more than

0.287"*sin(25.2)*sin(13) = +/- 27mas/yr

which, given a moderately favorable phase, would fall in Folkner's confidence interval, [-15,17]mas/yr.

The "extra" acceleration becomes apparent for spin-stabilized (thus accurately testable because they don't need attitude thrusters) space probes not in circular solar orbit. First let's consider the Galileo probe. Approximate its orbit as elliptical, with 1AU peri- and 5AU aphelion; consider an endpoint of the minor axis as typical. I find the "extra" sunward acceleration here, project it on the orbit, then project that again (on the radius to the sun) to estimate the result of tracking from Earth. The result is 6.7/10^8 cm/s/s, vs. slightly &gt; 8/10^8 observed by JD Anderson et al.

Also let's consider Pioneer 10 & 11. Here we must add the tidal acceleration due to Barbarossa, 0.00876 solar masses, 198.4 AU distant (circular orbit approximation). Luckily both Pioneers have been nearly in quadrature with Barbarossa (& going in nearly opposite directions). Put the Pioneers at 52.6 AU, which roughly is the midrange distance for Pioneer 10 during the relevant tracking. The total ("extra", plus Barbarossa tidal) sunward acceleration, is again 6.7/10^8 cm/s/s, vs. ~ 7.8 observed by JD Anderson et al. Furthermore, the time derivative of this theoretical total sunward acceleration, is approximately zero here, explaining the approximate constancy observed.

Now let's consider the effect of the jello ball's counter-rotation, and the compensating "extra" sunward force, on planetary apse advancement. Assuming that for small eccentricity, the rate of apse advancement is proportional to the perturbation in the first radial derivative of the acceleration (it has to be an odd derivative or the convolution is zero), the "extra" force is 3/2 as effective, as the change in Coriolis force with radius during the orbit. The latter exactly suffices to keep the apse stationary in the physical frame, so the net result, for H=74.43km/s/Mpc & infinitesimal eccentricity, is that the apse advances (3/2 - 1)* 28.65"/century = 14.33"/cent., exactly 1/3 the General Relativistic apse advancement. All the planets' apses would advance at this same rate, which of course contradicts the accuracy to which their apse advancements are thought to be explained.

Whatever the eccentricity, the gradient in Coriolis force causes apse regression just equal to the frame rotation; so, the right way to correct it for eccentricity, must be to integrate r^(-1) / r^(-2) weighted by either 1/r or 1/r^2. The former weight is more plausible: it equals the potential energy, and also causes eccentricity to increase, rather than decrease, the weighted integral of r^(-1/2) / r^(-2), by a factor 1 + e^2 * 3/16, with error = O(e^4). This increases the net apse advance by a factor 1 + e^2 * 3/16 * 3, and thus lessens the H needed (to give exactly 1/3 the General Relativistic apse advancement) to 72.70km/s/Mpc, for Mercury's e = 0.2056.

To achieve the observed lack of any net unexplained advance of the apses, it's necessary somehow to divide the slope of the 1/sqrt(r) "extra" force function, by 1.5*(1+e^2*3/16). If the "extra" force were a Bessel function, its envelope would approximate 1/sqrt(r) (see, inter alia, Jahnke & Emde, Tables of Functions, 4th ed., sec. VIII.2.a, p. 138). The Bessel function of the 2nd kind (a.k.a. Neumann a.k.a. Weber function) of order -1/3, N(-1/3)(x) (Jahnke & Emde, 4th ed., sec. VIII.1.c, p. 131) has peaks at abscissae whose ratios resemble those of the major axes of Earth, Jupiter, Saturn, Uranus and Neptune (Jahnke & Emde, 4th ed., Fig. 77, p. 141, shows the first three peaks; the peaks are thereafter almost exactly equally spaced). For Saturn, the correspondence is better with the second peak of the Bessel function of the 1st kind of order -1/3, J(-1/3)(x); Venus corresponds to the first peak of the Bessel function of the 1st kind of order +1/3, J(+1/3)(x) (Jahnke & Emde, Fig. 77 again). N(-1/3) & J(+1/3) are negatively infinite at zero; J(-1/3) positively infinite. Four of the first ten peaks of the 1/3 order Bessel functions, i.e. J or N (+/- 1/3), correspond to Venus, Earth, Jupiter & Saturn.

The orbit of the planet might lie between the peak of the appropriate Bessel function, and the nearby tangent point to the envelope, at an intermediate point where the slope is 2/3 (or, with Mercury's eccentricity correction, 0.6614) that of the envelope. Then the total apse advancement would be zero in the stellar frame; that is, the apse advancement due to the "extra" force would equal not 1.5x, but rather 1x, the apse retardation due to the effective gradient in Coriolis force for the elliptical orbit.

I found these points for N(-1/3)(x), using the ratio 0.6614 appropriate to Mercury, but the ratio 0.6667 appropriate for small eccentricity would have given practically the same results. First I expressed N(-1/3)'(x) as a sum of four J(q)(x) functions (i.e., Bessel functions of the first kind) using the definition of N, and the identity relating J'(q) to J(q-1) & J(q+1) (see, inter alia, Franklin, Advanced Calculus, McGraw-Hill 1944, sec. 154, eq. 134, p. 390). Then with an IBM 486 computer I found the solution by successive approximations using from 14 to 40 terms of the usual power series for J(q)(x) (in, inter alia, Apostol, Calculus, vol. 2, 2nd ed., sec. 6.23, eq. 6.59, p. 185). For the 1st & 2nd points (Earth & Jupiter), single precision was adequate; the 3rd & 4th points (Saturn & Uranus) required double precision; even this failed for the fifth point (Neptune), but the earlier points proved that by then, the interval between points had become practically constant. I found the corresponding point for Venus (the 0.66 slope point just to the right of the first peak of J(+1/3)(x)) graphically on Jahnke & Embde's Fig. 77, and likewise the (better than N(-1/3) ) Saturn point on J(-1/3). The ratio of each planetary major axis to the next, is accurately given by this theory, except for an unexplained constant factor:

Planet pair / major axis ratio predicted by N(-1/3) :: ratio observed

E:V / 0.89 (using J(+1/3) for Venus)
J:E / 0.873
S:J / 0.85 (using J(-1/3) for Saturn)
U:S / 0.81 ( " )
N:U / 0.832
U:J / (0.832)^2

All planets except the smallest, Mercury, Mars and Pluto, conform. The ratio, ~ 0.85, might be explained by a change of independent variable. Also the model underestimates the Galileo & Pioneer accelerations by ~ 6.7/7.9 = 0.85.

The measured "extra" force might equal max{several Bessel functions}, having a scalloped shape, so that the Galileo & Pioneer accelerations approximate the envelope of Fig. 77, while at a finer level of detail, the local derivatives adjust the apse advancement rates.

Cruttenden's main thesis, is that the entire solar system revolves in some way that is difficult to appreciate. The above facts suggest, that Cruttenden's thesis may well be substantially correct.

JK, If simple explaination is found in SN events way do you go to extreme ends to explain things? A SN event would eject about 5 solar masses of stuff and there have been millions of SN events in the Milkyway since it formed so all you need to understand is some tiny part of all that mass has come into the gravational field of the sun.

JK, It could be the moons of Jupiter are captured scraps of SN events from the way back times so maybe all the planets, moons and other stuff now captured by the gravity field of the sun also came from SN events. There could have been many more SN scraps passing this way in the distant past. All that stuff would alter your calculations-don't you think?

Lets say that our sun went type two supernova, tomorrow. As Joe pointed out, Jupiter and Saturn could survive but they would be sorry states, they would be reduced right down to their rocky cores. They would also be flung out of the solar system sling shot fashion.

Stuff like the Oort belt would stay in orbit but would be vaporised. Now it simply is never going to happen, our sun doesnt have the mass to go nova.

We can work out the probability of our solar system being within ten parsecs of a supernova, through its lifetime, as being about six events. When this probability was much higher, when we were in a stellar nursery, type two supernova would undoubtedly have had major effects upon the evolution of our system.

Type two supernova are massive young stars, they won't have planets but they will have lost angular momentum by spewing out giant jovian balls of material which later could become planets. They never get the chance as the young sun burns its fuel in a couple of million years. These gobbits, I cant even see them as proto-planets, would be torn apart by a super nova. A nova is not going to send out anything other than a hot gas of elements.

If the young sun is one of a binary, and the other star is within about 20 a.u. then when one goes nova, the other can be slung shot out at it previous orbital angular velocity. Though, even in a stellar nursery the chances of such a run away star coming anywhere near another star is miniscule.

Really, all that I can see as possible fairly Hefty bit of junk coming from a nova, would be the odd, much reduced, Jupiter or Saturn, from a type one supernova. A sun capturing one of these is so unlikely as to be ruled out completely. it would simply pass through on its way to god knows where.

This does leave the question of, what is the nature of this supernova event? Its an implosion followed by an explosive after shock. All of a sudden, all of the protons in a suns core have to change into neutrons. These are heavier than protons, so energy is needed from someplace. Gravitational energy can create mass, I would argue that electromagnetic energy is far to feeble to do the job on its own.

(Edited) Monkeying about with this, if we had a sun made of nothing but iron and hydrogen, then the iron core would be about 1.6E 25 kg. Multiply that by the proton mass divide by the neutron mass and take the result from the original mass. That give us about 2.2E 22 kg.

What I think is happening is that aether particles have to get out of the way to let the core collapse. An h amount of gravitational energy is converted to electromagnetic energy. This at the hydrogen iron boundary of the star, 2.2E 22 kg is a lot of bang for your buck over this small surface area.