Spare Me The Reepo Outrage & Media Hype Over Biden's "Garbage" Gaffe

 

                                              "I want all radical leftists shot for treason!"

                      Two "upstanding" Trump supporters  - Garbage or no?

"Biden utters garbage once and it is taken as an earthquake. Trump spouts the equivalent of garbage a thousand times and it is just Trump being Trump. Gee, the poor guy cannot get a break while Trump slides through mud like he is skiing on pure white snow."  - WaPo Comment

"Americans from both sides of the political spectrum should be alarmed by Trump’s words and behavior. The nation must confront the fact that beyond his hateful character, he is crippled cognitively and showing clear signs of mental illness. There’s no need to resort to armchair psychology to interpret what’s apparent. " - Las Vegas Sun Editorial 

 "Where is the responsibility of  the idiot Trump supporters for fueling and spurring on this obnoxious gasbag?  I mean, think of it, were it not for these supporters (''crazies" as Sen. McCain called them) Trump would have no oxygen, no credibility (via polls) at all. He'd be stuck somewhere around the 1 percent marker along with Lindsey Graham."  My comment from a July 21, 2015 post

Jeebus,  to hear and see all the nattering media nabobs squawking their asses off about Biden's "garbage" remark you'd think he bragged he could go in the middle of Pennsylvania Avenue and shoot someone and not lose any support.  What the fuck is wrong in this country that a president can be waylaid six ways from Sunday for an honest but off the cuff remark but a traitor, adjudicated rapist and convicted felon can see his polls climb no matter what he says?  Such as calling the carnival of hate at Madison Square Garden Sunday night a "love fest".   Or vowing to deport millions of immigrants using the military?  Or mobilizing them after the "enemies within" on his deranged list?  

Never mind the WSJ's Danny Henninger decries this " bottom-of-the-barrel" campaign, can we admit the nation as a whole is teetering at the edge of insanity? I believe we surely can and if you think this is "histrionic" take a gander at this WaPo piece:

As road rage rises, aggressive drivers in Texas try to understand their anger. - Washington Post

 I attribute 90 percent of the basis to over- exposure to Donald Trump's incessant verbal garbage, psychosis and rabid narcissism. And some want to put him back into office again? After he already showed his incompetence with the pandemic causing nearly an extra quarter million deaths.

Can we all agree there is a lack of proportion and proportionate response here, to Biden's knee jerk remark?  Just as in the media's demand that Kamala dazzle in every interview and be excruciatingly specific on her every policy position.  While the orange maggot is allowed to spout and say anything at will and none of the press or very few, blinks an eye.

Look this is very simple. Biden's error was in not being more nuanced. (Likely owing to another aging brain misfire.) But if you are an incidental and low information voter who simply believes (wrongly) Trump is better at economics, then ok, we (and Joe) would grant you a one-time 'mulligan'.  Lots of harm (but no intentional foul) if you happen to vote for the orange reprobate - either because of low IQ, brainwashing (by FOX) or simply not doing the research a citizen ought to do before a crucial election.

However, if you're not merely a misguided voter but an active supporter (who wears Hitler mustaches like Timothy Cusinelli) and cheered on the dregs and deranged "comics" at the Garden, while spreading your own Trumpian lies about Kamala on Reddit - then you are indeed garbage. There is no other way to put it. Because only garbage would back garbage in the person of a maggot who's vowed to terminate the Constitution, and in fact referred to this country as a "garbage pail". And who vows to exact retribution on all those he sees as enemies.

And by God, if you marched with the Nazis and Johnny Rebs in Charlottesville, you are also emphatically garbage.  I refer here to the execrable Neo-Nazi, White Supremacist 'Unite the Right' March in August, 2017

"Jews will not replace us!" shouted by Nazis in Aug., 2017

Of course, the demented Reeps and Trump's campaign imps have jumped all over Biden's gaffe like escaped lab monkeys on angel dust and coke. They believe in their guttersnipe excuses for brains this will trump (no pun intended) the ghastly hate fest at Madison Square Garden -  

Donald Trump | Kamala Harris

“Obsessed With Revenge”: In Dual Rallies, Trump Celebrated Fascism, but Kamala Exposed Its True Face

by Amanda Marcotte | October 31, 2024 - 6:12am | permalink

— from Salon

In the days since Donald Trump's hate-filled rally at Madison Square Garden on Sunday, what's striking is the pettiness of the stakes MAGA defenders have laid out. In the final days of a dead-heat contest for the most powerful office in the world, Republicans argued we must elect a textbook fascist to protect the sacrosanct right of a white man to be rude without being criticized for it.

Most of the racist diatribes at Trump's New York City rally were not jokes. But the comments getting the most media attention — especially calling Puerto Ricans "garbage" — were offered up in a joke-like cadence by podcast host Tony Hinchcliffe. This has allowed MAGA to pretend we're having a national debate about tastefulness, rather than fascism. Hinchcliffe said liberals have "no sense of humor." Trump's running mate, Sen. JD Vance of Ohio, said others should "stop getting so offended."

Trump, however, dispensed with the fiction that we are debating the subjective quality of humor. At a Tuesday press conference, he simply reified the true MAGA belief at stake: that Trump and his allies get to say what they want, and everyone else must shut up about it. This mostly came in the form of griping that Michelle Obama was allowed to criticize him: "Obama, his wife was very nasty to me. That was not nice."

which documentarian Ken Burns ('The U.S. and the Holocaust') has already compared to the American Nazi rally there in 1939.  

Meanwhile, the indiscriminate media has gone hair-on -fire screeching over the Biden gaffe, giving about 100 times more on air time to it than they did Trump's celebration of the haters on Sunday night. But this is what we expect from the lot who see it only in terms of inciting conflict to propel the 'horse race' - and snatch higher ratings and eyeballs however they can.

It may be a bitter pill to swallow but avid-active Trump supporters - by that I mean who share in his hate and pump it all over-  are indeed garbage.  Meanwhile, there is still a chance to rescue the incidental (or genuinely undecided) potential Trump voter - misled by FOX or his social media algorithms - but who can still be induced to climb back from the edges of the orange cesspool.

See Also:

Cue The Sane-Washing (& Psychobabble): Trump's Not Really Demented He's Just Experiencing A 'Flow State'

And:

Swing State Newspaper Slams Trump: ‘Crippled Cognitively’ With ‘Clear Signs Of Mental Illness’

And:

In A Stirring PA Rally Kamala Exposes Trump As The Fascist Nutcase He Is - Will The Mainstream Media Now Catch Up?

The Fourteen Characteristics Of Fascism - What Every Voter Needs to Know

 

"It’s been hard to avoid the conclusion that Trump is, if not fascist, at least fascist-adjacent. His former chief of staff John F. Kelly says so, as have other Trump administration alumni. (Notably, half of Trump’s former Cabinet members have either declined to endorse him or have outright opposed him.) If you find their testimonials unconvincing, listen to Trump’s public comments: He’s pledged to suspend the Constitution, throw journalists in jail, and sic the U.S. military on Americans he considers “the enemy from within,” among other highlights."-  'Only Care About Your Pocketbook? Trump is Still the Wrong Choice'  Catharine Rampell, The Washington Post

Now that fascism (and fascists) are back in the news cycle, I think it behooves every American voter to know what it is - given the extent of ignorance that's been spread over the airwaves the past two weeks.

The Fourteen Characteristics of A Fascist State*:

1. Powerful and Continuing Nationalism -- Fascist regimes tend to make constant use of patriotic mottos, slogans, symbols, songs, and other paraphernalia. Flags are seen everywhere, as are flag symbols on clothing and in public displays.

2. Disdain for the Recognition of Human Rights -- because of fear of enemies and the need for security, the people in fascist regimes are persuaded that human rights can be ignored in certain cases because of "need." The people tend to 'look the other way' or even approve of torture, summary executions, assassinations, long incarcerations of prisoners, etc. In country political enemies are often at the top of hit lists.

3. Identification of Enemies/Scapegoats as a Unifying Cause -- The people are rallied into a unifying patriotic frenzy over the need to eliminate a perceived common threat or foe: racial, ethnic or religious minorities; liberals; communists; socialists, terrorists, etc.  These groups are often denigrated as "vermin, cockroaches, rats" and other unseemly epithets denoting an unwanted "otherness."

4. Supremacy of and misuse of the Military -- Even when there are widespread domestic problems, the military is given a disproportionate amount of government funding, and the domestic agenda is neglected. Soldiers and military service are glamorized. Fascist leaders are also prone to deploy military forces against their own people to quell protests in often bloody ways.

5. Rampant Sexism -- The governments of fascist nations tend to be almost exclusively male-dominated. Under fascist regimes, traditional gender roles are made more rigid. Opposition to abortion is high, and homophobia and antigay legislation dominate national policy. Misogyny is also often used to keep women in their place.

6. Controlled Mass Media -- Sometimes the media is directly controlled by the government, but in other cases, the media is indirectly controlled by government regulation, or through sympathetic media spokespeople and executives. Censorship, especially in wartime, is very common. Peculiar to almost all fascist regimes, however, is one major outlet which generates propaganda to prop up such regimes or try enable them to retain power.

7. Obsession with National Security -- Fear is used as a motivational tool by the government over the masses. "They are coming for you!"  "There are millions of them!" 

8. Religion and Government are Intertwined -- Governments in fascist nations tend to use the most common religion in the nation as a tool to manipulate public opinion. Religious rhetoric and terminology is common from government leaders, even when the major tenets of the religion are diametrically opposed to the government's policies or actions. In the U.S. the manifestation is for Christian Nationalists to destroy church-state separation:

In a race they cast as good vs. evil, Christian hard-liners are fired up for Trump - The Washington Post

9. Corporate Power is Protected -- The industrial and business aristocracy of a fascist nation often are the ones who put the government leaders into power, creating a mutually beneficial business/government relationship and power elite.

10. Labor Power is Suppressed -- Because the organizing power of labor is the only real threat to a fascist government, labor unions are either eliminated entirely or are severely suppressed.

11. Disdain for Intellectuals and the Arts -- Fascist nations tend to promote and tolerate open hostility to higher education, and academia. It is not uncommon for professors and other academics to be censored or even arrested. Free expression in the arts is openly attacked, and governments often refuse to fund the arts.

12. Obsession with Crime and Punishment -- Under fascist regimes, the police are given almost limitless power to enforce laws. The people are often willing to overlook police abuses, and even forego civil liberties, in the name of patriotism. There is often a national police force with virtually unlimited power in fascist nations.

13. Rampant Cronyism and Corruption -- Fascist regimes almost always are governed by groups of friends and associates who appoint each other to government positions, and who use governmental power and authority to protect their friends from accountability. It is not uncommon in fascist regimes for national resources and even treasures to be appropriated or even outright stolen by government leaders.

14. Fraudulent Elections -- Sometimes elections in fascist nations are a complete sham. Other times elections are manipulated by smear campaigns against (or even the assassination of) opposition candidates, the use of legislation to control voting numbers or political district boundaries, and the manipulation of the media. Fascist nations also typically use their judiciaries to manipulate or control elections.

----
As the 1983 American Heritage Dictionary noted, fascism is:

"A system of government that exercises a dictatorship of the extreme right, typically through the merging of state and business leadership, together with belligerent nationalism."

*(Based on a feature article by Dr. Lawrence Britt, appearing in Free Inquiry magazine, Spring 2003 )

See Also:

Opinion | Only care about your pocketbook? Trump is still the wrong choice. - The Washington Post

And:

2024 Elections

This Is Not a Drill. Fascism Is on the Ballot

by Norman Solomon | October 29, 2024 - 4:49am | permalink

The conclusion that Donald Trump is a fascist has gone mainstream, gaining wide publicity and affirmation in recent weeks. Such understanding is a problem for Trump and his boosters. At the same time, potentially pivotal in this close election, a small proportion of people who consider themselves to be progressive still assert that any differences between Trump and Kamala Harris are not significant enough to vote for Harris in swing states.

Opposition to fascism has long been a guiding light in movements against racism and for social justice.

Speaking to a conference of the African National Congress in 1951, Nelson Mandela warned that “South African capitalism has developed [into] monopolism and is now reaching the final stage of monopoly capitalism gone mad, namely, fascism.”

» article continues...

And:

Donald Trump | Fascism

Learning To Trust Trump’s Generals: There’s a Reason Why His Military Men Now Call Him a Fascist

by Heather Digby Parton | October 24, 2024 - 5:52am | permalink

— from Salon

Before Donald Trump was considered nothing more than a circus sideshow, some of us noted during the 2015 GOP presidential primaries that his rhetoric and agenda bore all the hallmarks of the "f" word: fascism. Historian Rick Perlstein wrestled with it as early as September of that year. I wrote about it just a couple of months later. At the time, Trump was extolling the virtues of torture, talking about a massive surveillance program to be used against American Muslims and promising to send Syrian refugees, including children, back to their war-torn country. He hadn't yet declared his intention to ban all Muslims from coming to the U.S. but it was easy to see the writing on the wall. It was also very easy to see that fascism was on the menu in the United States of America if Trump won the election.

That was nine years ago and a zillions of words have since been written about Trump's dishonesty, corruption, unfitness and authoritarian philosophy. We've learned over the years, through many reports, memoirs and tell-all books that Trump tried to govern in a dictatorial fashion at every turn but was either too mentally undisciplined to follow through or was held back by people around him who kept him from acting on his worst impulses.

» article continues...

And:

Donald Trump

If Trump Wins, We’ll See You in Dachau

by Harvey Wasserman | October 30, 2024 - 5:30am | permalink

— from Down With Tyranny!

The first Germans Hitler sent to the Dachau concentration camp near Munich were labor organizers and social activists. If you think you are immune from a similar fate at a concentration camp established by Donald Trump, you are deluding yourself.

Dachau’s ovens mass-burned the corpses of countless political prisoners. Many were Jews, but many were not… including gays, non-Christians, cultural “sub-humans,” feminists, gypsies, Jehovah Witnesses, Social Democrats, Communists, democracy activists and “others” very possibly similar in some ways to you yourself. Likewise, Bergen-Belsen, where over 35,000+ dissident bodies lay lifeless (including that of Anne Frank).

In case you were wondering these are the camps where Hitler exterminated people:

» article continues...

And:

 "Liberal Fascism" is an Oxymoron. It Doesn't Exist Except in Right Wing Brains!

UFOs An Elaborate Ruse For Chinese Spy Balloons - And Framing Donnie Dotard As The Dupe - Not So Fast, Holman

 

Again, with Holman Jenkins Jr's most recent UFO disinfo piece ('Trump and the UFO Smokescreen', WSJ, Oct. 19-20, p. A15), we behold the pathetic efforts of an exceptionally small mind at work to reach for utterly ridiculous nonsense to try to make specious arguments.  In this case to invoke Chinese spy ballons to try to deny the obvious: actual craft from another world having their way in our airspace.  But in Holman's febrile brain this is all "a UFO snow job", writing: 

"Are we ready to admit the great UFO fluffball of 2017 was a smokescreen, exploiting a known susceptibility of the U.S. public to conceal rampant Chinese violations of U.S. airspace?  The game should have been up after last year's spy balloon fiasco, never mind this week's eye-popping Journal account of Chinese drones spying on U.S. military bases near Norfolk, VA."  

So this overpaid twit actually believes that the UAP reported by U.S. Navy pilots, e.g. 

https://youtu.be/Ce6ZevfbIK0 

are Chinese spy balloons or spy drones, and the Pentagon is trying to use fake UFO 'fluff' as a smokescreen to cover it up. How many ways can one put this as dumb even below Trump's mental capacity? Newsflash, Bozo, Chinese spy balloons (and drones) don't move at 7,000 mph.  Nor do they demonstrate the performance traits described by the Nimitz pilots in their 60 Minutes interview from 2019:

Navy pilots describe encounters with UFOs - YouTube

Indeed, the craft self-evident in the Nimitz pilots' video clearly shows we are in roughly the same position as primitive Neanderthals from 50,000 years ago trying to make sense of a 21st century craft that somehow found its way back in time.  Think of a Neanderthal trying to make sense of an F -117 Nighthawk aircraft.

 And you get the idea.   From the Neanderthal's rock- club- knife level of technology the Nighthawk screeching overhead would likely give him a heart seizure.   There is simply no way his crude 'technology' would allow him to comprehend - even in the most rudimentary way- the technology behind the Nighthawk.  The same analogy applies to us "modern humans" trying to make sense of the craft embodying UAP technology. 

Again, Jenkins Jr's  thinking is too pedestrian  (as well as duplicitous) and points to a failure of honest description-  as well as disdain for abstract reasoning. I suspect, as I've written earlier, that no amount of "more rigorous analysis" will reveal the UAP nature or underlying breakthrough technologies because it takes a more advanced technology to adequately analyze a given breakthrough  technology - as demonstrated by the UAP.  But Jenkins Jr. ignores this in favor of confecting yet more spurious ideations that the national security state is trying to trip (or trick) Trump.

Nor has Jenkins Jr. attempted to hide his fixation that UFO-UAP reports were really a ruse since a 2023 WSJ piece where he wrote:

For those who couldn’t figure out why I devoted four columns to the Pentagon UFO debate, this is why. It became clear that, whether from serendipity or design, national security agencies were using UFOs to hide something they didn’t want us to see. That something, it has slowly dribbled out since last May, was Chinese surveillance in U.S. airspace. 

What Jenkins Jr. deliberately refuses to get - likely never will because of an underwhelming IQ --  is that the military and media deflection pranks are all about the loss of  state “sovereignty” - so must be rationalized away.  In other words, it's not a case of something unreal (UAP- actual alien craft) being used to disguise a foreign spy craft invasion of our airspace, but rather the exact inverse: desperate prosaic "explanations" (ordinary drones, weather balloons, 'airborne clutter' etc.) being used to deter actual investigation of alien craft.  

In other words, classic diversionary psyops, such as the CIA employed in the JFK assassination to use "sheep dipping" to frame Lee Harvey Oswald as the assassin.  See e.g.

Frequently Asked Questions On the JFK Assassination (2): Oswald's Sheep-Dipping

but for which Holman is an obvious victim, writing in his WSJ screed:

"The unquenchable desire for Kennedy conspiracy theories arises partly from the continued classification of documents likely testifying to nothing but the intelligence community's embarrassment at failing to wrap up a conspicuous and known threat in Lee Harvey Oswald before the president's visit to Dallas."

 Oblivious to the fact all the salient files pertaining to the assassination have been released, see e.g.

• A Hard Fact: All Necessary JFK Files HAVE Been Released...

Those include the fact that Lee tried to warn of the existing CIA plot to take out JFK in Dallas by using a November 17, 1963 telex to FBI offices. (This was after an initial plot using a patsy named Thomas Arthur Vallee failed in Chicago.) 

In his book, Information Warfare, author Winn Schwartau described psy-ops as the tactic whereby "false information or misinformation is sown pertaining to a real event in order to deflect attention from it and at the same time destroy or compromise the reputations of any who reported the facts."

This is precisely what the agency did to sidetrack any serious conspiracy investigations in 1963-64 and what is being done now to dismiss the UAP craft as simply drones, balloons or "airborne clutter." And where Holman Jenkins Jr. has a role as a "useful idiot".

 The question of current humans (as less advanced) being confronted by an "unfathomable" technology is not preposterous. Go back to my example (in earlier related posts, e.g. Oct. 29 last year) wherein I've cited the futility of explanation -  for what the Nimitz pilots recorded- and the attendant implication of human inferiority.  This lack of explanation offends our egos and so - like Holman in his haste   - we too often dismiss the phenomenon as real.   This goes back to the tendency -  by government sources, as well as the military and the media - to reject the UFO as real - because it comes up against the human concept of state sovereignty.  This is based on a ground-breaking 2008 paper appearing in the journal Political Theory:

Sovereignty and the UFO - Alexander Wendt, Raymond Duvall, 2008

 Therein Wendt and Duvall note the phenomenon of the UFO tends to be rejected as a worthy subject for investigation because the human obsession with sovereignty trumps common sense, open inquiry and hence good science.  The basic  takeaway: Humans, particularly in the top echelons of government and academia can't handle the possibility of subordination of intellect to any kind of exterior (to Earth) civilization.  Hence they adopt the trope: "They can't exist therefore they don't."  This   "UFO taboo" has come to mean the aversion to scientifically studying this phenomenon because it risks larger societal derision and even ostracism.

Still, portions of Jenkins' latest twaddle give away the game, i.e. that his balderdash about Chinese balloons, drones and fake UAP, UFOs is really about trying to bail out Trump. What else can one think on reading:

 "It seems possible now that the UFO snow job was partly aimed at one person, the then commander-in-chief Donald Trump, to keep a president deeply distrusted by our national security establishment in the dark about that establishment's failure to control the national airspace. I will come back to this - the unfailing power of the UFO subject to distract."

So the imbecile's whole bundle of bafflegab is a sorry effort to show the "national security establishment" is employing an elaborate Macguffin to bring down poor Trump.  (As if the orange pestilence needed such especially after last night's Madison Square Garden spectacle of misogyny, racism and psychosis.)

Indeed, at the end of Holman's WSJ screed (as promised) he comes back to his central theme, with assorted yelps about "the government's own penchant for disinformation" (i.e. in the Russian "hoax" case as Holman has called it), e.g.

WSJ's Holman Jenkins Jr. Proves Again He's A Hack..

Confirmed when he adds in his current circuitous bunkum op-ed: 

 "Our press could rediscover the concepts of objectivity, truthfulness and intellectual courage that it consciously junked in the Trump era.."

I.e. the basis for Trump's two impeachments, as well as the Russian collusion with his campaign in 2016, and most recently the hush money NYC case which saw him convicted on 34 felony counts.

Holman, if he ever chose to be an honest broker of facts, would be better served by simply admitting that Trump is the most disreputable and despicable creature to ever ascend to the national political stage. And for any American that would actually cast a ballot for this POS says more about him-her than anything (or anyone) else.

See Also:

• Newly Released Pentagon UFO Files - Not A Laughing Matter...

And:

• Pentagon Brigadier General Doubles Down On UAP-UFO Whitewash...

And:

• Are Laser Plasma Holographs Created By "Foreign Adveraries" Really The UFOs Reported By Navy Pilots?

• And:
• Holman Jenkins Jr. In Latest WSJ Piece Shows UFO Topics Are Way Beyond His Pay Grade 

And:

Video Navy commander David Fravor gives detailed description of his encounter with a UAP

Mensa Polyhedral Graphs Brain Buster Problem

 

An interesting geometrical problem entails the representation of 3-dimensional solids in two dimensions,  The classic 3D solids are the Platonic solids first proposed by Plato, e.g.

Platonic solid - Wikipedia

The five basic Platonic solids are: 

1) Tetrahedron

2) Cube

3) Octahedron

4) Dodecahedron

5) Icosahedron

And each of which can be represented by a polyhedral graph which is shown in the top graphic.  The problem for the industrious reader then is as follows:

Identify which of the polyhedral graphs for the solids is Hamiltonian, which are Eulerian and which are "graceful".

A graph is designated Hamiltonian if there is a closed circuit along the edges of the graph that 'hits' each node exactly once.

A graph is Eulerian if there is a closed circuit that hits each edge exactly once.

A graph is called "graceful" if:

a) Each node gets a number from 0 to n, where n is the number of edges, and no node number is repeated.

b) Each edge gets a number equal to the positive difference of the node numbers on either side of it.

c) Provided no edge number is repeated given edges are numbered 1 through n.

Revisiting Numerical Analysis: Applications To The Kepler Equation Of Celestial Mechanics

 Given the importance of numerical analysis in solving a host of otherwise intractable problems, i.e. in plasma physics as well as  celestial mechanics, it is worth taking another look at it.  We can start with a relatively basic celestial mechanics application.

 The Problem in a nutshell: Given Kepler's equation:  

M =   E - e sin E 

Where M is the mean anomaly of an orbiting body, and E is the eccentric anomaly, with e the eccentricity of the orbit, how does one obtain E when M is known?  The simplest method is based on a formula:

tan E  = sin M/ (cos M - e)

But only works provided e   »  0 

Therefore more 'onerous' methods are needed for the more realistic case e > 0.

One possible approach is to use a Taylor series expansion,

An Introduction To Numerical Analysis - Part 1 (Preliminaries)

f(x) = f(x _o ) + f ’(x _o) (x – x _o) + f ” (x _o) (x – x _o)² / 2!  +……

Applied after reconfiguring the Kepler equation to show:

( E _o  -  e sin E _o )  =  M _o  

Representing a first iteration for starting values of E _o  and  M _o.

f(E) = f(E _o ) + f ’(E _o) (E – E _o) + f ” (E _o) (E – E _o)² / 2!  +……

Or,  substituting relevant values:

f(E) = ( E _o  -  e sin E _o ) +  (1 – e cos  E _o) (E – E _o) +  (E – E _o)²  (e sin E _o )/ 2

As a first approximation, let   E _o = M _o,  then:

f(E ₁) = ( M _o -  e sin M _o ) +  (1 – e cos M _o) (E – M _o) + (E – M _o)²  (e sin ME₀)/ 2

And:  E ₁  is computed iteratively so that:  

| E ₁ – E  | <   | E  –  E _o| 

But  The Newton-Raphson method is a more straightforward approach, e.g.

An Introduction To Numerical Analysis (3): Newton's Approximation Method

Which we will apply here. Begin by letting the eccentricity e = 0.5 and the mean anomaly: M' = 24^o .35 =  E _o

 Then convert to radians:  M' (rad) =  p(24^o .35)/ 180^o = 0.425

We use the basic Kepler eqn. to start:  M' = E - e sin E  

and rewrite it in the form:

E = M' +  e sin E

For starting the iterative process:   M' = E _o = 0.425    and the goal is to get the differences in E from iteration down to 0.001 rad or less.

 Write for E ₁

E ₁=  M'  +  e sin E _o   = 0.425  +  0.5 sin (0.425)

E ₁ = 0.631

And:  E ₁ - E _o  = 0.206

The aim then is to keep the iterations going until the difference in E values if less than one thousandth of a radian.

So next we have:

E ₂=  M'  +  e sin E ₁   = 0.425  +  0.5 sin (0.631)

E ₂=  0.720

And: E ₂ - E ₁  = 0.089

Still  not low enough so go to the next iteration:

E ₃ =  M'  +  e sin E ₂   = 0.425  +  0.5 sin (0.720)

E ₃ =  0.755

And: E ₃ - E ₂  = 0.035

Still  not low enough so go to the next iteration:

E ₄ =  M'  +  e sin E ₃   = 0.425  +  0.5 sin (0.755)

E ₄ =  0.768

E ₄ - E ₃  = 0.013

Still too large so another:

E ₅ =  M'  +  e sin E ₄   = 0.425  +  0.5 sin (0.768)

E ₅ =   0.772

E ₅ - E ₄  = 0.004

Within 'striking' range but not there yet:

E ₆ =  M'  +  e sin E ₅   = 0.425  +  0.5 sin (0.772)

E ₆ = 0.774

E ₆ - E ₅  = 0.002

Once more:

E ₇ =  M'  +  e sin E ₆   = 0.425  +  0.5 sin (0.774)

E ₇ - E ₆  = 5.968 x 10^-4

Which meets the threshold.

Suggested Problems:

1) The mean anomaly  (M) of Mercury is 179 ^o .796  and its eccentricity is e= 0.20563.

Use this to do a Newton-Raphson iteration to obtain the eccentric anomaly. 

2) The mean anomaly of Earth is 198 ^o .115  and its eccentricity is e = 0.01672.

a) Use this data  to obtain the eccentric anomaly E using a Newton-Raphson iteration.

b) Compare the preceding result with E obtained from applying the Lagrange  expansion theorem, viz.

E = M + e sin M +  ( e ²/ 2) sin 2M +  e³/3! 2e ²  [3 ²sin 3M - 3 sin 3M) + ...

c) How do the above results compare with E obtained from the simplest formula:

tan E  = sin M/ (cos M - e)