<br /><blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote"><i>Originally posted by nemesis</i>
<br />Sorry, I misunderstood... but wouldn't it be worthwhile to look for a planet of ~4 Earth masses at ~52 AU? It would still be very dim and could have been overlooked. And it shouldn't rule out Barbarossa.
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Thanks for emphasizing this. Barbarossa would be the dimmer, because (198/52)^4 = 250 = 6 magnitudes, not enough to compensate for the size difference between a Uranus (i.e., 5-15 Earthmass planet, even if of Earthlike density) and a Jupiter (i.e., quantum mechanical estimate of brown dwarf size). Unfortunately, the phase incoherence of the residual signal I find in Standish's data, leaves the phase indeterminate; furthermore it argues against a planetary cause at all.
The USNO Vol. XII (1929, according to the USNO library webpage) ephemeris for Neptune's RA (according to Standish, Fig. 8a) is consistent with Barbarossa in amplitude, period and phase. The USNO mission is to produce accurate ephemerides by any and all lawful means. Before radio, a cruiser might lose all hands, if the navigator lacked accurate information on the only 3rd mag. star he could identify on a partly cloudy night. Tomorrow, after electronic countermeasures, and the electromagnetic side effects of superweapons such as nuclear bombs, the navigator may well revert to the sextant. I doubt he'd sight Neptune, but if the equivalent of a thousand taxpayer working lives are wasted because the Navy's rocket to Neptune missed, the loss is, in a way, comparable to that of a cruiser.
Fig. 8a (Neptune) resembles the error in fitting 1.5 cycles (trough-peak-trough-peak) of an 80-yr sinusoid, to a cubic curve. For the 120 yr between 1830 & 1950 (Neptune was discovered in 1846, but Neptune's ephemeris can be extrapolated backward) the fit is good, but before and after that, the ephemeris for Neptune's RA deviates roughly as a cubic curve from a sinusoid. The USNO might have tried to adjust for some small unexplained error, by zeroing the discrepant RA, with a cubic curve, at 1930 (approx. date of the catalog), 1850 (approx. beginning of Neptune data) & 1890 (midpoint)(the three roots of the sinusoid). This attempt would begin to fail markedly a quarter cycle away, before 1830 and after 1950, as Fig. 8a shows.
James DeMeo had to fly to Cleveland to rummage through the Physics Dept. at Case Western Reserve Univ. (after tactfully getting permission) to rediscover the only extant copy of Dayton Miller's data, in a cardboard box in a dusty storeroom. Everyone involved with USNO Pubs. Vol. XII is deceased. If notes exist detailing all their corrections, finding them might be like rediscovering something in the Vatican Library. The USNO mission was and is, to produce accurate ephemerides. They understood that there are systematic observation errors, calculation errors, undiscovered planets, unknown forces and unimagined "new physics". A cubic curve might be used to correct a small, incomprehensible discrepancy.
The slope of the discrepancy (after inclusion of such a cubic correction term) in Fig. 8a, at 1830 and 1950 (a sinusoid trough & peak, resp.) would approximate the maximum sinusoid slope due to Barbarossa, i.e., +21.44"/century (see my earlier post).
Not only are the period and amplitude of the unexplained sinusoid (the 1929 USNO approximation of which by a cubic, results in Standish's Fig. 8a) consistent with Barbarossa; so is the phase. One of the times at which the sinusoid should have most negative slope, is c. (1830+1950)/2 = 1890. In 1890.0, I find Neptune's heliocentric ecliptic longitude was 63.5. Barbarossa's effective heliocentric ecliptic longitude was: 173.327 (for 1987.082) - (1987.082-1890.0)/2780*360 (for orbital motion) - 175/4/2780*360 (for retardation of speed change, by a Neptune-minus-Barbarossa quarter cycle vis a vis the tidal acceleration due to Barbarossa) = 155.1. Recalling the 2nd harmonic nature of the tidal force, Neptune's RA should have most positive acceleration at 155.1-45, most negative acceleration at 155.1-135, and zero acceleration, i.e., most negative speed, at 155.1-90=65.1, agreeing perfectly, considering the rough dates (1.6deg < 1yr), with the actual 63.5.
There are many reasons why Standish might find an ephemeris which excludes Barbarossa. However, the 1929 USNO Vol. XII ephemeris, supports Barbarossa's existence, indirectly but accurately confirming the amplitude, period and phase of Barbarossa's predicted tidal effect on Neptune.
