Joe, in that original thread I remember commenting I wasn't so certain a supernova explosion hundreds or thousands of AUs from the sun would have had such a drastic effect. ...

Thanks for your input! The articles I've seen suggest that supernovas so rarely have surviving planets, that in one rare instance of an apparent planet of a pulsar, they thought it was likely a stellar fragment instead. Let's make a calculation:

Utrobin, Astronomy Letters, abstract, Dec. 2005:

"...accordingly, the explosion energy of SN 1987A is (1.50 0.12) 10^51 erg..."

Let a planet have radius r, density 1 in cgs units, and distance R from a supernova like SN1987A. The planet's gravitational self-energy is

16*pi^2/9*6.673/10^8 * r^5

while with albedo, say, 50%, the absorbed energy is

50% * 1/4*(r/R)^2 * 1.5*10^51

so planetary survival barely occurs when

r^3*R^2 = 1.6*10^56 in cgs units.

For R=200AU, a low-density (Jovian-like) planet must have r=2615km. (A higher density helps because self-energy = density^2 for given r; on the other hand, once the planet starts to blow up, it's bigger and receives more energy.) For R=5AU, r=30580km, so by this estimate the giant planets, even Uranus, would survive, even if the sun went supernova. All the planets except Pluto would survive a supernova at 200AU.

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?

...The total energy of the [supernova] event can be reasonably estimated but how would the ejected mass be estimated?

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.

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

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 > 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

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.

Sloat, If a central mass of a system suddenly explodes in a SN event and a large fraction of the mass is no longer at the center of the system then the orbits of everything in the system are going to be altered even the Oort orbits-don't you think? How does the system survive? The mass is free of the system because of the event and its future is unknown.

Hi Jim, lets build a scale model of our solar system. Yeah I know you hate models but this model often surprises people in pubs. The sun is a billiard ball, where is mercury? Just about everyone points a finger almost touching the billiard ball. Mercury would be two metres away from the ball. The Earth seven metres. Jupiter would be forty metres, and pluto three hundred metres. The nearest star would be two thousand kilometres distant.

So, lets have our billiard ball go supernova. If I knew that billions of tonnes of hydrogen was about to hit me, travelling at thousands of kilometres per second, i dont think i would bother getting out of bed. It would simply vaporise the inner planets. Jupiter and Saturn would gravitationally respond to the suns centre of gravity, at first. However, once they were inside of the explosion envelope, most of the mass of the sun having past them at a great lick, they would flick away like a stone from a sling shot.

Past about twenty a.u. the gravitational influence of the explosion wall cannot compete with the influence of what remains of the sun. Orbits will alter but they will still be orbits of the parent body. It would be wrong to think that the wall is now fairly tolerable, it would still destroy Neptune and pluto, though there might be a few rocks left from Neptune.

I suppose we could do the sums to see whether the dirty snowballs that make up the Oort belt would survive, that might while away a pleasant hour. Barbarossa would survive and stay in orbit.

Again though, this cannot happen to our sun. Its a moot point about stars that become type one supernova. Do they have planetary systems? Is our solar system the result of being part of a failed binary system? We have about two hundred solar systems on record at the moment. They all seem to have gas giants close in to their suns. We need a new telescope in space to try and find terrestrial type planets.

Type two supernova must play their part in Joes ideas but not so much as to throw any of his calculations out of whack. Supernova in stellar nurseries will initiate star formation through the dust clouds and deliver stores of heavier elements. They cannot deliver chunks of planets, because they havent had time to build them.

Sloat, I don't hate models-my issue is in the overuse of models and making gods of them as is the case with the BB model. The thinking process is a captive of this modeling. Anyway, if the central mass of a system gains or loses mass everything orbiting that center is effected so Neptune and whatever is in the Oort belt is going to excape if the sun happened to lose most of its mass. And back to SN events-the ejected mass from the event that came our way would have an effect on the mechanics of the solar system even if it passed through leaving none of its mass and it seem likely some of the mass would be captured by the gravity system of the sun. So, if there is no way to know how many SN events have occured and effected the solar system during the past 10 billion yeaars why not just use the probibility that SN events have had an effect.

...The thinking process is a captive of this modeling. Anyway, if the central mass of a system gains or loses mass everything orbiting that center is affected so Neptune and whatever is in the Oort belt is going to escape if the sun happened to lose most of its mass. ...

"Past about twenty a.u. the gravitational influence of the explosion wall cannot compete with the influence of what remains of the sun. Orbits will alter but they will still be orbits of the parent body. It would be wrong to think that the wall is now fairly tolerable, it would still destroy Neptune and pluto, though there might be a few rocks left from Neptune." Is there any hard data about this "explosion wall" being able to "destroy" a large planet at Neptune's distance? Most of a supernova's energy is spent as electromagnetic radiation. I recall reading somewhere that every star in the galaxy could fit in a spherical shell the size of the solar system without touching. Space is big, really big.

nem, The SN event must be more than just light because the star before and after is a very different star. The event must eject a large fraction of the mass of the star before the event-or not--?

The value H = 72.70 km/s/Mpc, becomes 72.65 when all of the e^(2*n) terms are included.

The Bessel functions of order +/- 1/3 are related to the Airy functions, which often appear in mathematical physics, e.g. in Airy's original application, the caustics of light rays (Watson, Theory of Bessel Fns., sec. 6.4, p. 188; same for 1922 ed. or 2nd ed., 1952). Also, Bessel functions of large order can be approximated, by algebraic functions multiplied by Bessel functions of order +/- 1/3 (Watson, sec. 8.43, eq. 1, p. 249; either edition). In such approximations, the argument of the one-third order Bessel fn., is an algebraic function (of the original independent variable) which might approximate a logarithmic transformation. So, the pattern I noticed in Part II above, might occur because the actual "extra" force is a large-order Bessel function.

Im sure Joe wants to continue with his calculations and just make a note of supernovas and their effects upon star formation. Maybe another thread someplace?

((Major aside) Thinking about balls of jelly and the cores of neutron stars, ignore this bit, as its just a note to myself to look into something. We have the light speed being absolute lorentzian of Einstein, then we have a lorentzian for the possible speed of gravity, call it b. So, 1 - c^2 / b^2 = (1 / h *2GM) / rc^2 The h is just to scale things to my proposed speed of gravity. We get, rc^2 / (1 / h *2G) - rc^4 / (1 / h *2G *b^2) = M

The first term has to equal one, at the speed of light. The second term has to equal h at the speed of light. There has to be a variable missing in that first term, or h varies from its value to the value one.)

About supernovas, the estimates are that there are about one hundred million neutron stars in our galaxy.

Could all of the stars in the galaxy fit into a ball of the radius of plutos orbit? Yes.

Is most of the energy e.m? No, the explosion is busy making new heavy elements, which release em energy but we are not seeing total mass to energy conversion at any appreciable level. The explosion envelope is mainly matter doing more than 1000 km per second. A Neptune has a heat shield atmosphere but this wall of gas and heat that hits it is truly mind blowing.

The star that remains after the event is still going to be more massive than our sun. The orbit of any planets that survive are going to change but they cannot escape. Planets within twenty a.u. can be slung shot out of the system. The chances of our capturing one are minute, the effects of one hurtling through our solar system would be minute also.

(Edited) I just took a look at the orbital velocities of our planets, they are way too low. Their orbital eccentricities would alter but they wouldn't escape. The only thing that could would be a binary companion star.

Sloat, The SN event is real and the neutron star is a model. The real event seems to indicate mass is ejected if stuff astronomers believe are SNRs really are that. There must have been billions of SN events and if half the mass of a star is ejected in the SN event there is billions of solar masses of matter flying through the universe and a very tiny fraction must come our way. It might be the SN event happens at that rare and unlikely meeting of stuff flying at just the right parameters and just the right star. If a butterfly can start a chain of events---?

Hi Jim, I suspect that the estimate of how many neutron stars there are; and hence how many supernova, theres been, is based on the big bang theory. In another thread I argued that to get a one to one correspondence between gravitational space and electromagnetic space, the radius of the electromagnetic universe had to multiplied by eight thousand.

This was to allow light, travelling extremely slowly vis a vis gravity, to move a distance equal to the Compton wavelength.

The upshot is that our galaxy can be much older than is thought. It would have graveyards of neutron stars. These things are the mass of a sun but they have been crushed into something about the size of the Earth. They are therefore hard to see. There would be more of them than the stars we can see. I get about 8% of the galaxys mass being ordinary stars and the rest dead neutron stars.

The down side of this argument, is that neutron stars make an almighty row. They spin so fast that radio telescopes pick up their noise. Of course thats not all of them, their poles have to be roughly pointing towards us. The other points to bear in mind are, what is the mean birth rate of stars, and how many totally dead white dwarfs i.e. black cinders, are there.

Stoat, white dwarfs are about the size of Earth. Neutron stars are much smaller, a few kilometers across, smaller than many large cities. Also, the "noisy" ones are very young, a few centuries to around a million years old. A very old one, billions of years old, would have become quiescent and cooled to maybe a dull red heat. It would be very difficult to detect, even if nearby.

Hi Nemesis, yeah youre right, I was being a bit sloppy but I was just after rough sizes to see whether JIms model could hold up.

From the equation I gave a couple of posts up we can work out the Schwarzschild radius. For a sun of six solar masses, 1 - h = 2GM/r c^2 Might as well ignore that h and say its one. We get about 18 km radius. Now if we say that at that radius the refractive index of space becomes negative then we can alter the lorentzian to become 1 + hx up to the speed of gravity, which will give us 2 = 2GM/r c^2 Dump that two from both sides and we have another radius exactly half the Schwarzschild radius.

Instead of having a gravity well shaped like a V rotated round its vertical axis, we would have a gravity well shaped like a W. It can never become a black hole.

Now the idea that a white dwarf can radiate away to a black dwarf is fine. We wouldnt know where they are, even if they were pretty close. Neutron stars are a different ball game though. They will lose angular momentum in time, through the ginormous electrical fields they generate. I cant see them losing their energy fast. They are so close to that important radius that light has a hard job getting out, it will be red shifted enormously. As the star slows the red shift will drop over time, the problem then becomes one of, how does neutronium work?