In Defense of Cruttenden
Howard Carter's "Tomb of Tut" (vols. 1-2, 1923; vol. 3, 1933) was co-authored with "A. C. Mace", which according to ISU's library catalog was the pseudonym of Arthur Cruttenden. Apparently Walter Cruttenden comes from a line of Egyptologists. Mommsen championed the use of monument and inscription data in Roman history. Newcomb, Eckert, Brouwer, Clemence, and Rawlins all carefully studied Lalande's 18th century Neptune positions; Cruttenden, like Mommsen, takes this beyond old papers, to even older stones.
According to Heiskanen & Moritz' "Physical Geodesy" (Freeman, 1967) Sec. 9.6, pp. 349-350, Helmert in 1884 already had determined Earth's quadrupole ("J2") to 0.4% accuracy by considering its torque on the moon's orbit. Essentially repeating Helmert's work with artificial satellites, improved this accuracy to 0.02% or better, already by 1966. Various orbiters now have done similarly for Mars.
Earth's orbit around the sun precesses only 0.1"/yr (Mars' orbit, only a little more)(vs. 20deg/yr for the moon's orbit around the Earth) and almost all of that 0.1", is due to the planets. So, it's impossible to measure directly how much Earth's rotation is torquing Earth's orbit; i.e., how much Earth's orbit really is torquing Earth's rotation, assuming only Newton's third law of motion. However, the measured precessions of Earth and Mars (for Mars, see Edvardsson & Karlsson, AJ 135:1151+, 2008; Bouquillon & Souchay, A&A 345:282+, 1999) conform accurately to Newton's law of gravity, given the quadrupole values measured with satellites.
Cruttenden's first, astronomical, thesis is basically that the sun has a massive, distant, undetected companion. Cruttenden's second, physical, thesis is basically that the phenomenon of planetary precession is yet improperly explained. All I've written above on this messageboard, about a planet Barbarossa near 200 AU, could be used to defend Cruttenden's first thesis. In the remainder of this message, I make four lines of defense for Cruttenden's second thesis:
1. Bouquillon & Souchay, 1999, Table 5, p. 294, say Mars' J2 = 1964/10^6 (IAU value). This is 81% more than Earth's J2 = 1082.63/10^6, as published, inter alia, in Bomford's Geodesy, 4th ed., p. 418. Earth is only 40% denser than Mars; their days are practically equal. In the homogeneous case, Mars' J2 should be only 40% greater than Earth's. The case of a small dense core, gives the same J2 as the homogeneous case. Mars' J2 seems to me to be too big to be consistent with Newton's laws. Even Earth's J2 is suspiciously near the "hydrodynamic" (ball of water, or ball of sand) upper limit, and Mars seems to me to exceed that limit.
Maybe an extra precession, w2, equal for all planets, is imposed externally. If Mars' J2 were, as I calculate it should be, only 1.4x Earth's, then solar (for Mars) and lunisolar (for Earth) precession would impose, I calculate, 15x more precession on Earth than on Mars; call these precessions 15*w1 & w1 for Earth & Mars, resp. Solve the system
15*w1 + w2 = 50288mas/yr
w1 + w2 = 7576mas/yr
(Mars precession from Folkner et al, Science 278:1749+, 1997)
to find w2=4525mas/yr. Perhaps reversing the usual cause and effect, J2 then alters, to that consistent, via Newton's laws, with the total precession. This extra precession corresponds to a period, for the entire solar system, of 286,400 yr, a circular orbit of 4345AU = 0.07 lightyear (somewhat closer than the Type M7 Proxima Centauri is, to its companions), with solar gravitation at that distance, 3.18/10^8 cm/s/s. Mars' orbit is about a degree from the principal plane of the solar system, so suppose w1 & w2 differ in direction by a degree. Then w2 changes Mars' obliquity by as much as 4525*sin(25)*sin(1)=33mas/yr. Folkner (1997) thought the true confidence interval for Mars' obliquity change, is [-15,+17] mas/yr, i.e., 5 sigma, vs. the statistical confidence interval 1 +/- 3 mas/yr. The relative positions of the solar system's principal plane, Mars' orbit, and Mars' axis, multiply 33mas/yr by a sine not quite small enough to bring it into Folkner's confidence interval.
2. Jupiter, Venus, and Mercury have axes nearly perpendicular to their orbits (Mercury & Venus have slow spin-orbit locked rotation). Earth, Mars, Saturn, Neptune, and Uranus have greatly tilted axes. As seen from the sun, Mercury's mean angular diameter is slightly less than Earth's; but it is Mercury, Venus, and Jupiter, which have the largest angular diameters at perihelion. Here might be a form of gravity quantization: perhaps the sun "sees" the quadrupole of planets differently, when they subtend small angles. This could affect precession.
3. The coordinates of the planets' poles are found in, inter alia, the 1984 American Ephemeris and Nautical Almanac, p. E87. Uranus, Neptune, & Mars cluster between RA 295 & 318, while Saturn is only 6deg from Earth's pole, and these five lie approximately on a smooth curve. Not only are four planetary tilts curiously similar in magnitude; the spin angular momentum vectors of these planets plus Uranus cluster on a curve (while the other three large planets cluster at the ecliptic pole).
The five planets' spins make what NMR spectroscopists call the "magic angle" ( arccos(1/sqrt(3))=54.7deg ) with WW Campbell's approximate compromise solar apex motion vector (still called the "standard apex" as late as 2003; Drobitko & Vityazev, Astrophysics 46:224+, p. 229, 2003). At the bottom of the curve, Uranus' spin is 51deg from Campbell's apex (RA 270 Decl +30). At the top of the curve, Earth & Saturn are 60 & 63deg, resp. Mars is ~ 43deg. Most solar apex determinations find RA < 270 and Decl > 30, which equalizes the distances even more. Intermittent torque around the solar apex axis might maintain this configuration.
4. The ~ 300,000 yr presumed common precession period, might be the rotation period of an ether island or sphere, like a clear ball of jello centered on the sun, orbiting some body so that its same face always is toward it; or it might rotate in the absence of any such body. A stress in the ether, causing an extra force proportional to 1/sqrt(r), could compensate so that the orbital periods of the planets suffer no net effect.
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Mars has the same day as Earth, perhaps because Mars was, until geologically recently, Earth's distant moon. Maybe Luna was a moon of Mars and got cratered by asteroids on the side away from Mars. When Earth lost Mars, Earth took Luna but flipped it sunny side down, so we see the maria. Until the recent Earth/Mars separation, Luna wasn't close enough to Mars or Earth, to change their days much.
The Earth/Mars separation is geologically recent enough that Luna hasn't had time to slow Earth much. The date of the separation can be determined from when Mars froze. Maybe synchronized orbital pumping by Jupiter did it. Maybe benevolent ETs foresaw that primates would wreck Earth, so they put the spare (Mars) in the deep freeze, with our name on it in the form of monuments, so we couldn't reach it until we matured. Cydonia looks like a Planet of the Apes face because that was ET's best guess a few million years ago, or maybe ET was betting on the Planet of the Apes scenario after Homo "sapiens" fails, due to tampering with the nucleus of the atom, or tampering with the nucleus of the cell.
The Jacobi limits of Earth and Mars are just big enough for the foregoing model. It helps a lot, that tidal forces drop off as the cube of distance.
"[Q] values in the range from 10 to 500 are found for the terrestrial planets and satellites of the major planets. On the other hand, Q for the major planets is always larger than 6*10^4."
- Goldreich & Soter, Icarus 5:375, 1966
