Requiem for Relativity

The asteroid alignment on Dec. 21, 2012

Review: the asteroids 511 Davida, 39 Laetitia, 947 Monterosa and 1717 Arlon comprise the set of asteroids whose rotation period clusters near the minimum. Also, they have approximately the same rotation axis (Davida and Laetitia's axes precisely determined in the literature; Monterosa and Arlon's roughly determined by me using the classical "amplitude-phase" method with 8 to 15 USNO-Flagstaff 0.01mag observations at each of four points). Their rotation period is a special time period: the moons Deimos and Phobos of Mars; and Miranda, Ariel and Umbriel of Uranus, lap each other in exact whole multiples of this same period. Particles in all but the densest one, of the rings of Uranus, lap important moons of Uranus in half-multiples, 1.5 or 2.5, of this period.

These four asteroids happen to align with each other and the Sun, in Dec. 2012. Let's define best alignment of the asteroids along a line through the Sun, as minimization of the sum of squares of sines of angles asteroid-Sun-asteroid. By this definition, the best alignment is Dec. 15.58 UT, 2012. This result and in the next paragraph, use ecliptic coordinate positions, to 0.0001deg & 0.000001AU, interpolated quadratically through the dates Dec. 1, Dec. 31 & Jan. 30.

Alternatively, let's also include Uranus as one of the asteroids. Now the result is Jan. 29.46, 2013. On this date, the mean longitude (mod 180) is 183.72 deg, and mean latitude (using appropriate signs) +4.38 deg. With or without Uranus, the standard deviation in direction, i.e. sqrt(sum(sine squared of difference angle)/(n*(n-1)/2-1))/sqrt(2), is 0.20 radian/ sqrt(2) = 8.1 deg. The Standard Error would be 8.1deg / sqrt(5) = 3.6deg.

If I choose the Keck result for Davida's axis, my average of published results for Laetitia, and my 1st-4th harmonic result for Monterosa & Arlon, together with Uranus their mean axis (long, lat) is (284, 17). This is 98.5deg from the mean Jan 29.46, 2013 direction (long, lat) = (183.72, 4.38). Also, Earth's rotation axis (at 2013.0AD) is 95.8deg from the former and 87.5deg from the latter. Within the error bars, these three are an orthogonal triple; this orthogonality recurs about every fourth time for awhile, because 6340yr is about a fourth of Earth's precession cycle. So, the event this time might be especially mild or especially severe.

In an earlier post I noted that an imaginary object with half Luna's sidereal period, would be lapped by Earth's rotation, with period exactly equal to five times Monterosa's rotation period. The Mars sidereal rotation period given by TP Snow in "The Dynamic Universe" (1983) is 24.622944h, consistent with, though more precise than, the NASA Fact Sheet. Without loss of precision, I'll use Mars' sidereal revolution period 686.980d and Luna's, 27.32166d. The apparent rotation frequency of Mars, seen by an observer in solar orbit inferior to Mars, would subtract Mars' orbital frequency. With this motivation, I find

1/(1/24.622944 - 1/(686.980*24) - 1/(27.32166*24)) / 5 = 5.124679h

For Davida's rotation period, the IAU gives 5.1294h though the JPL gives 5.131h.

The "Bubble" seen from Mauna Kea June 22, 2011

A Support Astronomer for Hawaii's Subaru Telescope, "Ichi Tanaka" (quoted, secondhand from a messageboard, in the news website "Hawaii 24/7", article posted 9:08AM, June 29, 2011) says that the bubble was recorded by two different Mauna Kea video cameras (at the Subaru Telescope and at the Canada-France-Hawaii Telescope, known as the CFHT) and observed in real time by multiple persons at the Subaru Telescope location. Tanaka says he later communicated with astronomer Kanoa Withington, who was at the CFHT location. Tanaka says:

"It appears that the event happened not on the Summit area, but much farther away, according to the comparison of the two videos."

There is no "Ichi Tanaka" listed among the Subaru Telescope staff, but there are Support Astronomers named Makoto Tanaka and Miki Ishii.

This implies that the parallax was so small that it was not obvious to these professional astronomers. Comparison requires some care, because the center of the bubble was moving up and to the left at roughly a 30deg angle to the vertical (see, e.g. the two photos in "MailOnline", the online edition of the Daily Mail, 11:40 AM on 30th June 2011). Yet many stars were brightly seen near and through the bubble, so accurate comparison would be possible. The Subaru Telescope housing, according to their website, is at

* Altitude: 4139m (13,580ft.)
* Latitude: 19d 49m 32s N
* Longitude: 155d 28m 34s W

According to Wikipedia, the CFHT is at

* Altitude 4204m (13,793ft)
* Latitude 19d 49m 31s N
* Longitude 155d 28m 10s W

So, roughly, one telescope is 700m west of the other. If the bubble were directly northeast, then even a hasty effort, determining that the parallax was less than one degree, would correspond to a bubble distance of at least 700m/sqrt(2)*180/pi = 28km. Suppose the Daily Mail (MailOnline) photos are uncropped; this is probably so, because the same margins appear in the photo that Linda Moulton Howe put on her "Earthfiles" website, though it is a different frame. A 35mm film camera with a typical 50mm focal length lens has about 38deg field top to bottom; if the video camera is the same, then in the last Daily Mail frame, the bubble reaches ~20deg above the horizon, thus a lower bound for the height, is 10km. Tanaka says the bubble expanded to over 45deg. Strangely, the bubble's lower limb remained always near the horizon as the bubble rose and grew, so at more than 45deg apparent diameter the height would be over 24km. Also, the peak of Mauna Kea is about 27km from the nearest shore (which is northeast) as I measure on my roadmap; so, the presumed failure of the bubble to reach the shore, corroborates the presumed failure of the astronomers to notice parallax in excess of one degree.

Could a bubble in our atmosphere 24km high, or even 10km high, be so perfectly spherical? Cumulus clouds form "anvils" at the tropopause, ~30,000ft = 9km altitude. The speed of sound in a perfect gas of a given molecular weight is completely determined by its temperature: proportional to the square root of the temperature. The absolute temperature at the tropopause is typically 25% lower than at sea level; the temperature rises again, almost to the sea level value, at the stratopause, ~45km altitude (the molecular weight of the atmosphere is constant up to 100km)(Handbook of Chemistry & Physics, 68th ed., pp. F146-F147). With so much variation in the speed of sound, and refraction of sound, and presumably of shock waves also, the bubble hardly could be so spherical.

The atmosphere is halved in density roughly every 18,000ft = 5.5km. If the bubble is in our atmosphere, then the absolute humidity, i.e. the water vapor available for condensation (a phenomenon that often makes shock waves visible) is only a small fraction, at the top of the bubble, vs. at the bottom of the bubble. Yet the bubble appears almost as bright at the top as at the bottom. Likewise, if the bubble's brightness is due to spilled rocket fuel or other atmospheric contamination, the motion of the contaminant would be greatly impaired by the density of the lower atmosphere. So, the bubble is much higher than a mere 24km; it is mainly in outer space.

From the earlier of the two Daily Mail photos, it is easy to see that the bubble displays apparent (if not actual) flattening, like a rising moon, but the moon is only 1/2 deg in diameter, vs. 10 deg (if I am correct in my estimate of the frame size) for the earlier bubble in the Daily Mail article. The flattening is about right, to be due to atmospheric refraction: the 1 arcminute * tan(zenith angle) formula gives 20' at 3deg and 30' at 2deg, so the flattening of the part between 2 & 3 deg above the horizon would be about (30'-20')/1deg = 1/6, twice the flattening of Jupiter. I haven't measured it yet, but that looks about right. This flattening can happen in about the right amount, only if at 2deg above the horizon, the bubble is above, say, 1/2 the atmosphere. That gives a lower bound for the bubble height, of 5.5km*45deg/2deg = 120km.

For another rough estimate, I find that always roughly the bottom one degree of the bubble is below the horizon. (This could be determined accurately if the video width of field were known and daytime horizon photos were compared.) If the bubble is tangent to Earth's solid surface, then its distance would be 2*pi/180*7920mi/2 = 220km.

In sum, the drastic atmospheric variation, with altitude, of temperature and density, would prevent this bubble (whose height we know to be at least comparable with the tropopause, and probably with the stratopause or higher) from being so symmetrical in shape and brightness, unless the bubble is mainly in outer space, approximately tangent to Earth at all times while it grows upward. The dip of the bubble's limb below the horizon, agrees roughly with the depth of the bubble's distorted bottom portion, giving a distance of about 200km. A spherical bubble produced by a rocket's explosion, would not grow at just such a rate as to remain approximately tangent to Earth.

What is it? I'm not sure, but my best guess is, that it's "Bolon", the prophesied "ball".

"Bolon descends".

What Tortuguero Monument 6 is talking about. What the Mayan Long Count is about. An unknown astrophysical effect, which takes the form of a growing sphere tangent to Earth's surface.

could that bubble be a gravitational anomilly or do you think its electromagnetic ?...
what would be the distance and diamiter of mass causing the bubble ?...
does the bubble seem to be growing or moving changing in any way ?...
can the bubble be tracked accros the sky ?...
can you measure the frequency of light in the bubble ?...
or frequency of light at the center of bubble toward any atstroids
or planets in the center or center of the bubbles motion ?...

MARX

There is a video of the bubble posted in the online edition of the Honolulu Star Advertiser, a 1:30PM July 1, 2011 article by Jim Borg. The most important frames are

1. 3:39:43 top of bubble first appears
2. next frame 3:41:55
3. next frame 3:43:22.

The bubble rate of change of diameter between #2 and #1, is about the same as between #3 and #2. The difference in diameter between #2 and #1, is about 11deg, assuming the frame is 38deg high. Using 300m/s for the speed of sound, and remembering to multiply this by two because the bubble expands in all directions, the bubble height at its full 45 degree extent would be about

sin(45deg/2)/sin(11deg/2) * 300m/s * 2 * 132s = 316km, in fair agreement with the theory of the previous post.

According to the Am. Inst. of Physics Handbook, 3rd ed., 1972, Table 3d-9, p. 3-77, this value of the speed of sound is correct at 10km and again at 27km and at 69km, and never wrong by more than 10% in the range 2.5-80km.

So far, I haven't been able to gain control of any images of the bubble (due to the usual internet problems of not being able to view, save, or open files) though I've seen images on websites. I watched the CFHT video on the page of "Kanoa" (maybe Kanoa Withington of the CFHT) on vimeo.com, but apparently my attempt to save stills from it was unsuccessful, and now the video won't play on that website. All, or almost all, of the stills on the internet are from this CFHT video.

Many continuously playing Subaru videos (they have domes in the background and are not the same as the CFHT video) are on the internet, though I've not been able to magnify it enough to read the time stamps, or learn how to stop it to make a still. The Subaru video shows Jupiter to the right, a fairly easily identifiable Cassiopeia in the upper left, and identifiable (with a star map in hand) stars from Perseus, Triangulum, Aries, and Andromeda in or near the path of the bubble. I've not been able to identify the stars in any CFHT stills, however, whether colored or in a black & white version.

Another person on a messageboard remarked that the center of the bubble should not be moving, but it is. This indicates to me that the source isn't any kind of conventional explosion in the atmosphere. If a supersonic source moved while continuously exploding (e.g. a moving supersonic rocket) it would make a cone; in no projection would this cone resemble a sphere with a moving center.

Earth's rotation at 20deg latitude (i.e. Mauna Kea) is 435km/s. If the bubble were exactly NE, this projects to 435/sqrt(2) = 308km/s; leaving an unexplained vertical bubble rise of roughly 308*cot(30) = 533km/s, if the bubble's lateral westward motion is due to its stationarity as Earth rotates.

The locus of points for which their distances from two fixed points, have the same ratio, is a sphere (or in the plane, a circle). If the ratio, r, is almost one, then as r increases asymptotically to one, the center of the sphere moves away along a line to infinity, while the bottom point of the sphere (the point between the two fixed points) moves little. This geometric situation might arise from some undiscovered physical force.

The most accurate, obvious, and by far the easiest way to find the distance to the bubble, is by parallax between the two observatory's videos. Falsification of the background stars in the CFHT video would prevent this. Without knowing the distance to the bubble, the size of the bubble is unknown. Because the azimuth of the initial bubble is apparent in the videos, if the distance to the bubble were known, the point in the ocean where the bubble originated, would be known and could be searched.