Requiem for Relativity

Dr Joe, I don't understand what the "isothermal speed of sound" means. How can sound exist in the vacuum of space? I suppose the existence of sound needs matter unlike light that exists even without matter.

<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 />Dr. Joe, ...what the "isothermal speed of sound" means. ...vacuum of space?...
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Hi Jim,

My source for the formula, was Hausmann & Slack's old college physics text. There isn't any definite cutoff at which sound disappears. For example, a rocket can exceed the speed of sound even though the atmosphere is very thin at very high altitude.

There are a few hydrogen atoms and/or protons per cubic centimeter in interplanetary space. It would be difficult to impart much sound energy to such a medium using, say, stereo speakers, but something huge like a nova could impart much sound energy to it. Also, the continuum approximation used for studying sound, would apply (in interplanetary space) only to long wavelengths.

Isothermal means that the temperature of the medium is constant over time. The speed of sound isn't the same, if the sound isn't isothermal (i.e. if the medium is significantly heated and cooled by the compression waves each cycle).

- Joe Keller

Dr Joe, Sound waves transmit energy but, not much even in dense matter. How much of an effect would sound waves have when the density is a few particles per cubic meter?

<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote"><i>Originally posted by Joe Keller</i>
<br />Roland, Iowa March 16, 2007

Open letter to the Director of the Lowell Observatory

...Assuming a circular orbit and making first order approximations to correct for Earth parallax, Barbarossa has period 2640 yr. and is 191 AU from the sun. Accordingly, the resonances of the orbital periods of the outer planets have discrepancies which advance prograde with periods

Jupiter:Saturn 5:2 2780 yr
...
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In March, 2007, I told the Lowell Observatory (in direct emails similar to the above "open letter" on p. 8 of this messageboard thread) that Barbarossa's orbital period is similar to the period of advance of a Jupiter-Saturn conjunction; that is, Barbarossa shepherds the Great Inequality.

In 2009 I fitted an elliptical orbit to the sky surveys. At the latus rectum of an elliptical orbit, the relationship between distance and angular speed, is the same as for a circular orbit. So, near the latus rectum, as Barbarossa has been in recent decades, a circular orbit will fit the (geocentric) observational data with only a small error. In its actual elliptical orbit, Barbarossa's angular speed at its latus rectum, matches the average speed of advance of the Jupiter-Saturn conjunction.

Using the 6339.36 Julian yr orbital period and 0.610596 eccentricity, I find at Barbarossa's latus rectum (reached at 2003.94 AD) an angular speed consistent with a period of 3148.7 Julian yr. At Dec. 21, 2012 (true anomaly = 91.022deg) I find (heliocentric) angular speed consistent with a period of 3218.4 Julian yr.

The mean period of advance of a given Jupiter-Saturn conjunction point (i.e. a given corner of the "trigon") is exactly 3x the "Great Inequality", i.e. 3 * 1/(5/S - 2/J) where J & S are the periods of Jupiter & Saturn, resp. The present-day Great Inequality (as in the time of Laplace) is about +900 yr, but

"...the GI's average period is...1092.9 years;..."

- Ferenc Varadi et al, "Jupiter, Saturn, and the Edge of Chaos", Icarus 139:286-294, 1999, p. 287, col. 2

Three times the average GI given by Varadi, is 3278.7 yr, only 1.9% longer than period corresponding to the heliocentric angular speed of Barbarossa at the end of the Mayan Long Count.

Most of the discrepancy disappears when the motion of the trigon point, is projected onto Barbarossa's orbital plane. Barbarossa is inclined ~14.5deg to the angular momentum-weighted mean orbital plane of Jupiter + Saturn (about the same as the principal plane of the solar system) and at 2013.0AD is ~68deg past its descending node on that plane. So the angular speed of the trigon point, projected onto Barbarossa's orbital plane, corresponds to a period of roughly

3278.7 * cos(14.5*sin(90-2*(90-68))) = 3224.5 Julian yr

only 0.19% longer than the period, P = 3218.4 yr, corresponding to Barbarossa's angular speed at the end of the Mayan Long Count. A more precise calculation of the projection, using a modern value of the Jupiter + Saturn combined angular momentum vector, and spherical trigonometry, gives

3278.7 / 1.02287 = 3205.4 Julian yr

which is 0.40% shorter than P. A 0.4% error in the speed of the trigon point, corresponds to only 1 part in 30,000 error in Jupiter's average orbital period.

According to NASA's Fact Sheets, for sidereal years of the planets, J = 4332.589 days, S = 10,759.22 d, U = 30,685.4 d, N = 60,189 d, P = 90,465 d, M=686.980 d, and V = 224.701 d (I'll use Wikipedia's V = 224.70069 d). Also, E = 365.25636 d. The Neptune-Pluto inequality is 1/(3/P-2/N); this is -41,068 Julian yr (the same length as the Milankovitch cycle), and also equals the period of regression of the Neptune-Pluto conjunction point. The Jupiter-Neptune inequality is 1/(14/N-1/J) = +1528.0 Julian yr. To get the period of progression of the conjunction point, this must be multiplied by 14-1=13, giving +19,864 yr, (negative) half the Neptune-Pluto regression period. Likewise 1/(11/N-2/S) = -874.9 yr; *(11-2) = -7873.8 yr, a fifth of the Pluto-Neptune regression period. We have

S / J = 2.48 and
19864 / 7907.9 = 2.52

that is, the mean conjunction points of Jupiter (13 points, i.e. a 13-gon) and Saturn (9 points, a 9-gon) with Neptune, move in the same 5::2 ratio as do Jupiter and Saturn themselves, though the J-N conjunction is the slower, and the S-N conjunction moves retrograde.

Earth's conjunction points with Jupiter (an 11-gon), move prograde with period equal to the Great Inequality:

11*1/(12/J-1/E) = 944.0 Julian yr

Varadi gives the average value of the Jupiter-Saturn Great Inequality as 1092.9 yr, but the current value is

1/(5/S-2/J) = 883.19 yr

so the Jupiter-Earth mean conjunction progression is between the current and average values of the GI.

The Venus-Earth conjunction point moves retrograde, with period 5*1/(13/E-8/V) = -1192.8 Julian yr. This is also rather near the long term average value of the GI.

The mean conjunction of Saturn and Uranus moves prograde with period 2*1/(3/U-1/S) = 1135.4 yr. Suppose that originally the PI had its average value, and the Saturn-Uranus conjunction moved forward with period equal to the PI. If the semimajor axes of Jupiter and Saturn are conserved, and their eccentricities remain small, then conservation of angular momentum between Jupiter and Saturn requires that the increase in Saturn's angular speed almost exactly equals the decrease in Jupiter's angular speed. So, half the change in the PI is due to Saturn and half to Jupiter. If the Saturn-Uranus interaction is comparatively small, then the decrement in the frequency of the Saturn-Uranus conjunction progession would be due only to Saturn and would be 1/2 * (3/2)/(5/3) = 9/20 as much as the increment for the Jupiter-Saturn progression (proportionally, 9/20*1/3 = 3/20):

1092.9 / (1 - 3/20*(1092.9/883.19-1)) = 1133.3 yr

only 0.19% less than the actual value. Because the (proportional) change in frequency due to the Jupiter-Saturn interaction, is only 3/20 as much, this might afford a better estimate of the average PI:

1092.9*1133.5/1130.9 = 1094.925 yr

then times 3, and correcting for projection of the Jupiter+Saturn plane,

1094.71*3/1.02287 = 3211.33 yr

only 0.22% shorter than P above.

Let's consider Mars analogously to Uranus. Most online sources use NASA's value of 686.980 d for Mars' period, though some still quote 686.95 d (the older accepted value, e.g. Inglis, "Planets, Stars & Galaxies", 3rd ed., John Wiley, 1972). Mars' eccentricity and proximity to Earth and Jupiter make exact long-term average orbital period calculation hard. Proceeding anyway, I find that the Mars-Jupiter conjunction point progresses with period

(19-3)*1/(19/J-3/M) = 2376.955 yr = 2*1188.48 yr.

Analogously to Uranus, I get the fraction 1/2*(19/16)/(5/3)*2/3 = 19/80 and

1188.48*(1 - 19/80*(1092.9/883.19-1)) = 1121.46 yr

which is about 2/3 of the correction needed to get the average PI.

From Wikipedia's recent values (citing Chapront, 1991), for the various kinds of month lengths with their linear secular trends, I find P = period of progression of the Lunar apse and N = period of regression of the Lunar node. A mean conjunction of the node and perigee (one of the points of the trigon of three conjunctions), progresses with period

3*1/(1/P-2/N)
= 549.49 Julian yr = 1098.98/2 for epoch 2013.0AD
= 546.98 J yr = 1093.96/2 for epoch 2013.0AD-6339.36 J yr = ~4328BC

Using instead, the fourth degree polynomials for accumulated advance or regression, in Simon et al, Astronomy & Astrophysics 282:663+, 1994, p. 669, sec. 3.4.a.1, I find

549.48 Julian yr for epoch 2012.97 AD and
547.36 Julian yr for epoch 2012.97AD-6339.36 = ~ 4328BC

(Chapront's linear corrections for the month lengths, amount to second degree truncations of Simon's formulas.) There is a small error from defining the nodes relative to the fixed J2000.0 plane as in Simon's sec. a.1 formulas, but Simon's a.2 formulas refer to the equinox & ecliptic of date; when I use Newcomb's linear formula, for the precession in 4328BC, these a.2 formulas give 547.30 yr, in excellent agreement with a.1.

Doubling the progression period of the Lunar perigee/node conjunction, and using spherical trigonometry to correct precisely for the projection of the present ecliptic (the 6000 yr change in the ecliptic is less than significant, at this precision) on Barbarossa's orbital plane, I find period

547.36*2/1.018001 = 1075.36 yr

and tripling this, 3226.09 yr, only 0.24% longer than P, the period related to the instantaneous angular speed of Barbarossa on Dec. 21, 2012. (Earlier I estimated that my orbit fitting to the sky survey points involved about +/- 0.11% error in the period.)


*********

Digression (Nov. 11, 2010): Force is a signal, not a field.

In late 2000, almost a decade ago, I discovered a new theory of force. I immediately gave a copy of the calculations to Prof. T. at Oxford.

In my freshman physics course at Harvard, Prof. Purcell emphasized the well-known fact that field lines from a relativistic electron in rectilinear motion, point toward its present position, not its retarded position: as if lightspeed were infinite. If the electron is accelerated, then the field lines point as if lightspeed were infinite but the motion were linearly extrapolated from the time the light signal left the electron.

It seems to me that not only must the observer detect a signal from the electron; also the electron must detect a signal from the observer. A lightspeed signal goes from the observer to the electron, and an answering signal immediately returns from the electron to the observer. Each time, the body detecting the signal responds to the linearly extrapolated position of the body emitting the signal.

My theory in 2000, which I quantitatively verified, was that general relativistic perihelion advance, arises simply from force transformed according to special relativity, assuming that there is such a two-way interaction. The general relativistic effect, is the difference between ideal instantaneous transmission, and the actual two-way lightspeed transmission which adjusts itself to emitter motion only to linear order each way.

Gravity between Barbarossa and, say, Jupiter, could be summarized as BJB or JBJ; this is two-trip force, the simplest possible. The next simplest kind of force would be four-trip force, e.g. BJBJB or BJBSB; the latter, rather than any tiny (two-trip) gravitational advantage, would explain Barbarossa's effect on the Jupiter-Saturn resonance (which Barbarossa saves from chaos). Another four-trip force would be JBEBV, which starts and ends nearby, rather than at Barbarossa, therefore must be adjusted by the reciprocal of the projection factor used above. Next, let's use this theory to reconcile the E-J and V-E resonances with the GI.

*********

The difference between the E-J and V-E conjunction progression (or regression) rates corresponds to the period

1/(1/944.0 + 1/1192. = 526.96 yr

times 6 and *multiplied* (because it is a four-trip four-body interaction; see "Digression" above) by the projection factor for Earth's orbit,

526.96*6*1.01800 = 3218.7 yr

only 0.01% longer than P, a perfect result to the significant digits available.

In Bretagnon et al, A&A 400:785+, 2003, Table 2, the 7th degree polynomial for accumulated precession (equivalent to a 6th degreee polynomial for precession rate) gives a precession period of 26,391.5 yr at 2012.97AD - 6339.36 = ~4328 BC. This is about eight times the GI, and with correction for projection of the ecliptic onto Barbarossa, gives

26,391.5 / 8 / 1.018001 = 3240.6 yr

only 0.69% longer than P.

Collecting these results, which are corrected for projections *onto* Barbarossa's orbit (or for the Venus relation, *of* Barbarossa's orbit):

Varadi's average Great Inequality x3 underestimates P by 0.40%
presumed average Saturn-Uranus resonance x3 underestimates by 0.22%
Lunar perigee/node resonance x6 @ 4328BC overestimates by 0.24%
modern E-J minus V-E resonance x6 overestimates by 0.01%
4328BC Earth precession /8 overestimates by 0.69%

The five estimates averaged together exceed P by 0.06% with Standard Error of the Mean +/- 0.19%. Omitting the Earth precession result, the average is 0.09% less than P, with SEM +/- 0.16%.

Summary. Barbarossa's angular speed at the critical point in its orbit (at Dec. 21, 2012AD) equals the *average* mean rate of change (*according to Varadi*) of the longitude, in Barbarossa ecliptic coordinates, of the Jupiter-Saturn conjunction trigon at Barbarossa's longitude. The Saturn-Uranus conjunction, the Earth-Jupiter conjunction, and the Venus-Earth conjunction, all progress or regress at ~3x the rate of the Jupiter-Saturn conjunction; for the Saturn-Uranus conjunction, the period of progression equals exactly the average Great Inequality, after correcting for Saturn's contribution to the change in the Great Inequality from its average value. The difference between the E-J and V-E rates, and the Lunar perigee / Lunar ascending node conjunction rate, both progess at 6x the speed rather than 3x. Earth's precession is at 1/8 the speed.

With projection onto Barbarossa's orbital plane at Barbarossa's longitude, the synchrony with Barbarossa is very exact, using 3x the theoretical average Great Inequality, either as given by Varadi or as accurized via the Saturn-Uranus conjunction. It is also very exact, for 6x the mean Lunar perigee / Lunar node conjunction period.

Hi Joe, something that may be of interest. I was taking on a webpage to a woman who is writing her second book on myth and christianity. She asked a question about the planet Mercury, as she was looking at astrological charts. I explained a it about elongation and told her to get a copy of the free Celestia star program.

Then she came back on and cried for help. Wikipedia had given a list of solar eclipses in historic times and there was one for Jerusalem in 303 bce. She's looked at it and nothing! Then she'd found a really good eclipse for the year 301 bce with the aid of the program. She also said that it lasted all day!! I explained that thee date was to with the changes made in the calendar and there being no year zero but with a year zero for astronomy. Two years and ten days error. I also said that a total eclipse can't last all day.

So I looked at the event in celestia. Highly unusual, the moon does partially eclipse the sun for the whole day. Now I've said to her that the drop in light intensity would be difficult to notice, as the human eye is very good at adjustment but the temperature drop over the day would be noticed, and animals would be going ballistic all day. Then we've got Venus in the sky ahead of the sun and Jupiter and Sirius appearing at sun set.

Have you got anything on what the temperature drop would be in Jerusalem?

(Edited) I think I should stress here, that the partial eclipse seems to be a particularly good fit for this eclipse in Jerusalem. Saros cycle?

Sloat, You can use the NASA JPL horizons generator to determine when events like this occurred. I'm confident the NASA generator is the best available but not exact because basically its just a model.