Requiem for Relativity

<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 />Dr. Keller, is it possible Hubble has imaged the Barbarossa system?
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Thanks for your suggestion! I found a search form on:

archive.stsci.edu

My rough estimate of the tidal distortion of Frey/Freya due to Barbarossa (using the preceding model) indicates that for reasonable planetary interior temperature and pressure, the viscosity of molecular hydrogen would suffice to give 55K blackbody surface temperature. (Tidal distortion implies slippage of one layer of fluid over another for distances comparable to that distortion, and over an area of interface, comparable to the area of the planet.)

If the brightening of the streak (visible using blown-up Aladin pixels) were due to planetary rotation during this 1hr exposure, the rotation would be near Poincare's disintegration limit. Also, Barbarossa would need an Iapetus-like asymmetry of albedo. (The short trail at opposition, yet bright apparent magnitude, show that Barbarossa is large enough that it must be spherical with mainly gravitational cohesion.) Such asymmetry of flux can be caused instead by other, non-resolved point sources, i.e., moon(s).

My pixel analysis of Barbarossa's DSS-2 Red image, indicates a moon (or possibly unresolved pair of moons, i.e., Frey+Freya) about 2.5" (+/-) 0.1" E and 0.2" (+/-) 0.1" N of Barbarossa. It indicates that these moon(s) are 1.2 (+/-) 0.1 magnitudes dimmer than Barbarossa. If the brighter of the two Red USNO-B catalog magnitudes of my Object #3, is that of Barbarossa, and the dimmer that of the aliasing moon (Freya), then Barbarossa is +18.57. So, +18.57 + 1.20 = +19.77 indicates Frey+Freya as for Object #8 (which gave +19.65 for, apparently, Frey+Freya).

My pixel analysis also indicates a third moon 1.7" (+/-) 0.5" W and 0.4" (+/-) 0.5" N of Barbarossa. It is 1.6 (+/-) 0.2 magnitudes dimmer than Barbarossa. So, +18.57 + 1.60 = +20.17, suggests that there is a third moon, separate from the others, probably with a smaller orbit, and with about the same magnitude as Frey.

I considered the 4x7 block of 1" square pixels on which Barbarossa appears, and the nine grayscale levels of those pixels. "One arcsecond [atmospheric] seeing" would give a standard deviation of about 1" to the photons. So, 3" away from the main source would be 4.5 natural log units dimmer, roughly consistent with 0.5 natural log units per grayscale level.

First trying a single source, I found that for best overall least-squares fit between the predicted and observed logarithm of the flux detected in each pixel, the source did not lie in the interior of the darkest pixel. However long the streak, made by a constant-intensity point source, the midpoint of the streak must lie within the darkest pixel. Since a single source of such diameter hardly can (see above) rotate fast enough or be asymmetrical enough, there must be multiple sources.

I then adopted a compromise position for Barbarossa, 0.2" E and 0.1" N of the center of the darkest pixel. A rough preliminary search assuming two objects, had placed the moon(s) 3" E & 1" N of Barbarossa. So, my final search, which took almost an hour on a Pentium processor (the first time I've needed anything faster than a 486, for any of my work on this messageboard), adopted a finer grid concentrated there for one moon, while looking for a second moon on a coarser grid everywhere else.

The viscosity of [molecular] hydrogen gas at one atm and 1000K, is 200 micropoise (Handbook of Chemistry & Physics, 44th ed.). Branley's Astronomy, & TP Snow's The Dynamic Universe (1983), give 3,000,000 atm for the maximum pressure inside Jupiter's liquid H2 outer mantle; Snow gives 10,000K temperature within this mantle (the liquid H2 mantle is thought to extend 1/3 of the way to the center, hence comprise 2/3 of the volume). If the typical pressure inside the mantle is proportional to the (planetary density)^2 * (planetary radius)^4, then Frey or Freya, whose hydrogen would have slightly lower density and whose radii are about 1/4 Jupiter's, would have typical mantle pressures &lt; 3*10^6 / 4^4; perhaps 5000 atm.

Empirically from the Handbook's table for hydrogen, viscosity increases as temperature^(2/3). Tidal heat generated will be proportional to viscosity, so blackbody surface temperature will increase as (internal) temperature^(1/6): it isn't a sensitive function of internal temperature. Assuming a 1000K typical mantle temperature (much less than the estimated mantle temperature of Jupiter), the viscosity of the molecular hydrogen in the mantle of Frey/Freya, in the (rough) ideal gas approximation, is 0.000200 * 5000 = 1 poise. This is the viscosity of light machine oil at room temperature and 1 atm pressure.

I still don't know the date of that plate (Object #3) showing Barbarossa. Querying some Aladin and ESO archive regions to one side or the other, so far has yielded no relevant dates.

I emailed the ESO help team, asking them, but they told me they were too busy to do anything except give me three (irrelevant) web links. Then today I emailed six astronomy faculty members at the U. of Strasbourg, including photos of the ESO plates with coordinates.

I've still received no response from the USNO (three FAXs & two postal letters). The chief of the Iowa State Univ. observatory (24" telescope in rural area) refused to look and didn't want the coordinates or the photos.

Bradford robotic telescope images, the first is at 11 07 24, -6 38 50
next at 11 06 02. -6 28 27

Go to the Bradford web site and look at the latest jobs, these are nem2 and nem3. Perhaps if we decide on an exposure we can put the same job up a few times and then do a blink comparison in photoshop.