Showing posts with label oblateness. Show all posts
Showing posts with label oblateness. Show all posts

Thursday, November 15, 2012

Mail Call Brane - Readers Seeking Answers!

(Note all the following questions were received in 'comment' format but with the askee requesting no special comment space rather the question(s) collated into one blog ....this one!)

Q. President Obama in response to a question yesterday at his news conference stated that one can't be sure if superstorms such as Sandy are really caused by climate change. What is the take of the climate science community on this? - Roger B., Minneapolis, MN

A. This is a tricky question, and Obama can be forgiven for dodging it in a way at his press conference, because let's face it: most of the press corps possesses the attention span of gnats.

The truth is that one aspect of climate change does show a causal relation to the genesis of Superstorm Sandy. That is the phenomenon known as the North Atlantic Oscillation (NAO) and its geographical distribution at particular times of the year. The NAO embodies the atmospheric pressure over a particular region (in this case it was the U.S. northeast) and it can be either 'positive' or 'negative'. In the case of the latter, which was what we observed preparatory to Sandy's arrival, the jet stream displayed a pronounced southward dip. In a positive display the jet stream would have more straddled the higher latitudes (e.g. 45N) and not bent so far south.

Now, here's the kicker: research by Charles Greene at Cornell University and other climate scientists has shown that as more Arctic sea ice melts   e.g. in the summer because of global warming (as I noted before, see my blog of  Sept. 21) then the NAO is more likely to be negative, i.e. jet stream sloping way south. This condition then set the stage for a superstorm in two stages: 1) the warm Atlantic water off the eastern U.S. coast fed energy into the system, and 2) the encounter with the cold air ensconced in the southerly jet stream added the energy equivalent of 5 single megaton nuclear bombs to the system and dramatically expanded its reach - incepting the massive destruction we beheld.

We can predict then, that if northerly moving hurricanes become a more common feature, as does a continued negative NAO, then we will see more superstorms like Sandy. The east coast and its cities will then have to decide whether or not it will spend the money, as the UK has, to construct a massive system of dykes etc. to ward off the storm waters, waves. If not, we better have no more wars, because we're going to need all that money for constant rebuilding!

Q. Reading about your brother ('Fighting Cancer, Fighting Your Brother') I can't believe you had to put up with all his crap while you were recovering from prostate cancer! What gives with the dude? Is he 52 cards short of a full deck or just ornery or what? - Mitch C., Stanford, CA

A. Well, what would you think of a guy that once circulated an idea to put all atheists in the country on a "national registry" like sex offenders?  Granted, he had to be saved from himself (he received over 400 death threats via email from outraged atheists across the world) but all that meant is that he shut down the 'Pastor Mike' blog and started a new one ('Straight Talk with Mister Mike'). The bottom line is I don't know what his main problem is, but as I said in blogs from a few years ago, I suspect IF he has mental issues they arise from believing an insane fundamentalist brand of religion. His 'god' - if you can call it that, is totally batshit insane, since it has no problems allowing a son to be killed for mouthing off against parents - as per Deuteronomy 21;18-21, or adulterers (say like Petraeus and Broadwell) to be stoned to death by Deut. 22:22 or chldren to have wild bears set loose on them if they mock "prophets". (By 2 Kings 2: 23-24). Oh, his god also approves of genocide when it means "cleansing the earth" - as in Gen. with the slaughter of the Canaanites.

As I've said many times before, tell me the concept of god in which you believe, and thence the morality you uphold,  and I will forecast your odds of going nuts. Indeed, I can tell how much of a nut you already are. If you accept or believe in batshit crazy gods you will be a batshit crazy person, and likely end up in a straight jacket on thorazine, if not in some other horrendous end.

Q. I read your blogs on prostate cancer with great interest. My husband, age 43,  recently had a biopsy and it came back with four cores at Gleason 3+4. He's in a dilemma as to the treatment but as in your case, the urologist said watchful waiting wasn't an option. He dreads all the post-operative issues to do with surgery including difficulty with sexual relations, but isn't sure about radiation either, and doesn't want to face the prospect of having the cancer come back after having done the radiation. Any ideas, suggestions?  - Marilyn F., New Orleans, LA

A. In the end the choice of treatment is a highly personal one. Apart from the information already given in the blogs, I can only suggest he obtain the two books cited as well: 'The Invasion of the Prostate Snatchers' and John C. Mulhall's  'Saving Your Sex Life: A Guide for Men with Prostate Cancer". (Note: Dr. Mulhall is the Director of the Sexual & Reproductive Medicine Urology Service based at the Memorial Sloan- Kettering Cancer Center.) Mulhall's focus is also highly on the issue of "penile rehabilitation" : http://brane-space.blogspot.com/2012/10/penile-rehabilitiation-what-most-docs.html .

The aversion to post-op problems following surgery is understandable. Incontinence and erection problems are often mentioned (but the solutions to these were given in the blog link, based on Mulhall's book) but the acute or short term problems are also turn-offs for many men: including risk of infections, having a catheter inserted in the bladder for possibly as long as 3 weeks, coping with the pain, constipation arising from use of pain meds, and risk of rectal injury during bowel movements because the rectal wall becomes much thinner following surgery - after removal of the prostate which originally adjoined the rectum. All this is detailed in the UCSF Patient Guide for Radical Prostatectomy which also includes sections dealing with sexual recuperation, other treatments -meds for incontinence, etc.

I chose the high dose rate brachytherapy because: 1) I didn't wish to be laid up weeks with post-op difficulties or catheters, or bowel problems, 2) I didn't want to be possibly faced with months or years of incontinence limiting my travels, freedom, and 3) I didn't want to go to extraordinary lengths for "penile rehabilitation" including having to have an implant operation, or reduced to continually using Viagra, vacuum pumps or injections. But again, each man has to make his own choices!

Q. I found your blog on solar oblateness fascinating, and wondered if you would be so kind as to provide the oblateness formula for the planets from Earth outwards.to Neptune. Thanks! - Mick, Trenton, NJ

A. The oblateness formula depends on the planet's equatorial diameter, a and its polar diameter, b. Then:

f = (a - b)/ a

The values are as follows for Earth outwards to Neptune:

Earth: 1/ 298.257

Mars:  1/ 154.409

Jupiter: 0.06487

Saturn: 0.09796

Uranus:  0.02293

Neptune:  0.0171


Q. If your Aug. 22 blog on 'the biggest spy center on Earth' is to be believed, Gen. Petraeus had much to worry about churning out all those emails. Should he have known about this spook kingdom and how they can scoop up emails, tweets on a whim? Or was he just dumb? - Andy K.,  Tucson, AZ

A. I don't believe the general was 'dumb' but perhaps in the heat of his affair his brain cells didn't process that anything committed to cyberspace or that gets infused into the 'cloud' - is there for years for any spook to grab, save and see. In the blog you referenced, I specifically mentioned (from the cited WIRED piece, 'The Black Box'):

"The mammoth Bluffdale Center will have another important and far more secret role that until now has gone unrevealed. It is also critical for breaking codes. And code-breaking is crucial because of the data that the center will handle: financial information, stock transactions, business deals, foreign military and diplomatic secrets, confidential personal communications, legal documents and anything else initially heavily encrypted."

I also added:  "Everyone's a target, everybody with communications is a target."


So, it boggles the mind that Gen. Petraeus could have been that careless. Also, virtually anyone that spends any time on the net has to be aware that the FBI's "Carnivore" program - for ferreting out emails- is still in play. Also, the 4th amendment protections against extraordinary searches have essentially vanished since the critical provisions of the Patriot Act (mainly to do with wiretapping without the need for warrants) have been extended twice (by Democrats and Repubs - at least it's one thing they can agree on.)

My advice to anyone is that if you don't want the spooks to be amassing all your (saved) Facebook pages, blogs or tweets, then the best step is not to post them. If you don't care, it's no biggie. Btw, for those who want to learn more about the national security state we've erected (to keep us "safe") since 9/11 be sure to get hold of James Bamford's book: The Shadow Factory: The Ultra-Secret NSA from 9/11 to the Eavesdropping on America.

Tuesday, November 13, 2012

Solar Oblateness May Be Constant Over Time




As with all rotating celestial bodies - planets included - the Sun is "oblate", meaning that it "bulges" at the waist, i.e. solar equator. The measure of this bulge is then the ratio of the equatorial diameter's excess (i.e. over the polar dia. or (a- b)) to the polar diameter (b) itself. Or:

Obl = (a - b)/ a

Solar oblateness came to the fore some decades ago when it was invoked to challenge the standard Einsteinian General Relativity. This was as part of the Jordan- Brans- Dicke theory of gravity proposed by Robert Dicke of Princeton and Carl Brans - my former mathematical physics prof at Loyola University ca. 1966.(See, e.g. http://chn.loyno.edu/physics/bio/carl-h-brans)

What Brans and Dicke hoped to find, to validate their theory, was a departure from spherical symmetry large enough that it had the potential to affect Mercury's orbit. This quantity, dubbed 'eta' by Einstein, referred to the advance of the perihelion in seconds of arc, over a century. It is instructive to first revisit this and show how Einstein obtained his value of 43 seconds of arc per century.

Thus: eta = [24 (π)^3* a^2]/ T^2 *c^2*(1 - e^2)


where 'eta' is the advance of perihelion in seconds of arc, T is the period of revolution in seconds, c the velocity of light in cm/s and e the eccentricity of the orbit. From a Table of distances, Mercury's semi-major axis = 0.387 AU or:  a = (1.5 x 10^13 cm) (0.387) = 5.8 x 10^12 cm

The period, T (in seconds) is just the length of Mercury's year (in days = 87.96, again from a Table) multiplied by the seconds-length of an Earth day, or 86,400 s:

T = 7.6 x 10^6 s

The eccentricity, e from a similar Table is e = 0.205.

Substituting all these values into the given equation yields: eta = 5.036 x 10^-7 radian

However, this is not in seconds of arc but radian measure. To get the equivalent seconds of arc (or arcsec) we use the fact that 1 rad (radian) = 57.3 deg and one degree has 3600 seconds. Thus, 1 radian = 2.063 x 10^5 arcsec

So, the associated arcsec for eta will be 5.036 x 10^-7 rad) x (2.063 x 10^5 arcsec/ rad) =0.104 arcsec

We are still not finished because the quantity is defined per CENTURY

At this point, you need to recall the PERIOD of Mercury is 0.24085 YRS.

So, the number of arcsec of perihelion advance per Earth years is:

0.104 arcsec/ 0.24085 years = 0.431

and over 100 years:

eta = 100 yr x (0.431 arcsec/ yr) ~ 43.1 arcsec, compared to the value of 42.98 "/century predicted by Einstein.

Interrelated with the above is the fact that an oblateness gives the Sun what is called a "quadrupole moment" which we designate J2. The dimensionless parameter J2 is defined (cf. 'Gravitation and Spacetime' by Hans C., Ohanian and Remo Ruffini, W.W. Norton, p.18):

J2 = Q^33/  2M R^2

where M is the mass of the Sun, R is its radius, and Q^kl = Q^33 is the mass quadrupole tensor (op. cit., p. 17).  To assess a baseline perspective, if the Sun were rotating totally uniformly oblateness effects minimal) then J2 would be roughly 1 x 10^-7. In this case, the corresponding contribution to the advance of Mercury's perihelion would be a few hundredths of an arcscond per century, or in other words, within the observed value of the uncertainty for 'eta'.

Interestingly, Brans and Dicke (1961), originally proposed a 'scalar-tensor' theory of gravitation which avoided conflict with the Einstein GR prediction. In their field the scalar field replaced the gravitational constant and becomes instead a function of space and time, so oe gets a variable value for G - the Newtonian gravitational constant. Effectively, on is looking at a quantity G'/G where G' denotes the first time derivative, or dG/dt/

Meanwhile, in 1967, Dicke and Goldenburg obtained an unexpectedly large J2 ~ 2.4 x 10^-5 which would show significant deviation from the Einstein eta. It would also have required that the solar interior rotate at a much faster rate than the surface.Such a large quadripole moment would have led to an additional 3 arcsecs per century over Einstein's value. Thus, leading to eta ~ 46"/ century. This large value has never been confirmed, and indeed, Dicke et al (1985) using a solar vibration method found J2 = 1.7 x 10^-7.

Quite obviously, what the preceding showed is that better methods of measuring oblateness (and hence the quadripole moment J2) were needed, which exceeded optical methods, including digital photocells, and also oscillatory -vibration methods. Such an advance on observational quality became feasible in 2010 with the launch of NASA's Solar Dynamics Observatory (SDO). This Observatory was able to measure with record precision the shape of the solar limb (the solar disk's edge) and in addition ascertain variations in the limb over a solar cycle.

The results forthcoming were simply amazing, i.e. that the Sun's equatorial radius exceeded its poalr radius by 7.2  + 0.5 milliarcseconds, and with NO evidence of departure from constancy. Given the Sun's diameter of 1.4 miilion kilometers subtends a half degree in the sky (1800" roughly) then the difference between its equatorial and polar radii would amount to barely 5 km. In other words, it's almost perfectly spherical. Most remarkably, the 5 km difference is small even when compared to the turbulence on the solar surface

Further refinement - especially useful over solar cycles - was obntained by incorporating best -fit quadrupole (C2) and hexadecapole (C4) coefficients. The to 4th order the difference between equatorial and polar radii is given by:

D = -3C2/ 2  - 5C4/8

Amazingly, within the range of observational uncertainties, both C2 and C4 have been consistent with constancy over two years. Moreover, C4 is effectively zero (contributes very little to solar oblateness) so:

D = -3C2/ 2

Further analysis using Legendre polynomial multipole data discloses a marginal hint of correlation between C4 and the sunspot cycle - which may or may not assume importance for future sunspot -flare forecasts. This association, for the time being, is theorized to be "a result of magnetic stresses localized at mid-latitudes or in near surface flows". (Physics Today, Oct., p. 14).

Of course, we must not be too hasty in drawing firm conclusions about constancy of oblateness from just two years of observation. But thus far, it looks pretty good.