Requiem for Relativity

By the methods above, I estimate 355 AU distance and a 6680 yr period for circular orbit. However, today I discovered that five of the nine proportionally small discrepancies ( < 10% ) in the resonances (m:n for m,n < 11) of the giant planets' orbits (periods per TP Snow, "The Dynamic Universe", 1983) are simple multiples of a discrepancy consistent with a retrograde influence with period about 4430 yr. This would (assuming that the 2:3 ratio is mere chance) correspond to 270 AU distance, 0.0107 solar masses, and a planet with magnitude +16.75, for 5.7% albedo.

This might be a more accurate estimate than that derived from the COBE and WMAP surveys with their nominally large error bars. Alternatively, the orbit might be moderately elliptical ( e > sqr(6680/4430) - 1 = 0.23 ). The other four of the nine discrepancies were related to multiples of Pluto's orbital period; mostly, these were less accurate resonances than the five above.

[] It doesn't look like they have a plate of that region of the sky. Perhaps that's good news, as if they haven't, then they haven't looked [] Maybe the Australian Schmidt would be worth a look, it's been running for about thirty years.

<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 />[] It doesn't look like they have a plate of that region of the sky. Perhaps that's good news, as if they haven't, then they haven't looked [] Maybe the Australian Schmidt would be worth a look, it's been running for about thirty years.
<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">

Above, I've specified a search disk including 0.25 square degrees of sky. Please note that I changed the region slightly to correct a sign error in the increment between (II) & (I).

Planet X will be dimmer than most asteroids but brighter than most Kuiper belt objects. It will move more slowly across the star background, and also retrograde. The average asteroid orbital plane is inclined one degree below the ecliptic near the vernal equinox, so ecliptic longitude -11 in Leo is 10 degrees from the line where asteroids can be seen most often. An extensive plot showed that asteroid inclinations of 10 deg are about 1/2 as common as 0 deg. If the inclinations make a bell curve with half-maximum at 10 degrees, numerical integration (the singularity in the integrand is "removable") shows that asteroids will be seen only 1/10 as often there.

Besides direct observation and studying old photographic plates, I've invented another method of search. The billion-star USNO-B catalog contains bogus objects which arise from two asteroids being accidentally at the same place on plates made at different times (DG Monet et al, Astronomical Journal 125:984+, p. 990). In part because of the unreliability of the magnitudes, the catalog was not filtered for discordant magnitudes. My method is to look for USNO-B catalog objects along the presumed track of Planet X, which have:

1. A difference of 2 or more, between the whole number parts of R1&R2, or B1&B2. E.g., B1=16.98 & B2=18.03.

2. At least one of their published magnitudes ("B1", "B2", "R1", or "R2") between +16.00 and +18.99.

3. Proper motion in either RA or Decl greater than 2 standard deviations from the mean.

In the "VizieR" online catalog, automatic filters can be set to accomplish (2) & (3). Because the typical midrange age of the plates used for a star is 30 years, one should go back 60 years, i.e., 3.2deg.

Three square degrees out of 41,000 in the sky, would have 10^9/14,000 = 70,000 stars, but the automatic filters could remove 90-99% of those depending on the setting. This is a manageable number of stars to check by eye for criterion (1). Asteroids and Kuiper belt objects occasionally would appear in this region of sky, but Planet X might be there all the time. A trail of bogus or dubious objects might be plotted.

I was going to set two plates up on top of each other in photoshop, and blink one of them off and on, to check for movement.

If 10,800 B.C. is the date for a major holocaust (Younger Dryas-major upliftment/volcanism,possible polar shift) on earth due to the possible gravitational interference from the returning retrograde extreme elliptical orbit of a brown dwarf sister sun; then, a 3600 year period fits perfectly with a year zero (was star of David our sister sun?) and we would not see the so called planet X for another 1593 years.

John