Wednesday, June 19, 2013

Introducing Some Advanced Astrophysics (3)

The fact stable stars like the Sun exist shows that a pressure-gravity balance must obtain within them - layer by layer. To see how this can be quantified, consider an element of  a defined layer of width dr and lying between layers at distances r and (r + dr) from the center. Let P be the pressure at r and let the increment in P be dP. The difference in pressure dP represents a force, -dP,  acting on the mass element considered in the direction of increasing r.


The mass of the element considered is: r dr. Then the force of attraction between M(r) e.g. the mass enclosed inside the sphere of radius, r and r dr is the same as that between a mass M(r) at the center and    r dr at r. By Newton’s law this attractive force is given by:

F = G M(r)  r dr/ r2


Since the attraction due to the material outside r is zero, we should have for equilibrium:

- dP = G M(r) r dr/ r2

Or:

dP/dr = - G M(r) r / r2


Note that P has been used to denote the total pressure. Thus P is the sum of the gas pressure and the radiation pressure.

Consider now the mass of the shell between outer  layer A and deeper stellar layer C. This is approximately, 4p r2 r dr, provided that dr is small. The mass of the layer is the difference between M(r + dr) and M(r) which for a thin shell is:

M(r + dr) -  M(r) = (dM/ dr) dr

Equating the two expressions for the mass of the spherical shell we obtain:

dM/dr = 4p r2 r


The two equations, for dP/dr and dM/dr represent the basic equations of stellar structure, without which the innards of a star would be inaccessible to investigation.

A third equation of stellar structure may be derived using by using the equation for dM/dr in combination with the fact that a star’s luminosity is produced through the consumption of its own mass. This may be expressed mathematically as:
 
dL/dM = e
 
where e denotes the rate of energy generation. For the proton-proton cycle (for stars like the Sun- and designed for cgs units!):
 
e= 2.5 x 106 (r  X2).· (106 /T)2/3 exp[-33.8(106 /T)1/3]
   

Problems for the budding astrophysicist:

1) In a given layer for a 10 solar mass star, the composition is 90% hydrogen, 10% helium. Assume the layer is in local thermodynamic equilibrium. The temperature is taken to be 3.14 x 106 K. Take the density of the material as r  = 20.2 kg m-3.  Find the relative contributions of gas and radiation pressure in the layer and the thermal energy per kilogram of the material. (Assume the gas is totally ionized).


2)  Derive a third equation for stellar structure where dL/dr is the subject. (Hint: Make use of the energy generation form for dL/dM and the chain rule for derivatives).

3) From one or more equations of stellar structure, obtain an estimate for the Sun’s central temperature and pressure. (Take the solar radius R = 7 x 108 m and the solar mass M = 2 x 1030 kg, and the density r = 1400 kgm-3. )

Between the Skeleton Key and the COG: How Close NSA Mass Surveillance Really Is to Tyranny

"“So what 50 plots did NSA break up? A U.S. flag burning party in Yemen? A harsh letter to a U.S. Senator? Graffiti on the walls of a building saying ‘NO more WAR!’ – comment on UK Guardian website yesterday.


"Let's see: the costs tallied make it $2.5 billion for each 'plot' broken up. Is that really worth it?" - comment on UK Guardian site


"Sen. Dianne Feinstein and others cavalierly assert that the NSA’s surveillance of law-abiding citizens is “lawful.” Seriously? Of course it is. All you need to do is enact legislation approving tyranny and, as if by definition, tyranny becomes lawful. Add to that a “secret interpretation” of the law. Lawful? How are citizens supposed to abide by the law when it is subject to secret interpretation? It doesn’t get much more arbitrary than that. We may have less to fear from the terrorists than the overreaching zealots who would suspend the Bill of Rights" - Letter in Denver Post today from Richard Mignogna


“First of all I don’t understand this being bamboozled into thinking that you have to do this to find bad guys. That’s false. There’s very simple principles you can use to find out who is the bad guy and who isn’t and you can do this without violating anybody’s privacy”.- Former NSA code breaker Bill Binney commenting on Keith Alexander's NSA spying testimony and breaking up plots, this morning on CBS Early Show.


"I know the capacity that is there to make tyranny total in America. And we must see to it that this agency and all agencies that possess this technology operate within the law and under proper supervision so that we never cross that abyss. That is the abyss from which there is no return.” - Sen. Frank Church, referencing the NSA in 1975.



Now that we've heard and seen the PR stunt bloviations of Keith Alexander on the Hill, it's time to get real. People need to get their thinking and heads straight and at least try to separate wheat from chaff, signal from noise, bull crap from substance. After being treated to a parade of busted plots yesterday by Alexander, I had to scratch my head and ask: "Wait, only 20% of the 50 plots were in the U.S. - so you had to use an all out, indiscriminate mass dragnet surveillance of every freaking American to do that? And even if fifty Americans might have been killed in these plots (a big IF), that's still fewer than the 55 slaughtered in the Virginia Tech and Newtown massacres .....which most people have forgotten by now!


My point is that our priorities are totally fucked up vis-a-vis our basic rights. We have tens of thousands of deaths by gun each year and basically snooze about it, and maybe we prevented 50 deaths from terrorists - if that- and we go batshit crazy and extirpate all our 4th amendment rights? WTF gives?


Let's ask the question first: What did Sen. Frank Church know 38 years ago that evidently has most Americans sleeping at the citizen switch, according to polls that show 48% have no problem with the NSA PRISM and phone data gathering program while 47% oppose it. (I call the latter group, real citizens, awake and aware – or at least more probably aware of the risks).


Note that Sen. Church didn’t mince words, he used "make tyranny total”  in reference to the NSA’s potential for harm – if not properly collared by the democratic process. It is possible that he was aware of a deep cover, deep secret Cold War-originated program started under Ike and fully validated under Ronnie Reagan. I hadn’t been aware of it either, I must confess, until reading an article in The UK Guardian yesterday along with comments following where one commentator referred to the “fact” the NSA program isn’t designed to thwart terrorists as claimed, but American citizens themselves. He gave it the initials COG for “Continuity of Government”.

I then set to work Googling and found the following information, including an article originally published in Counterpunch by deep politics expert Peter Dale Scott (who has also made singular contributions in his Kennedy assassination research).


- In the 1980s, a secret group of planners inside and outside the government were assigned, by an Executive Order of Reagan, to develop a response to a nuclear attack in which the U.S. government had been decapitated, forcing an alternative to the constitutional rules of succession. Two of these planners were Dick Cheney, then a Congressman, and Donald Rumsfeld, then a private citizen and CEO of the G.D. Searle drug company.


- Though some reports prematurely stated the program was “abandoned” (i.e. Tim Weiner of the New York Times, April 17, 1994), in fact Reagan’s Executive Order 12656, issued in 1988, remained in effect. The order stated that Continuity of Government procedures were called for in the event of "any occurrence, including natural disaster, military attack, technological emergency, or other emergency, that seriously degrades or seriously threatens the national security of the United States."


- In the 1980s COG planning was being handled by Louis Giuffrida. According to an article by Alfonso Chardy (‘Reagan Aides and the `Secret’ Government’, Miami Herald, July 5, 1987.) Giuffrida’s plans included "suspension of the Constitution," along with detailed arrangements for the declaration of martial law.


- According to the 9/11 Commission Report (p. 326; cf. p. 38), "Contingency plans for the continuity of government" were implemented on September 11, 2001. But what measures were invoked remains unclear, though Giuffrida’s template was believed to be integrated into it and former Reaganites were in the WH at the time, who had shared earlier in the architecture (Rumsfeld, Cheney etc.)


- Those suspicious of what COG means today have pointed to a number of post 9/11 steps to facilitate the implementation of martial law, including the creation of a new military command (NORTHCOM) for the continental United States. They note also Homeland Security’s strategic plan “Endgame”, whose stated goal is the creation of detention camps designed to "remove all removable aliens," including "potential terrorists."


- Even worse, later mutations of COG under the Bushites  equated political dissent with treason. (Now we know why the security state was so hot to trot to squelch all OWS protests, including beating the living shit out of them when they tried to approach Wall Street and the Stock Exchange!)

Five years ago, investigative reporter Christopher Ketcham disclosed the extent of the spying which was confirmed last week by whistleblower Edward Snowden. Ketcham reported:

"The following information seems to be fair game for collection without a warrant: the e-mail addresses you send to and receive from, and the subject lines of those messages; the phone numbers you dial, the numbers that dial in to your line, and the durations of the calls; the Internet sites you visit and the keywords in your Web searches; the destinations of the airline tickets you buy; the amounts and locations of your ATM withdrawals; and the goods and services you purchase on credit cards. All of this information is archived on government supercomputers and, according to sources, also fed into the Main Core database.”

Got your attention yet? Ketcham went on:

There exists a database of Americans, who, often for the slightest and most trivial reason, are considered unfriendly, and who, in a time of panic, might be incarcerated. The database can identify and locate perceived ‘enemies of the state’ almost instantaneously.” He and other sources note the database is sometimes referred to by the code name Main Core. One knowledgeable source claims that 8 million Americans are now listed in Main Core as potentially suspect. In the event of a national emergency, these people could be subject to everything from heightened surveillance and tracking to direct questioning and possibly even detention.”

You think this is a joke? Conspiracy theory nonsense? Then you’re not paying attention, especially on how the hammer of the security state was brought down on Occupy Wall Street protestors two years ago! See e.g. http://www.thiscantbehappening.net/node/1494
and my December, 2012 blog post: http://www.brane-space.blogspot.com/2012/12/national-security-state-spied-on-occupy.html


Clearly most COG plans are shrouded in extreme secrecy, effectively unregulated by Congress or the courts. But what ought to get the hackles of any sentient American up is their potential to be yoked to an overreaching surveillance state—as seems to be the case with the “Main Core” database . In this case, even sober observers must weigh whether the protections put in place by the federal government are becoming more dangerous to America than any outside threat.


To emphasize that and ram home the point that even right wing gun owners aren’t safe in their little domeciles if previous FEMA and FBI lists are any indication, the Main Core database includes dissidents and activists of various stripes, political and tax protesters, lawyers and professors, publishers and journalists, gun owners, illegal aliens, foreign nationals, and a great many other harmless, average people….including bloggers like me who may have railed against U.S. military imperialism and capitalism.


Note the “gun owners” included in the lists. So why aren’t the lists used to take away the guns or limit them now to reduce gun deaths? Because it would incite premature alarm and rebellion! The point isn’t to remove the guns now but later after martial law is declared and COG goes into effect. Can’t have any citizen resistance after all, to the forces of the military that will then occupy every U.S. major city.


The point is that the massive PRISM program and data collection is all that’s needed to assist COG plans coming to fruition in the case of any future “emergency” – real or confected. In that case, the terrorists won’t be the targets it will be “troublesome” Americans who still have a yen to express their displeasure by protesting – whether in writing or possible street protests. One thing you may be sure of is that the authorities here don’t want to see mass protests like we’ve beheld in Turkey or Egypt. Those would be the exact pretext by which to launch full COG clamp downs including martial law and suspension of the Constitution – just like Hitler’s Enabling Act did to once democratic Germany.

Think of PRISM then as a "skeleton key" to unlocking the fascist state imperatives incipient in COG. As any master locksmith knows, the skeleton key is the one which unlocks all locks, whatever their design. The principle in making a skeleton key is simple: the exclusion of everything redundant or non-essential combined with the concentration on the minimum effective part. This very efficiency and economy of technique brings the reward of massive application. In the case of PRISM, using existing technology to pinpoint every single American and paint him as "friend" or "potential enemy of the state" - if a future "emergency" is declared. It is also absolutely necessary if COG is to be effective whenever unleashed on an unsuspecting citizenry or using the pretext of the next terror attack - if one should occur.


Robert Sheer in his latest blog (‘The Terror Con’) has referred to “threat inflation” by which the security state keeps weak-kneed "citizens" panting for more protection like screaming school girls petrified of spiders. Keith Alexander's performance yesterday (and also today) are examples of such threat inflation - since while he tells us the number of threats and some vague ancillary info he gives no details on what made them important, or why mass surveillance was required to achieve the null outcome.


Sheer also referenced a June 11 column by Thomas Friedman who warned that if there was a second 9/11-type attack, "we would lose all of our civil liberties, so we should be grateful for this trade-off". WHY lose our civil liberties? Because a bunch of zealots take out maybe thousands of lives? Fucking LESS than lost each year to gun violence! Shit, we who lived through the 1962 Cuban Missile crisis – minutes from nuclear annihilation - find this preposterous! That a nation priding itself on freedom could give up all rights like a bunch of screaming sissies just because of a limited attack! Time columnist Bill Keller also seems to support the “Screaming sissy” hypothesis as when he writes:

“Tom’s important point was that the gravest threat to our civil liberties is not the NSA but another 9/11-scale catastrophe that could leave a panicky public willing to ratchet up the security state, even beyond the war-on-terror excesses that followed the last big attack.”


A panicky public? How about a bunch of pusillanimous pussies that don’t deserve freedom? A bunch that really wants their asses kicked to wake them from their scarifed terrorist-bogeyman coma....which has repercussions on the rest of us (real citizens - not consumers) who value liberty over security! But maybe Keller and Friedman are on to something as when Friedman wrote on June 11:


“I believe that if there is one more 9/11—or worse, an attack involving nuclear material—it could lead to the end of the open society as we know it,”


Yeah, so the deep politics citizen must ask: What isn’t he saying Maybe that he knows COG will come into play and under its mandates, martial law will be permanent and we’ ll inhabit a full Nazified police state. How quickly that freedom went! Barely lasting 230 odd years! But maybe most of us were too damned cowardly and comatose to deserve it. We believed it was a "gift" as opposed to something one had to fight for every single day with every fiber of his mind, and might.

As Sheer puts it:

“No nation in history has ever possessed such an imbalance of military superiority and the ability to ward off foreign threats without sacrificing its core values. Never has this country been as vulnerable to foreign attacks as when the founders approved our Constitution with its Fourth Amendment and other protections of individual sovereignty against an intrusive government. They did so out of the conviction that individual freedom makes us stronger rather than weaker as a nation. In short, they trusted in the essential wisdom of the people as opposed to the pundits who deride it.”


But evidently, as soon as too many citizens became mostly consumers they devolved into crying infants and fucking babies who needed the Pappy Spy State’s protections. "WAAAAHHHHH! Please Gen. Alexander, hold me widdo hands! I don't wanna die from dem der  t'errists!" More important to get that new X-box, Ipad or Notebook than to tend to one’s liberties, after all. Gotta make the country safe for shopping! In this case it may be too late, and the nonchalance evident now amongst the 48 percent will mutate into memory loss of the seventy percent in another few months, evoking Bradley Manning’s and Edward Snowden’s greatest fears: that their leaks won’t have made a difference at all.


“Those who forget the past are doomed to repeat it” – George Santayana


Take a trip back in time:

On March 23, 1933, the newly elected members of the German Parliament (the Reichstag) met in the Kroll Opera House in Berlin to consider passing Hitler's Enabling Act- which was officially called the 'Law for Removing the Distress of the People and the Reich.' (Think of it in neo-Orwellian terms, like "the Patriot Act")

If passed, it would effectively mean the end of democracy: no more labor unions, end of voting, free speech and a free press in Germany and establishing the legal dictatorship of Adolf Hitler. The vote was taken - 441 for, only 84, the Social Democrats, against. This achieved what Hitler had wanted for years - to tear down the German Democratic Republic legally and end democracy, thus paving the way for a complete Nazi takeover of Germany.

Point? “Laws” can be implemented as abominations! Just because we are told mass spying is "lawful" or "legal" doesn't make it so - not if the original law was altered to make it conform to lawlessness. Will ‘Muricans perk up and take notice now lest history repeat, or go back to their Twitter and texting or TV? Sentient Americans have the right to know whether a COG program is still in effect, and whether the spying on our phone calls and Internet usage stems from such COG plans. Indeed, 9/11 was horrific and shocking, but certainly not a decapitating nuclear strike on our leaders as might have transpired if the Cuban Missile crisis hadn’t ended the way it did! In this case, COG and the state of emergency mandates under it should be lifted.


If COG plans are not still in effect, we the People have the right to demand that “enemies lists” and spying capabilities developed for the purpose of responding to a nuclear war be discarded , as we have not been hit by nuclear weapons … and our civilian leaders – on Capital Hill, the White House, and the judiciary – are still alive and able to govern. Let's not have an American Enabling Act take us down and a de fact dictatorship because of the fear of a terror attack. Shit, the Brits in WWII went through years of pounding and terror by V2 rockets raining down and they didn't turn to jelly like we seem disposed to!
-------

To see Peter Dale Scott's article 'Showdown' (on which some of this blog material is based) in Counterpunch, go to:

http://www.counterpunch.org/2008/03/31/the-showdown/

Tuesday, June 18, 2013

Advanced Astrophysics (2) - Solution

For a uniform sphere with a polytropic index n = 0 for uniform density, show that V = -6/5 (GM2/R). Take the potential to be:

W=  3/ (n – 5) (GM2/ R )

For any polytropic gas sphere.


Then we may simplify using n = 0 to get:

W=  3/ (0 – 5) (GM2/ R ) = -3/5 (GM2/ R )

We have already shown that: V = 2W  so:

V = 2W  = 2 [-3/5 (GM2/ R )] = -6/5 (GM2/ R)

Should Black Forest Homes Be Rebuilt? Probably Not

A house is fully engulfed by the Black Forest Fire. The Black Forest fire, after burning up 24 square miles, leaving two dead and destroying over 500 homes, is now nearly out for good. It is easily the most disastrous fire in the state's history, having consumed nearly $800b in property (estimated) and exacted fire fighting resource costs of nearly $36 million, according to the Denver Post (June 16).  Of course, watchful waiting is still needed, as fire fighters still can't relax but must move through and across the scorched forest grounds digging up to six inches deep to excavate still burning embers and pine cones beneath. Even a single spark then can start a new conflagration, if precautions aren't taken, especially as "fire weather" resumes tomorrow with temperatures in the 90s and low humidity, winds.

Meanwhile, the families affected hanker to get back and re-build their homes, yes, in the same Black Forest. Is this a good idea? No, I don't believe so for reasons I will get into.  But recall, this is one year after the Waldo Canyon fire which also blew out of a forested area last year and took 346 homes with it, at a cost of rebuiliding at nearly $450 million. That's nearly a half billion dollars.

Are we now to see these damned fires every year? Yes, according to Prof. Frederick 'Skip' Smith, of Colorado State University and head of the Warner College of Natural Resources Department of Forest and Rangeland Stewardship. According to Prof. Smith, these annual fires are now the "new normal:". Persistent drought conditions, combined with the ravages of the mountain pine beetle (turning forests into tinder) have made the likelihood of destruction by wild fires a near certainty and yes, every year! Worse, people are contributing to the mayhem by deliberately moving into forested areas that themselves are becoming increasingly overgrown.

To highlight this, Colorado state district forester Larry Long - quoted in the Post article (p. 21A) and noting a fire in the densely wooded Black Forest had long been feared:

"They need to take about half of the trees out and then come back and take another third out. It would be a stark contrast to what it is now. But that is a healthy forest. It looks very nice, it gets park like."

The implication clearly is that no one ought to be rebuilding until such time the forest is thinned out.

Beyond that, no home - not one - ought to be built until every last bit of burnt, dried tinder left behind is removed, every last charcoaled tree stump. Moreover,  each new home needs to be re-designed with fire-mitigation structures, techniques in mind.  Same ol', same ol' cannot work ....not any more, and it is supreme stupidity to allow people to just rebuild according to original specs.

As Smith said:

"It's going to mean we are going to have to do a better job of designing these communities and making them defensible in the face of the certainty that these fires are going to happen."

That includes building homes that don't ignite as easily, having infrastructure in place for fire fighters and having escape routes for homeowners as well as fire mitigation plans integrated into all future building codes.

This is extemeley important given over 540,000 Coloradans currently inhabit forested danger areas and that growth in the wildland-urban interface is expected to increase 300 percent in the next two decades, according to Joe Duda - the state's interim forester.

Prof. Smith himself isn't enamored of any more building-construction of homes in these fire prone areas. As he put it (Ibid.):

"We're not going to be able to live with it. The costs are too great. The amount of money we spend for fire suppression is huge and not sustainable. And continuing to put young people at risk to fight fires is not something we want to do."

Bingo!  Additionally, as noted in today's Post (p. 1A), insurance specialists have observed that the premiums paid by home owners living in forested areas don't reflect the risks - so they will undoubtedly have to go up. This should be no different from what happened to those living in the Hurricane Charlie storm zone on Florida's SW coast in 2004. In particular, after Charlie damaged my folks' place in Port Charlotte their insurance premiums shot up 75%. The new premiums were so high that they had to move into a senior apartment complex.  They hated to leave their home of 22 years, but at the same time were relieved to be away from having full responsibility for a hurricane-prone domecile.

In addition to higher premiums, a task force appointed by Gov. John Hickenlooper is looking into the implementation of yearly 'risk' fees such as apply currently in California. There, home owners in wooded risk areas pay $150 each per year for fire protection services that may be used. The total collected last year came in at $90 million which provided enough to fight CA wildfires this year. People are simply going to have to get used to paying for the privilege of living in these isolated, wooded areas. To quote one letter writer in today's Post:

"A tragedy befell those folks who moved out in the woods — perhaps to get away from it all — under the illusion that they are independent of the rest of the world. In fact, they moved all their material stuff to a naturally fragile environment, now under severe stress due to a number of factors, the most prominent being massive climate change. Anyone who lives in such an area needs to understand that they are placing themselves literally in the line of fire while their own presence further damages a suffering ecosystem of plants and animals. " - Linda J. Drake

Meanwhile, the origin of the fire is now suspected as arson, and investigators are going through the scene where it putatively started to ferret out clues. Whoever did this, well...they merit the ultimate penalty.

Monday, June 17, 2013

Introducing Some Advanced Astrophysics (2)

Note: Some readers may first wish to review this basic physics blog here: http://www.brane-space.blogspot.com/2011/05/basic-physics-thermodynamics-pt-12.html

Besides gas pressure, there is also the radiation pressure:

P R = aT4/ 3

where a is the radiation density constant which is equal to:  7.55 x 10 -16 Jm-3 K-4 and T is the absolute temperature (in K degrees).  The equation above is valid only if the material is in thermodynamic equilibrium (i.e. the distribution of radiation is that of a black body). This is generally true, but some exceptions do exist.

In dealing with stars, energy considerations also arise. In particular, the thermal and gravitational energy of a star are very closely related.  In a perfect gas, the total thermal energy is found by multiplying the number of particles N by the degrees of freedom, f, possessed by each particle. The thermal energy per unit volume is then: ½Nf kT.

The number of degrees of freedom f is also related to the ratio of specific heats (g) of the material by:

g         = (f + 2) / f


where g is the ratio of the specific heat at constant pressure to the specific heat at constant volume (if confused, refer to link given above)  or:

g  =  C p / C v

Using the equation for a perfect gas and introducing the thermal energy per kg, U, we find:

U = P/ (g   - 1) r

Bear in mind the material inside a star is highly ionized and in physics a fully ionized gas or plasma is mono-atomic, for which g = 5/3.

Using the previous equation for U in conjunction with the virial theorem, it can be shown that for a star with g = 5/3:


2U + W  = 0

where U is the thermal energy for the whole star and W is the gravitational energy such that:

W  =  - G ò o R  M(r) dM(r) / r = - GM2/ 2R

But the potential energy, V = 2W = - GM2/ R

This can be put into an even more useful form based on the kinetic theory of gases, for which:

P = r v2/ 3

And: -  W  =  3 ò PdV = 3 ò (P/r) dm

Whence:

3 ò (P/r) dm = 3 ò v2dm/ 3  =  m v2   = 2 K


Where K denotes the (gravitational) kinetic energy, which is also expressed:

K = GM2/R

Then in terms of the gravitational energy, W:

-  W  =  2K   or  2K + W  = 0

But: W= - GM2/ 2R  so: K = -W/ 2 = GM2/ R

Which checks out.  We are left with these conclusions:

1) 2K + W  = 0 applies to any spherical system in equilibrium where K is the gas kinetic energy and also the gravitational kinetic energy. (K = 3/2(g - 1)U). As we saw before:

U = P/ (g   - 1) r  so:  P/r  = U (g   - 1) 

Then: 3 ò (P/r) dm = 3 ò U (5/3   - 1) dm = 2 K


2) The binding or total energy of a star ET is then:

 ET  = K + V  = GM2/ 2R  + (- GM2/ R) = - GM2/ 2R

Or: ET  =  W/ 2 = -K

Thus, the total energy of a star is negative and equal to half the gravitational potential energy or the negative of the gas kinetic (or gravitational kinetic).   From the preceding we see that if for some reason ET  decreases, then K increases but W decreases (e.g. the sphere must contract).

Problem for the budding astrophysicist:

For a uniform sphere with a polytropic index n = 0 for uniform density, show that V = -6/5 (GM2/R). Take the potential to be:

W=  3/ (n – 5) (GM2/ R )


For any polytropic gas sphere.*

* Polytropic gas spheres are basically mathematical entities used for modeling of actual stars. As usual, some basic assumptions are made (often in terms of temperatures, pressures, potential energies etc.) and these are then used to develop one or more "polytropic" models to test to see if they can work for a given star. Or, more likely, be employed as a guide to model a star.


A primary objective is to develop a basis for a self-gravitating sphere. In the most desirable of cases, one works to attain a simple relationship between the pressure P, and density (r) of a form:

P  =  K (r) (1 + 1/n)

where K and n are constants, and n is known as "the polytropic index" and K the "polytropic constant".

The polytropic index n can be defined:

n = 1/ (g - 1)

(where 'g ' is the ratio of specific heats.)

The problem thus asks the reader to regard the hypothetical uniform sphere as having a polytropic index n = 0 associated with a sphere of uniform density, and adopting the given mathematical form for the gravitational energy.
 

Cheney Calls Snowden a Traitor? HAHAHAHAHA!

It was a hoot and a holler this morning seeing the frothing, outraged mug of Dick Cheney on network television calling Edward Snowden a “traitor”. I was so struck with the irony of it: the putative biggest traitor since Benedict Arnold "calling the pot black", that I doubled over with laughter, even incepting another bronchitis -coughing spasm. Let’s recall here that it was Cheney who had a plan underfoot to bogusly attack Iraq from 1992  (under the banner of the 'Project for the New American Century') operating under the presumption that Poppy Bush (George the First) would be re-elected. Well, he wasn’t, Clinton took the election thanks to Ross Perot splitting the ‘puke vote. This meant Cheney’s plan had to be put on hold until another Bush could get in, and that wasn’t until 2000 – when five treasonous Supreme Court justices interrupted a Florida recount to hand the election to Junior.

Even then it wasn’t a done deal, a pretext still had to be found for invasion and occupation. The gift fell into the laps of Bush, Cheney and their Neocon warmonger cohort with the devastating 9/11 attacks. People will argue over 9/11’s real origins until their dying day but one thing we do know: the Bush Criminals profited handsomely in the wake, with Bush’’s approval rating shooting up into the 90s (from below 35%) even as the national security state and military –industrial complex got the go ahead for the biggest spending in 60 years. At the very least, while many of us don’t believe these vermin deliberately blew up the Twin Towers, we do think it highly probable they KNEW what was coming and sat back and did nothing. In other words they let it happen.  It was simply too great a benefit ‘plum’ to do otherwise. See also: http://brane-space.blogspot.com/2012/09/how-responsible-was-bush-for-911.html

It also finally enabled the original Cheney Iraq invasion-occupation plan to be put into motion. All the Neocon memos surfacing from just after 9/11 (many from Paul Wolfowitz & Cheney) showed repeated underscored emphases like: “TIE SADDAM TO 9/11! HOW?” Indeed, how? Since Saddam was a resolute secularist who had no tolerance for religious extremists of either the Sunni or Shi’ite Muslim stripe. But the traitor Cheney and his Neocon ilk were determined to make the connection and have the corporate U.S. media coopted to assist in the PR blitz that lasted from October, 2002 until March, 2003 when the Cheney-bred dogs of war were unleashed. To that end, the Cheney-directed Neocons employed every sort of ruse - from 'yellowcake' to aluminum tubes and alleged claims of WMD (from an Iraqi traitor rat named 'curve ball') - to pump up a bogus case for invasion just like Hitler and the Nazis did (using faked imagery of German fraus being raped by Poles) to justify an invasion of Poland in 1939. Once he had the U.S. corporate media on his side it was merely a matter of drum beating a sheep-like American public into giving him the poll numbers he desired to launch an invasion in March, 2003.


The end results were absolutely disastrous, for both the Iraqi people and the U.S.: a wasteful occupation that in the end cost us over $3 trillion and more than 4400 American lives as well as 600,000 innocent Iraqi lives (according to WHO, the World Health Organization). Meanwhile, the bloody Nazified takeover as well as hyped rhetoric (“Axis of Evil”) drove the other two members of that defined “axis”, Iran and North Korea, to develop their own nuclear weapons – realizing this would likely be the only deterrent to the crazed Amerikkan pre-emptive warmongers. So, if Iran and North Korea do have ‘x’ atomic bombs today, you can lay the blame on Dick Cheney’s lap as well as his accomplices, aka the Neocon rats like Paul Wolfowitz, William Kristol, Richard Perle et al.


Make no mistake that Cheney is the real traitor, whose costly pre-emptive war will cost us well into the future, including the brain-damaged vets needing aid, and benefits. To call a real hero like Snowden a traitor is not only to miss the mark on the meaning of the word, but how far our own country has gone down the sewer of decline and mental damage in the last twelve years. The fact the media would put a turd like Cheney on to bloviate and cast aspersions on Snowden also reveals the extent to which the media itself have devolved into total state propaganda whores. (Evidenced even now as most pile onto Snowden, decrying everything from his lack of education, to going to Hong Kong for his revelations and being a "narcissist". Many other people I once respected have disclosed themselves to be shills, including Bob Schieffer and Debbie Wasserman-Schulz)


As for Cheney's claim that the current NSA dragnet surveillance would have stopped 9/11, don't make me freakin' laugh! The actual problem was that the Bushies ignored reams of key information, such as the August, 2001 President's Daily Brief highlighting "Bin Laden Determined to Strike in U.S."  Bush received this while at his Crawford, TX retreat. (He took more vacations than any other president in his first year alone.) And how did Bush respond to this? He gave a quick glance then went to clear some ....bush. But what ought to have made his eyeballs pop out was the short paragraph reading (9/11 Commission Report, p. 255-56):

"An Egyptian Islamic Jihad (EIJ) operative told an [—] service at the same time that Bin Ladin was planning to exploit the operative’s access to the US to mount a terrorist strike."



Then there was the monumental intelligence failure documented by former FBI agent Coleen Rowley who  testified in front of the Senate and for the 9/11 Commission about the FBI's internal organization and mishandling of information related to the September 11, 2001, attacks. She noted how  the FBI failed to take action on information provided by the Minneapolis, Minnesota Field Office regarding its investigation of suspected terrorist Zacarias Moussaoui.

In contrast to Cheney's bullshit claims, the fact is that there was a surfeit of information and data - so much that the Bushie brats either chose to ignore it, or be over selective in what they'd attend to. But again, that's being generous, Those of us who are deep politics citizens and standard politics cynics can't leave out the conviction the Bushies allowed 9/11 to occur on their watch, to reap massive political gain. The past twelve years' growth of the military and super spy complex more than validates that, not to mention how Bush's history has now been so reconstructed at his Dallas' library that only Americans paying attention would know how much of it is bull crap.

See also:  http://www.informationclearinghouse.info/article1544.htm

---------------
Footnote: In a live Q & A on The Guardian website, Snowden fired back at Cheney, lambasting him as the one who engineered the warrantless wiretaps - before the FISA law was revised to make the illegal, legal. See Snowden take down the lying mutt Cheney in the Q&A published at: http://www.guardian.co.uk/world/2013/jun/17/edward-snowden-us-fair-trial?guni=Network%20front:network-front%20aux-1%20Mini-bento:Bento%20box%208%20col:Position1

In the course of the Q&A Snowden also gives much more background into the NSA surveillance program including the use of  "weasel words" by the spy masters to try to squirm out of what they're really up to. I guaran-damn tee you this is the only place you will see these things revealed.
Snowden also pointedly observed that to be called a "traitor" by the likes of Cheney was actually an honor, given, of course, Cheney is the real traitor!

Sunday, June 16, 2013

Astrophysics Solutions (1)

1.  We know:   P = (N o + Ne) k T

Where N o  is the number of atoms of all kinds, both neutral (unionized) and ionized and  Ne  is the number of free electrons (the greater this number, the higher the degree of ionization). The total gas pressure therefore is the sum of the two pressures:
 
P = N o k T + Ne k T

Then:

Ne k T =  (1.45 x 10 19)( 1.38 x 10-23 J/K) (5650 K) = 1.13 Pa

But P, the total gas pressure is 8.3 x 103 Pa, so:

P = 8.3 x 103 Pa  =  N o k T + Ne k T = N o k T + 1.13 Pa

Then: N o k T = 8.3 x 103 Pa   -  1.13 Pa » 8.3 x 103 Pa 

N o = (8.3 x 103  Pa ) / k T =

(8.3 x 103  Pa ) / (1.38 x 10-23 J/K) (5650 K)


N o = 1.06 x 10 23

Where N o    is the total number of neutral and ionized atoms.


2) We assume negligible amounts of heavier elements so:

m        = 4/ (6X + Y + 2)

Where X = 0.9 and Y = 0.1.  Substituting those values:

m        = 4/ (6(0.9) +   0.10 + 2) 

= 4/ (0.54 + 0.10 + 2) = 4/ 2.64

m        = 1.51

(Note that this molecular weight is in proton masses)

3)  We have: 

1/ m  =  (2X + 3Y/4 + ½Z)

But the no. of electrons is:

N=   r /H [X +  (Y + Z)/ 2]  »  r [1 + X]/ 2H

1/ m  =   H Ne /  r  =  (1 + X)/ 2

m =  2/ (1 + X)