Requiem for Relativity

Posted to several Harvard, Ivy League and Astronomy e-groups (feel free to post widely):

I am doing my own research on climate change, which relates asteroid alignments to the Mayan Long Count, and a 6340 yr cycle of natural disaster (yet-unknown physical forces seem to be involved). At the end of the Mayan Long Count, all four asteroids known to have approximately the critical 5.13hr rotation period, align with a peculiar object in distant solar orbit, which is found on four sky surveys. Two of these asteroids have the same rotation axis. I seek to prove that the other two also have this axis. This overwhelming improbability (four out of four asteroids, with the critical rotation period, align with the object and perhaps even have the same rotation axis, at the end of the Mayan Long Count) might be enough to "break through" the prejudiced resistance of the astronomy bureaucracy, and force them to break their usual protocols, and image the region (i.e., get their heads out of the sand and look with a big telescope). Thus some progress could be made. There are still three years to prepare for the coming "Younger Dryas", or panoceanic megatsunamis, or whatever it turns out to be this time.

To prove that the other two asteroids have the same rotation axis, I need their "lightcurves". It takes several years to get lightcurves at all ecliptic longitudes. The only way to get the job done quickly, is to access the lightcurves that already have been made by various astronomers, mostly at universities in Europe and the U.S. I can do this (it's freshman calculus and many journal articles give the formulas) but all my emails to them, requesting these lightcurves, have gone unanswered, perhaps because I am not a professional astronomer (i.e., don't have a union card). When I sought help from Harvard's Minor Planet Center (the International Astronomical Union Minor Planet Center, which is at Harvard) their associate director told me, "We do not deal with lightcurves." This flies in the face of their own homepage, which advertises a "Lighturves" section which is the most complete bibliography of lightcurves I have found on the internet (though the actual lightcurves remain in the possession of the investigators or, sometimes, published in various obscure newsletters which generally do not seem to be online) . I realized that I had run into typical "Harvard bureaucracy", familiar to all Harvard alumni (for example, my classmate who was told quite seriously by Harvard bureaucrats that he should simply go by another name for four years rather than bother them to correct his erroneous ID card).

Here is how you (Harvard alumni especially, but all help is welcome) can help. Contact the bureaucrats who are asking you to make bequests to Harvard. Tell them you might consider making a bequest, but for the outrageous behavior of Harvard's bureaucracy: for example, the refusal of Harvard's Minor Planets Center to assist a certain Joseph C. Keller in obtaining "Lightcurves" which he needs for the first PRACTICAL use of asteroid data since, perhaps, the Age of Atlantis. Because Harvard is the headquarters of minor planet research, all the researchers in possession of those lightcurves certainly would jump to email me the files, if Harvard said jump.

Sincerely,
Joseph C. Keller
B. A., cumlaude, Mathematics, Harvard, 1977

This site might be able to give you some data Joe. www.asteroidoccultation.com/2009_04/0414_947_18705_Summary.txt

<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote"><i>Originally posted by Stoat</i>
<br />This site might be able to give you some data Joe. www.asteroidoccultation.com/2009_04/0414_947_18705_Summary.txt
<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">

Thanks for the information.

Monterosa's rotation axis differs ~9deg from Davida's or Laetitia's

Today I made the first estimate in history, of asteroid 947 Monterosa's rotation axis. I had to tailor my method to the data I have. My method is rough, derived by elementary mathematics. I ignore shape, so there is no "inversion problem".

I have the Monterosa lightcurve by Berger, Bosch, Vagnozzi et al (downloaded from Prof. Behrend's website, ref. 34 in the IAU Minor Planet Center online bibliography) from observation March 29.6, 2003. Berger gives the variation as 0.15. Berger's smoothing curve is grossly nonsinusoidal but has almost perfect antisymmetry (i.e., a Fourier series with sine terms only).

I do not have (but expect soon to have) the Monterosa lightcurve by Warner (ref. 119 in the IAU Minor Planet Center online bibliography) but from the online Collaborative Asteroid Lightcurve Link ("CALL"), I find that it is from observations Jan. 1 through Jan. 7, 2007, and that its amplitude is given as 0.23 +/- 0.02.

CALL mentions a "[confirmed] previous unpublished CALL posting" which might be a third extant Monterosa lightcurve. I have no further information about it.

I ignore the asteroid's ecliptic latitude. That is, I assume that the asteroid orbits in the plane of the ecliptic.

The observation of the asteroid, is essentially an interaction between the Sun and the Earth, mediated by the asteroid. The light wave equations governing this interaction are time-reversible. So, the Sun-Earth interaction is symmetrical. To a good approximation, the geocentric and heliocentric ecliptic longitudes of Monterosa (which happen to differ only ~20 deg anyway, at Berger's or Warner's observations), may be replaced by the mean of the two. (I averaged the JPL heliocentric and geocentric celestial coordinates.)

So, I put the asteroid in the plane of the ecliptic, and move both Sun and Earth to the Sun-Earth midpoint.

The amplitude of lightcurve variation is, approximately, maximum (asteroid shapes usually are moderate, and albedo variations usually are slight) when the rotation axis is perpendicular to the observation axis. The amplitude is, in this approximation, zero when the rotation axis is parallel to the observation axis, but the amplitude changes sign and increases rapidly as the axis moves through the parallel position. So:

(minimum amplitude)::(maximum amplitude) = (sine beta)::1 (Equation 1)

where beta is the ecliptic latitude of the axis.

As the asteroid moves around the ecliptic, the amplitude oscillates between its minimum and its maximum, approximately as a sine wave with period 180 deg:

Amplitude = (minimum amplitude) + 2*A*sin^2(theta-lambda) (Equation 2)

where theta is the asteroid's ecliptic longitude, and lambda the longitude of its axis.

To find A, beta, and lambda, I need three data. I've been given two data outright: Berger's and Warner's amplitudes. My third datum is, the antisymmetry of Berger's lightcurve. The symmetry, or rather antisymmetry, of Berger's lightcurve, suggests that Monterosa's rotation axis then was at a cardinal position, either perpendicular to, or maximally slanted toward, the observation axis. Berger's amplitude is smaller than Warner's, so the latter choice must apply.

This gives lambda = 134 (mean of heliocentric and geocentric ecliptic longitudes of Monterosa, at Berger's observation) and, using Eq. 2, 2*A = 0.086. Using Eq. 1, beta = arcsin(0.15/(0.15+0.086)) = +39.5. My method implies fourfold ambiguity of solution: beta can be negative, or 180deg can be added to lambda. So, as good a solution, is, that 947 Monterosa's rotation axis = (lambda, beta) = (314, +39.5) (ecliptic coordinates).

This differs only 9 deg from the average (including 180 degree longitude correction when needed)(weighting Davida and Laetitia equally) of all ten of their axis determinations I found in the literature: (306, +33.6). My average of the seven 39 Laetitia axes was (307, +38), and of the three 511 Davida axes, (302, +22). The chance that any of the fourfold solutions of my method, would lie randomly within 9 deg of the predetermined Laetitia/Davida axis, is p = 2.5%.

Hi *******,

The IAU Minor Planet Center bibliography links to a note on *******, that you, or at least the *******, did lightcurves on 947 Monterosa in ***. My Monterosa lightcurve determination is cruder than usually is attempted nowadays, so I want as much lightcurve data as possible in usable form, so I can make a more refined, irrefutable axis determination. I want to say:

"These four asteroids have the same rotation period, the same rotation axis, and lie on the same line at the end of the Mayan Long Count, all lined up with the CMB dipole and also with something I found on the sky surveys. Realize there is a new phenomenon here. Get out your big telescope and look (now). This is like Kepler discovering that the planets' orbits are, inexplicably (then) ellipses. Just because I can't explain it with tensor calculus doesn't mean it isn't real or important."

Meanwhile if anyone else, such as the Nathanael Berger - Jean-Gabriel Bosch - Antonio Vagnozzi group for Monterosa, or that huge Walter Cooney group for 1717 Arlon, or the Federico Manzini - Laurent Bernasconi group for Arlon (their lightcurve is on Prof. Behrend's website, but never downloads properly when I've tried so far) will send me their lightcurves, or do axis determinations themselves, that would be great. I've found a few of their email addresses on the internet but so far those have bounced or gone unanswered.

Sincerely,
Joe Keller

Dr Joe,Palmer Divide Obs has the light curves. I have more info if you need it.