Requiem for Relativity

In an earlier post I recently found that the smallest standard deviation of the heliocentric ecliptic longitudes (modulo 180deg) of asteroids Davida, Laetitia, Arlon and Monterosa, occurs Jan 4.4, 2013. Another measure of their closeness, is the sum of the four distances Davida-Sun-Arlon-Laetitia-Monterosa.

This sum of distances, i.e. the length of the piecewise linear curve from Davida to the Sun and then always outward to the other asteroids, is minimum Jan 22.9, 2012. There are other measures of closeness, but they also would be expected to be minimized near this same Jan 4 - Jan 23 time interval. (This post had to be corrected Jan 1 because I discovered a data entry error in my program.)

To the asteroid-based dates Jan 4.4 & Jan 22.9, I can add another asteroid-based date, Dec 10.6. This is the time when the sum of the three break angles is minimum, in the broken line described in my Dec 26 post, the total length of whose four segments is minimum Jan 22.9. A meta-analysis of these three estimates, gives mean Jan 2.3, standard deviation 21.7 days.

Measuring the asteroids' longitudes in the plane of Jupiter's orbit instead of Earth's (i.e. Jupiter ecliptic coords., using the 1992 World Almanac orbital elements for Jupiter corrected from 1990 to J2000 coords.) I find, as expected, similar results. The minimum standard deviation of the longitudes is 3.37deg, and occurs at Jan 4.7 instead of Jan 4.4.

August 15 crop circle at Wappenbury: indicates Feb 17, 2013

From the photos and diagrams on cropcircleconnector.com, I count

6*6 + 6*6 + 3*6 + 8*12 + 7 = 193 circles

Aug 15, 2012 + 193d = Feb 24, 2013

but perhaps the innermost tiny 7 circles signify sidereal lunar months. Then we have

Aug 15, 2012 + (193-7)d = Feb 17, 2013

while 193/7 = 27.571, roughly equals the length of the sidereal month, average 27.322d, and almost exactly equals the average length of the anomalistic month, 27.555d.

Resonance of Miranda, Umbriel, Titania, Oberon: same frequency as Chandler wobble

The period of Earth's Chandler wobble, nowadays usually is said to be 433 days, or to vary between 416 and 433 days. Some claim to explain this by a complicated interaction of ocean currents and whatnot, but then again, maybe the Chandler wobble is caused by the same force that causes four of the five moons of Uranus (all except Ariel) to resonate with a 431 day period.

For my investigation, I got the JPL ephemeris times of zero and increasing, J2000 Uranocentric ecliptic latitudes for the five major Uranian moons, arbitrarily using the increasing zeroes occurring Jan 15-18, 2013. Then I used the JPL orbital periods, and the near-circularity of these orbits, to find the angles from this point for any time. I considered angles modulo 180.

Four of the five major moons (Miranda, Umbriel, Titania, Oberon) achieve true anomalies (the same as mean anomaly, for circular orbits) (modulo 180 deg) with standard deviation about 5 deg, every 431 days for at least several cycles forward and backward. Furthermore the common ecliptic latitude is near zero at these times. That is, they align every 431 days, with the nodes of Uranus' equator, on the plane of Uranus' orbit.

The nearest to my origin and therefore my most accurately calculated resonance, is at Nov 13.446 GMT, 2012. The standard deviation of the ecliptic latitudes (modulo 180) is 5.42deg at minimum, and the mean latitude then is +1.76deg.

The most massive Uranian moons are the ones whose orbital planes are closest to the equator of Uranus. That is, Miranda's inclination is 4.22deg, Ariel 0.31deg, Umbriel 0.36deg, and Titania & Oberon 0.10deg. At my January reference dates, Titania & Oberon have ecliptic longitudes 167.63 & 167.73, resp. I can estimate the invariable plane of the solar system (excluding the Sun's rotational angular momentum) as an average of the orbits of Jupiter, Saturn, and Neptune, weighted by their orbital angular momenta. The angle of each plane above the ecliptic, in the direction of longitude 167.68deg, is proportional to sin(167.68 - ascending node) and the result is +1.46deg (Neptune by itself is +1.65deg). Including the Sun's rotational angular momentum, multiplies the result by (1-0.034) and adds a term 0.034*7.25*cos(167.68-166) giving +1.66deg.

So, these four Uranian moons align, with a standard deviation, modulo 180deg, of about 5deg, every 431 days (same period as Chandler wobble) typically only 0.3deg from the plane of the solar system's "ecliptic", i.e. the invariable plane (excluding the Sun) or 0.1deg (including the Sun). This is more evidence that there are forces at work in the solar system, that we do not yet understand.

Dr Joe, I wonder how much of the unknown force you reference above is nothing more than error within the generator. As you know I have been asking about this for many years and I'm very happy to read your latest comments on all the facts you have obtained from the generator. You have a real talent for using this generator at JPL and I for one hope you keep working on it. happy new year.