Friday, January 14, 2022

Solutions To Basic Astronomical Trig Problems

 1) Estimate the distance of Venus from the Sun at its most recent maximum elongation, if the angle of max. elongation was 46 degrees.


The diagram for Problem 1 is shown below, including the angle of maximum elongation:

We know, from the geometry:

SV/ SE = sin (SEV)

Then Venus' distance is:

SV = (sin(SEV)) SE

where: angle SEV = 46 deg and SE = a(E) = 1 AU


SV = sin (46) 1 AU = (0.719) 1 AU = 0.719 AU

2) A recent observation of Mars 36.5 days after opposition showed an angle of elongation = 136 degrees. Find the distance of Mars from the Earth if Mars' orbital period = 687 days.


The diagram for the configuration is shown below:

 We are given t = 36.5 d, and we need to find the "gain" angle:

Θ = 360 (1/P - 1/P') t

where P, P' are the sidereal periods, or P = 365.25 d (Earth) and P' = 687 d (Mars)


Θ = 360 (1/365.25 - 1/687) (36.5) = 16.o8

which is none other than angle E1Sp1.

Now, angle E1p1S is required in order to get the distance - as the information at the bottom of the depiction shows.

We know:

Ep1S = 180 - [SE1p1 - E1Sp1]

and SE1p1 = 136 o  


Ep1S = 180 - [136 o - 16. o 8 ]= 27. o 2  

Again, from plane trigonometry:

sin(p1E1S)/ Sp1 = sin(E1p1S)/ SE1

and, the ratio of planetary distances at time t:

Sp1/SE1 = sin (p1E1S)/ sin (E1p1S)


E1p1S = 27. o2

and p1E1S = SE1p1 = 136 o


Sp1/SE1 = sin (136)/ sin (27.2)

Sp1 = (0.694/ 0.457) a(E) = 1.518 (a(E)) = 1.518 AU

Are Elite Private Schools Really "Indefensible"?

  Mgsr. Edward Pace High in Miami, where I attended

 Caitlin Flanagan’s article ('Private Schools Are Indefensible')  in the April, 2021 Atlantic,  doesn't mince words, i.e. that "money is their god"  and there shouldn't be any public (tax) support. They're getting plenty already with endowments and donations while poor public schools remain in the dregs.  Her piece comes two years after an earlier effort ('The Fury Of The Prep School Parents').  Here is a link to the latter, embodying all (or most) of the vexation Ms. Flanagan shows in the more recent piece.  The basic thesis is that there is too little quality education as well as resources to go around, and the elite private schools seem to be getting most of it.  The corollary is that the paucity of school choice inevitably leads to a kind of 'dog eat dog' landscape in education.  This view is epitomized in a quote from Ms. Flanagan's 2019 Atlantic piece, e.g.

"The shortage of spaces at elite colleges has driven these people mad, and there is nothing at all left to contain their behavior; their true motivation for sending their kids to these schools has been laid bare. But they would have sent their kids to barracks to watch the Flintstones for 4 years if it came with guaranteed admission to Harvard......They are like people who arrive at a five star hotel only to find there aren't enough lounge chairs by the pool and the main dining room is fully booked at $750 a night?  That's not going to stand"

Is she being histrionic or hyperbolic? No, not when one saw the lengths to which the parents involved in the "Varsity Blues" scandal went  - in order to get Johnny or Janie into what they believed was an "elite" school.  The real question in all this is what is driving the insane, mad rush propelling the parents to be so obsessive - compulsive about school-college choice?   Indeed, a Wall Street Journal analysis from 2016 puts the kibosh on the notion that elite colleges confer any special earning advantage, say over state colleges or universities.  The Journal's report (Feb. 1, 2016, p. R1) looked at 7,500 college grads 10 years after graduation and divided their majors into several categories: business, engineering, social sciences,  humanities, education and 'other'.   They also cross-referenced three categories for college type: "selective" (covering 'elite' schools), mid tier and less selective (covering schools with open enrollment).

As the Journal report authors (Eric R. Eide and Michael J Hilmer) put it:

"What we found startled us. For STEM-related majors, average earnings don't vary much among the college categories. For example, we found no statistically significant differences in average earnings for science majors between selective schools and either midtier or less selective schools."

This is truly amazing and also important to know. It means, basically, one will not be significantly better off (with earnings to come), say in the physics field - graduating from Harvard or the University of South Florida.  One may actually be worse off financially graduating from Harvard with only minimal financial assistance.   As the WSJ authors go on to point out (p. R2):

"Our findings are crucial for families to understand because chasing a prestigious STEM degree can leave students burdened with huge amounts of unnecessary debt."

Also, this confirms an earlier (2011) MONEY magazine investigation which found it is more the name and reputation of the specific department that confers long term benefits than the name of the school itself. As the MONEY authors write:

"Don't assume an Ivy League education is better than one from a public or state university."

So there is no need to go helter-skelter crazy, "helicoptering" and losing sleep trying to get a kid into a perceived elite college.   Certainly not to the extent Flanagan describes (p. 54, April 2021) of being told by pediatricians "these kids are starting to crack" and getting docs to prescribe "study drugs" like Adderall, and "sleep drugs".  This is, let's be blunt, batshit crazy.   If the kids are starting to "crack" as the doctors. Flanagan cites claims, it's because the parental expectations are excessive for the kid, and hell, the competitive gusto and drive shouldn't be this extreme anyway.

 Indeed, the stratification already exists in terms of the percentage of Americans who attend or finish college in the first place - whether a state university or an Ivy.  In fact,  about  two-thirds of Americans over 24  never started or completed a 4-year college degree.  Technically that ought to put any graduate of an accredited 4-year university in the driver's seat for future success. This would, in fact, be the case if the parents collected their wits enough to grasp it is the particular academic departments  that ought to be the focus, not the particular university.

So why the insane, quasi-Darwinian rush to pile into only a handful of schools perceived to be "exceptional"?  Well, because as Flanagan notes, parents perceive a "dog eat dog" world now where benefits that accrued to them may not extend to their offspring, so they feel they must fight harder. But there is also the PR and branding factor of the elite universities - super charged up by assorted college rankings, ratings - See e.g.

 These go a long way to fire up latent parental anxieties, expectations, tensions....and sleepless nights.  In the words of psychologist Robert Evans as conveyed to Flanagan (ibid. p. 54) "What's changed in the past few years is the relentlessness of parents. ...Many can't let go of their fears their child is being left behind."  

But what about elite private schools in general? Are they responsible for the mass of kids getting left behind? And if this mass of "underprivileged" kids were suddenly granted free educations at Choate, Exeter, Spence, Brearley, Dalton School or Delbarton, would they really make the most of it?  Or fritter away their extra time with video games, Instagram and other assorted nonsense?  Inquiring minds want to know, because I for one am unconvinced there'd be a sudden spectacular uplift in U.S. secondary education.  

For sure, I am unable to get as worked up as Flanagan does, maybe because I attended a private Catholic high school - Mgsr. Edward Pace in Miami (see top image)  - which today is perhaps the best private high school for the money ($14,000 /yr.) in the Miami area.  (If one checks out its website including the teacher student ratio, 15: 1, as well as the proportion of staff with Masters or Ph.D. degrees (85%))   Not to mention the plethora of AP course offerings and advanced computer facilities.

The education Pace afforded me was one I could never have obtained at the public schools in the area in 1961, e.g. Carol City High - which my three younger brothers attended. (Only one brother, Jerry, passed the Pace entrance exam but after a year he decided to leave to attend Carol City High.) My preference for Pace also echoes the take of one Atlantic letter writer (Abigail Sylvor Greenberg)  who transferred to an elite private school (Brearley)  in NYC and responded to Flanagan:

"I transferred there in high school, and as a humanities lover coming of age in a STEM-centric, test-score-focused, preprofessional educational climate, I felt I’d stumbled into intellectual paradise. I am certain that my school’s first value (before boosting its capital or launching its graduates into the professional stratosphere) was and is learning, joyfully, for its own sake.

That, I think, is something rare enough to be worth preserving, something that would be hard to replicate, something to which more students, not fewer, should have access. It’s not independence that is indefensible. It’s inequity."

 Learning for its own sake!  What a concept! That is exactly what I found at Chaminade High - the first private Catholic HS I attended (in Hollywood, FL, 1960-61) and then at Pace (1961-64). The ability to do independent research especially - which led to my award-winning science fair project, e.g.

This was something I couldn't have done at Carol City High (1,500 students compared to 340 at Pace) given its imposed 'cookie cutter' template- same standard courses, same times every day, with no opportunity for independent achievement. Compare Pace's independent research opportunity to that advertised at Choate-Rosemary Hall:

The Science Research Program (SRP) offers motivated and independent science students the chance to step beyond the traditional classroom structure to explore their area of interest. Coursework is focused on training in the basics of scientific inquiry and experimentation.

Jerry's opting out of Pace clearly shows not every kid may be cut out for elite schooling no matter its special benefits or available resources. Jerry could never have thrived at Pace because the academic rigor didn't appeal to him. He was more interested in hands-on mechanical pursuits like auto and a/c repair which were available in Carol City High's Shop classes. (This may also suggest a dire need in the U.S. to provide more trade school opportunities like the apprenticeship programs in Germany.)

 Indeed, my 'theory' is if a reluctant kid is pushed too far in this direction of academics and educational exceptionalism there may be self-sabotage. We saw that emerge some years ago when a bunch of teens bound for Harvard got derailed with their 'Harvard Memes for Horny Teens' social media inputs, e.g.

Brane Space: Harvard Rescinds Admissions To Ten Right Wing Garbage Purveyors - But This Is No 'Free Speech' Issue! (

What if the kid really wants to enjoy the richness of what an elite academic emphasis on education can provide, but can't?  Ms. Greenberg refers to the "inequity" being indefensible, but how does inequity arise?  Basically, it is from way too many chasing a perceived unique good, in this case a superior quality education that includes love of learning for itself.  But even if we excluded all those like my late brother Jerry, who preferred shop and mechanics to Socratic discourse and books,  that leaves millions pounding on the doors to get into Pace, Chaminade (now Chaminade-Madonna), Choate- Rosemary Hall, Phillips Exeter, Dalton School or Brearley.  

Since the demand for exceptional quality education exceeds the ability of all the private schools in the nation to "supply" it, this means one must think outside of the box, to use the old cliche.  One solution would be to let a subset of these special elite schools televise classes, or in-house lectures (if such exist) much as Yale University does with lectures now, e.g. this introductory lecture about Dante's Inferno:

ITAL 310 - Lecture 1 - Introduction | Open Yale Courses

The televised classes, whether in English Lit, Geometry or AP Calculus would provide examples of quality teaching methods to less well-endowed schools. Might even inspire their staffs to use similar approaches. Could such an ambitious undertaking really be done?  I believe so especially given most of the endowments and other donations, just to a place like Delbarton,  e.g. 

 Delbarton School | A Benedictine Catholic School for Young Men in Morristown

Or Dalton School, e.g.

Homepage (

Or  Choate- Rosemary Hall:

Choate Rosemary Hall | Private Boarding & Day School

(Where JFK attended when it was Choate)

Can run into the tens of millions a year. (Flanagan cites one $1.3 billion endowment just to Exeter) By merely using a fraction of these support funds for academic outreach  lectures - a la the Yale example shown above - an enormous amount of good will can be purchased.  This would also surely - lessen the journalistic blowback,  such as Flanagan's Atlantic pieces arguing  elite private educations are "indefensible".  Such a bold initiative would also address Flanagan's core question (April, p. 52): 

"Why should any public school parent support these elite private schools?"

And after all, what was one of Choate - graduate JFK's most famous quotes when President?

"If a free society cannot save the many who are poor, it cannot save the few who are rich."

See also:

The Best High Schools In America (


by Robert Becker | January 14, 2022 - 7:44am | permalink


America's pushing dumb and dumber, while dumbing down the next generation. Astonishingly, at least to the over-educated, we are willfully blind to how rapidly and profoundly the key engine for our high living standards is slipping away. Whether running a family or a conglomerate, you can't fix stupidity, signaled by not learning from failure. Terrorists stick to actual caves, but we are constrained in mental frames.

The crucial imperative is feeding innovative, intellectual capital across the boards, from K through advanced studies, public and private. Do we need another Sputnik to rouse us from smugness?

Thursday, January 13, 2022

Researchers At Univ. of Colorado Show How To Escape Omicron Infection Using Common Sense Approaches


Recall  I've used multiple posts to warn how the Repukes and their cult TV network (FOX) used lies and propaganda to drive down the numbers of vaccinated and spread Covid infections, e.g.  

In order to try to drive Biden's poll numbers down (with largely brainwashed, gullible respondents) and make him a one term president so Trump can return.  So far, this has largely succeeded even though the red state- unvaccinated have let their Covid body bags pile up by the hundreds of thousands. All at the beck and call of Tucker Carlson and FOX News. "Better to be dead than Dem" is their motto!  The success was brought to the fore today with WSJ Troll Dan Henninger's latest trash column (p. A17) where he refers to the latest AP/NORC poll posing the question:

  • “Thinking about the problems facing the United States and the world today, which problems would you like the government to be working on in the year 2022?”

And the response? Naturally 68 percent indicated inflation needs attention, but that will not likely be solved until near year's end after most supply issues are resolved with the latest (omicron) wave.  But the real show stopper, according to the poll, was that only 33% "want government to continue to work on Covid 19" - a 20 point drop from last year.  This is nothing short of amazing but shows most don't get it.  They are taking their despondency about the delay in returning to normal (pre-pandemic) and blaming it on Biden and the Dems.  They fail to grasp the GOP strategy has consistently been to discourage and distrust government as a solution  - this despite the fact it has been the only solution (since Trump left) under Biden and the Dems. But this has always been the Repukes' shtick: to obstruct, carp and incinerate truth and facts to try to show governance is ineffective -  when it is their forlorn cult which is.

So pardon me if I remain unimpressed by Henninger's latest babble. Anyway, two researchers at the University of Colorado, Jose Luis-Jimenez and Zhe Ping, have recently had published  a synopsis of their work (in Denver Post) showing the best ways to avoid omicron infection.  The first thing they ask readers to note is that the SARS-CoV-2 virus spreads by airborne transmission. So the key

So the key to avoiding transmission is to understand  how airborne particles behave which requires knowledge from physics and chemistry.   As high school physics students learn, air is a fluid comprised of rapidly moving, invisible molecules.  This can be most dramatically demonstrated using an apparatus similar to that shown below:

In which a heated gas expands to move a piston confining it, thereby increasing its volume from V1 to V2. The air particles under pressure move more randomly and rapidly when heated. In a confined space, such as shown above or in a room, the particles of air will also effectively transfer and carry virus particles.  The concentration of these particles, say in people in the confined space yelling or talking loud, increases and enhances transmission probability.  The closer you are to these viral sources of emission the more likely you will be to get infected. 

The longer you spend time in such a closed room and in proximity to such sources the greater the likelihood of inhaling air containing virus particles. The greater chance then of becoming infected. Step outside in an open air space and the chances for infection plummet because the once-concentrated virus particles are now dispersed. The space is essentially "infinite". (Think of simply removing the piston in the diagram from the top of the once confined air.)  

All the above enabled the two CU researchers to arrive at  a quantified study that took into account such parameters as: mask wearing (and type, i.e. cloth vs. N95), room size, occupancy, vocalizing of those inside, inside vs. outside space of socializing, and ventilation levels in inside spaces. Their conclusions were summed up thusly -starting with a transmission table: 


A surefire way to catch COVID is to do a combination of things that get you into the dark red cells in the table. For example:

  • Gather together with lots of people in an enclosed space with poor air quality, such as an under-ventilated gym, nightclub or school classroom
  • Do something strenuous or rowdy such as exercising, singing or shouting
  • Leave off your masks
  • Stay there for a long time.

To avoid catching COVID, try keeping in the green or amber spaces in the table. For example:

  • If you must meet other people, do so outdoors or in a space that’s well-ventilated or meet in a space where the ventilation is good and air quality is known
  • Keep the number of people to a minimum
  • Spend the minimum possible amount of time together
  • Don’t shout, sing or do heavy exercise
  • Wear high-quality, well-fitting masks from the time you enter the building to the time you leave.

While the chart gives an estimated figure for each situation, the actual risk will depend on the specific parameters, such as exactly how many people are in a room of what size. If you fancy putting in your own data for a particular setting and activity, you can try our COVID-19 Aerosol Transmission Estimator.


It is my contention that if the preceding prescriptions and advice are rigorously followed, then more infections could be avoided and the pandemic brought under more rapid control.  But will the FOX, Tucker Carlson viewers and other Repukes cooperate, or continue trying to torpedo Biden? Only time will tell.

See Also:

Omicron mild cases could still get out of hand - The Washington Post

Solutions To Planetary Sidereal Period Computation Problems

 1) Recall we defined the synodic period to mean the time interval for the revolution of a planet as determined from the same phases, or the same geometrical configurations, i.e. "western elongations". Then the sidereal period of an inferior planet that appeared at greatest western elongation exactly once a year would be from:

1/ S = 1/P1 - 1/P2

     Bear in mind if the planet is inferior then P1 refers to the planet's sidereal period and P2 refers to Earth's.


1/P1 = 1/S + 1/P2

where: S = 1 yr., P2 = 1 yr.


1/P1 = 1/1 + 1/1 = 2

so: P1 = 1/2 yr.

2) Saturn is a superior planet so we apply:

1/ S = 1/P1 - 1/P2

but now with P1 = Earth's sidereal period, and P2 = Saturn's. Thus we have:

1/P2 = 1/P1 - 1/S

where S = 1.03513 years

1/P2 = 1/1 - 1/1.03513 = 1 - 0.966 = 0.0339

P2 = 1/ 0.0339 = 29. 4 yrs.

3) From the diagrams in Fig. 1(a)-(b) of previous (Jan. 11)  blog post it is evident that an inferior planet's maximum elongation is still less than 90 degrees - i.e. when its geocentric radius vector is tangential to its orbit configuration. By contrast, the elongation of a superior planet can vary from 0 deg at conjunction to 180 degrees at opposition.

Hence the planet must be a superior one.

4) Again, we employ:

1/ S = 1/P1 - 1/P2

Bear in mind, that since Mercury is inferior then P1 refers to the planet's sidereal period and P2 refers to Earth's.

Then: P1 = 88 d and P2 = 365¼ d


1/S = 1/88 - 1/ (365¼ days)

1/S = 0.01136 - 0.00273 = 0.00863

S = 1/ (0.00863) = 115.8 days

The Dystopic Sci-Fi Classic 'Soylent Green' - More Prophetic of 2122 Than 2022


                               Crowd scene from 'Soylent Green' in year 2022

The sci-fi classic 'Soylent Green' this year celebrates its 49th anniversary.  Why the big deal, as opposed to waiting for the 50th next year? Because the film is set in the year 2022.  One WaPo piece, e.g. 

‘Soylent Green’ (1973) predicted the world in 2022: climate change, inequality - The Washington Post

 has already explored the alleged "similarities" between the portrayed year and this one, but it's mainly all a stretch as readers can discern just from this trailer of the original 1973 film:

Soylent Green (1973) Official Trailer - Charlton Heston, Edward G Robinson Movie HD - YouTube

In fact, as  I will show, the film's assorted data points, low points, and "forecasts" are a lot more apropos of the state of our nation in 100 years.  Here are the main points of reference to consider:

- Soylent Green: Software engineer Rob Rhinehart’s real-life Soylent meal replacements in 2013. Soylent today is available in powder and bar form. It “meets the Food and Drug Administration’s standards for a whole raft of healthy claims,"   However, unlike in the movie, it's not made of any part of re-processed human corpses! (Which is what our cop hero 'Thorn' discovered at the very end.)

'Furniture':  As depicted in the movie, adult females are treated as "furniture" if not attached or employed in any official capacity. They are used then re-used, and if a cohort dies or is killed (like Simonson in the film) they remain at the abode for the next owner, buyer, renter.  Obviously there is no parallel to that horrific circumstance in our 2022. (Sex slavery is not exactly the same thing, though it may appear so at a superficial level, but viewing the film will dispense that.)

Technology:  The technology depicted, alas, is a lot like we saw in 1973.  There are no cell phones, no drones visible, and the video games available - such as shown in Simonson's elite digs - more or less are like later versions of "Pong".  On the larger scale, it is evident the main power grids have collapsed - likely from excess demand so we see the electric infrastructure, what there is (mainly for the upper 0.0001%),  is on its last legs, and power for the masses iffy at best.   Saul has to get on his bicycle and peddle hard as a form of mechanical energy generation to keep lights on, etc.  No one can travel because there aren't any means or modes of transport.  All of which would be expected assuming the trajectory we're on, by 2122.

Books-education: Books no longer exist except in small, cloistered enclaves where the few remaining scholars (called "books") gather to do research and share their findings with each other.  From the appearance of the landscape in which Saul and Thorn exist there also don't appear to be any kids. At least none I could see. It is as if the mere struggle to line up for daily water and "food"  (Soylent varieties of "tasteless, odorless crud" in Saul's parlance) have sapped the energy from all living adults to even reproduce. 

- Population:  The movie forecasts NYC with a population of 40 million, or about 5 times the number density of today. That is near preposterous given there would barely be space to move, let alone live. In the film Thorn notes homicides being logged at 137 per day, and this would be expected in a city so densely populated. We know aggression is triggered by increased population density and crimes of all forms explode, especially in a setting of dwindling resources.  We don't have such a condition in NYC today, thank goodness.

  Apart from that the writer (Harry Harrison) and film producers,  failed to envisage how land, rental prices would skyrocket - leaving the city mostly unaffordable.  The greatest human numbers conceivable for the city - even by 2122? Maybe 9.5 million. More likely far less, as the exodus from urban areas that began with the Covid pandemic continues for the next 100 years.

Assisted Suicide:  There is assisted suicide in the film's version of 2022, as there is in ours The difference is that it is carried out by a techie in a centralized theater kind of setting.  It is assumed - and rightly so - this world is so god-awful horrific that many will choose a final escape and that is the case with Thorn's 'book', Saul.  (Especially after learning the secret of Soylent Green, that it is basically reprocessed human corpses.)  The process is that the person is given a robe then a nice comfy couch to lie down on while viewing a 30 minute video of scenes from the old Earth.  The one where river waters and the ocean were still clear, mountains had snow, and cities weren't overrun with garbage, smog and people.  By the end of the video the person is put to sleep, permanently with those visions of what the planet used to be dancing in his or her head.

- Heat/ Greenhouse effect: The elderly character, a "police book" named Saul Roth (played by Edward G. Robinson) refers at one point to a "heat wave" (in the 90s) all year round.  This means we have passed the first year of no seasons (projected to be 2040, by David Suzuki) and are at the cusp of the runaway Greenhouse effect or just past it.  Indeed, the rate of ocean warming, e.g.

The Ocean Absorbed 20 Sextillion Joules of Heat in 2020 | Earth.Org - Past | Present | Future

Means that, as reported in the UK Guardian, the oceans have absorbed heat equivalent to  7   Hiroshima- scale atomic bombs, detonating each second,  24 hours a day  365 days a year.  

According to the next to last IPCC report:

"Crossing the 2°C global warming level in the mid-term period (2041–2060) is very likely to occur under the very high GHG emissions scenario (SSP5-8.5), "

In that SSP5 -8.5 scenario we will see an increase of 5.7 C  by 2100,  which is the level expected by the Bulletin of the Atomic Scientists - which noted two years ago that IPCC climate report understated the threat.  By logical extension, this current one also does.  Do the math.  If the current rate of CO2 concentration increase is at  2.5  W/ m2  the CO2 concentration is increasing at 2.5 ppm/ yr.  

Then add 75 yrs. projected increase to the current mean yearly value of 415 ppm.  In 75 years that means an additional (2.5 ppm/ yr.  x 75 yrs.) = 187.5 ppm or 415 ppm + 187.5 ppm =  602.5 ppm.  But most climate scientists - such as Prof. Gunther Weller-  take 600 ppm as the threshold for the runaway greenhouse effect.

The projected 75 years yields close to the year 2100, e.g. 2097.  But well within the limits of uncertainty for the actual runaway Greenhouse to begin.  Thus, 2122 could be the actual start. How so? Well, the fact the heat is unrelenting as depicted in the film, and also clearly all the food chains have collapsed-- which is why beef is next to impossible to find (not enough water to support cattle raising) , a head of lettuce, 2 tomatoes and a leek retail for $279 and a jar of strawberry jam can cost $150.  The only form of nutrition for the billions of hoi polloi then is the stuff ("tasteless crud") produced by the Soylent Corp. - and we know where that comes from!

Wednesday, January 12, 2022

Introduction To Basic Astronomical Trigonometry

      The most basic and intuitive method for measuring a star's distance employs elementary trigonometry. It is called the  "parallax  method"   because it uses the phenomenon of "parallax". One can get a simple idea of this by holding an index finger at arm's length- then looking at it  with  only  the  right eye open,  then only the left. What you'll see as you do this alternatively  is the visible shift of your index finger against the given  background. Say from one part of your book shelf to another. (A very tiny shift.)

The angle that is subtended between the different background points, with respect to your nose ("vertex" of the resulting triangle), say,  is the "parallax angle".  The diagram below shows how it is measured:


Here, the points E1 and E2 represent Earth at two opposite points of its orbit around the Sun. The star indicated is the one for which the distance(d) is sought. Using photographs of the star taken at the points E1 and E2, we can measure what is called the angle of parallax p. The solution for the distance can be obtained from:

d = r/ tan(p)

that is, equal to the radius (R) of the Earth's orbit, e.g 1 A.U. or astronomical unit = 93 million miles = 1.5 x 1011  meters) divided  by the tangent of  the angle  p. (which will be a very small angle).  The tangent is a function which denotes a ratio of lengths for a right triangle. In this case, the tangent of the angle p is defined:

tan(p) = opposite/ adjacent = R/d

i.e., the side  opposite the angle (R), divided by the side (d = distance to star)  adjacent to the angle (d). Using algebra, one then makes d the subject, which means solving for it.

    It can be shown, from the above, that for angle p = 1" (one second of arc, or 1/3600 of a degree! ) the distance to the star is always 1 pc (parsec).   Bear in mind 60' = 1 deg and 60" = 1' or 1 minute of arc) the resulting d = 206, 265 A.U. or astronomical units (206, 265 x 1.5 x 1011 m).

The exact term logically chosen for this particular distance is the parallax-second or parsec and doing the math (tedious, but possible) shows the distance turns out to be:

1 parsec = 3. 26 light years.

     Now, given this relationship , it follows that any proportionate decrease in the angle p allows one to work out the resulting distance! Thus, if p = 0.5" then d = 2 parsecs or 6.52 Ly, if p = 0.25" then d = 4 parsecs or about 13 Ly and so on. Thus it was found that even the nearest stars were light years distant - using the simplest conceptual method available. The first successful parallax measurements - so far as we know - took place around 1838, when Friedrich Bessel (Germany), 
and Friedrich Struve (Russia) detected the parallaxes of the stars 61 Cygni, Alpha Centauri and Vega, respectively.  

Another application of basic trigonometry in involves obtaining the relative distance to an inferior or superior planet in relation to the Earth. As we've seen before, it's easy to apply Kepler's 3rd law to obtain the basic dimensions of an orbit, namely the semi-major axis of the orbit - or the mean distance from the Sun. But things become somewhat more difficult when we seek to find the distance say, of the Earth to the planet, or the planet at a specific time - say before it commences retrograde motion.  

So we consider two cases in the diagram below:

Case (A) Inferior planet
As  seen above, the maximum elongation occurs when the planet's geocentric radius vector (pE in diagram A) is perpendicular to the planet's heliocentric radius vector, pV. Then by a careful measurement of the angle SEp, say over a series of nights around maximum elongation, one can obtain a value for the angle of maximum elongation. At such time the angle SEp is right-angled hence:

Sp/ SE = sin(SEp)

    The quantity Sp/SE is the distance of the planet from the Sun in terms of Earth units or AU, (i. e.  astronomical units). Let Sp = R and SE = a(E) the semi-major axis for Earth's orbit, then:

Sp = R = sin(SEp) [a(E)]


    If the angle SEp = 60 deg, find the planet's distance from the Sun.

    Then: sin(SEp)= sin (60) = Ö3/2 = 0.866

    So: R = 0.866[a(E)]= 0.866 AU

Case (B) Superior Planet

In this case, we apply diagram (B), showing the planet at two successive positions, p and p1 and the Earth at E and E1. This is a more difficult case but can be worked if the planet's synodic period S is known.

     Here, we let the planet p be in opposition at some given time with the Earth and Sun (e.g. showing the alignment S-E-p in diagram (B). As we know, with opposition, the elongation is a straight angle or 180 degrees. Then after t days have elapsed the Earth's radius vector SE has moved ahead of the planet’s as shown in comparing SE1 to Sp1. As can be seen, this reduces the angle of elongation from 180 degrees at opposition to angle SE1p1. This is then measured.

    Now, over t days, the angle ESp will have increased from 0 (at opposition) to a value Θ given by:

Θ = [n – n p] t

where n, n p are the mean daily motions of the Earth and the planet, respectively. Using relations for the periods seen in the previous chapter, we may write:

Θ = 360 (1/P - 1/P') t

where P and P' are the sidereal periods   (See my post of Jan. 11th) for the Earth and the planet, respectively.  Then it follows:

Θ = 360 (1/S)

 So, since t and S are both known, Θ can be obtained - that is, angle E1Sp1 is calculated. Hence, angle E1p1S can be found from:

angle E1p1S = 180 - angle SE1p1 - angle E1Sp1

From plane trigonometry we then obtain:

sin(p1E1S)/ Sp1 = sin(E1p1S)/SE1


Sp1/ SE1 = sin(p1E1S)/ sin(E1p1S)

again, giving the distance from the Sun in terms of Earth's distance unit.


1) Estimate the distance of Venus from the Sun at its most recent maximum elongation, if the angle of max. elongation was 46 degrees.

2) A recent observation of Mars 36.5 days after opposition showed an angle of elongation = 136 degrees. Find the distance of Mars from the Earth if Mars' orbital period = 687 days.

Tuesday, January 11, 2022

Succumbed To "Worry Porn" Because We Warn Of U.S. Democracy Demise? Why Holman Jenkins Jr. Remains An Ignorant Asswit

"The next national election will almost inevitably be viciously (perhaps violently) contested. It is fair to say that the right-wing threat to the United States — and its apparent goal of laying the groundwork for a power grab, if necessary, in 2024 — is politically existential. Yet many Americans seem to be whistling past the graveyard of American democracy. ..

A right-wing minority — including many elected politicians — is now practicing a form of brinkmanship by threatening to unilaterally destroy American democracy, daring what it hopes is a timid and somnolent majority to resist. But that majority has the benefit of warning ahead of 2024." -  Jonathan Stevenson and Steven Simon, 'We Need To Think The Unthinkable About Our Country', NY Times

Can we all agree that Holman Jenkins Jr. is perhaps the most productive troll in the Wall Street Journal Op-ed stable of trolls (which includes Dan Henninger, Kimberley Strassel, William McGurn)?  The question that remains isn't the magnitude of Holman Jr's  assholinity and ignorance, but whether he actually believes the garbage that fills each column he churns out.  

Exhibit A in the recent cavalcade of codswallop is his Saturday, Jan. 8 brain rot tripe ('Why The Jan. 6th Big Lie Narrative Will Fail', p. A13) in which he basically mocks all those who have warned of our democracy's demise- despite more than one-third of voters (and 70 % of Republicans) continuing to believe Trump's Big Lie.  Which - in case it escaped  little Holman's attention -  has acquired jet fuel acceleration over the past year with even formerly benign "little grannies" now buying into it.  This according to WaPo columnistCarol Leonnig appearing on MSNBC 'Deadline White House' last Friday - noting how she was shocked when a granny in a book club actually asked her about the "rigging of our elections."  To say she was gobsmacked is putting it mildly, and yet Holman treats it all basically as a joke, the media - especially -being too immersed in "worry porn".  In his words:

In the cavalcade of Jan. 6 remembrances-cum-worry porn, NPR’s “Morning Edition” took the trophy, being the first out of the gate with a lengthy report on experts who outbid each other in predicting Donald Trump’s election “big lie” will lead to a civil war or coup d’état in 2024. This formula you now have seen everywhere, including in the speech of Joe Biden.

And lest we forget, recall I had praised Biden's speech in my post last Friday, e.g.  

So I suppose I am among the lot who have succumbed to Jenkins'  "worry porn" too. I think not!  The warning signs are all there and what Jenkins' Jr. misses (whether intentionally - or because he had one too many  MJ candies with his brewskie I am not sure-  is that the real coup attempt was not manifested in the actual physical assault,  but behind the scenes  - as the GOP continues to do, e.g.   

'Slow-Motion Insurrection': How GOP Seizes Election Power | Georgia News | US News

The violent physical attack, with the rabble in Trump -MAGA gear,  was merely intended to delay the certification of Biden's election long enough for the actual (on paper, "legal") plotters led by Jeffrey Clarke - if he become acting AG-  to cast out the Biden electors and insert alternate Trump ones instead.  This lot of traitors were then hoping for a 269-269 electoral count tie which would have thrown it to the House of Representatives - where state delegations only would vote.  Given Reeps hold the numbers edge in these state delegations Trump would have been handed the victory.(Trump lawyer John Eastman and other allies - like Jeffrey Clarke - had suggested pressuring VP Pence to accept alternate state electors for Trump.  All the Reeps in congress had to do for this to work was to ensure majorities in House, Senate objected to the state electors for Biden.  We know Eastman had at least seven states in his crosshairs, and fortunately the efforts to invalidate Biden electors - for Arizona and Pennsylvania-   failed in the House by a handful of votes. It may not go as well next time.  The confusing statute regarding objecting to electors arose after the 1876 disputed election between Rutherford B. Hayes and Democrat Samuel Tilden.)

Nonetheless, in high ignorant  dudgeon with his "worry porn" meme, Jenkins goes on, failing to process the details and differences:

And yet, lo, the anniversary also treated us to journalism that actually examines the subject it purports to examine, rather than executing a previously planned narrative. In a valuable piece of reporting, the New York Times describes how many defendants before judges have expressed regret and embarrassment over their behavior in the Capitol riot. 


In another valuable piece of reporting, the Post on Thursday dwelled on a crucial and overlooked truth: If the Capitol Police had done their job, we would be having a different conversation today.

In each of these cases, Jenkins Jr.  is totally lost at sea, and maybe chooses to be.  For example, the rabble -rousing insurrectionists now blubbering are only a fraction of the hard core total (over 750) who actually committed aggressive crimes, including using chemical sprays and flag poles as spikes to strike the officers. Their "regrets"  mean nada if all they  translate to are regrets  for being caught and getting their own just desserts.  (And kudos here to the amateur sleuths who used thousands of images and social media responses to ID the brigands). Moreover, the claptrap Holman dumps here says nothing of the newer minds being poisoned by the same  Big lie, which will be poised for new attacks in 2024.  

This isn't partaking of "worry porn", but rather merely checking out the extremist sites' latest chatter.  The mistake a year ago was not taking them seriously - as Jenkins repeats in this latest twaddle- and resulted in inadequate forces arrayed against the insurrectionist MAGA mob. That inadequacy, of course, also included Trump's early orders NOT to have any National Guard ready to help the Capitol police - the better to watch all the fracas unfold on his 55 -inch widescreen TV - which had the maggot mesmerized for hours.  To see the full details of how the actual insurrection -coup would have unfolded check out:

Transcript: The Rachel Maddow Show, 12/21/21 (

Hence, Jenkins' piling onto the D.C. cops for "not doing their job" is pure, outrageous horse shit to cover for Trump's behavior, i.e. in failing to give the National Guard orders for support so he could be entertained by the assault by his MAGA mutts on FOX.  Is Holman ashamed?  Why would he be, given he's totally in Trump's barnyard of slobbering sycophant hacks, hogs and trolls.

To get an education on the power of lies and its relation to the destruction of democracy and democratic ideals,  Jenkins needs to read William Davies' book: 'Nervous States: Democracy And The Decline Of Reason'.  Because the precise reason his arguments fail is he takes no account of the mammoth power that manipulation of reality -  via lies - and of the "dramatic implication it has for the status of knowledge and emotion in society."  (p. 125)  In the words of Davies (ibid.):  

"The most serious threat is not that we lose any respect for truth as such, but that truth becomes a political issue which heightens disagreement and the potential for conflict"

Adding that this may be "exactly what Russian defense strategies are seeking".

 Jenkins Jr. then is unable to see that  Trump has effectively weaponized language to divide the nation and is the primary ongoing engine for "the mob to quickly spiral into a desire for and celebration of conflict - as a means of collective invigoration and purification."  

All of this accounts for the  right’s descent into this abyss and GOP complicity with it.

 It can't possibly just end in 2024, or this year, or any other year because never will Trump voters' "rage subside" -  given  any new emission of lies from Trump will have the same exact effect, i.e. of energizing his MAGA mob into renewed celebration of conflict and acts of terror.    This is the way weaponization of language via lies works, but Holman doesn't grasp it - perhaps because he himself engages in it. The only way it ends is if the lies end, and the only way that happens - so far as any rational person can see - is if Trump is no longer around to spew them.  Unfazed by reason thus far, Holman goes on:

Unvoiced for obvious reasons is the most comforting Jan. 6 reflection of all: The Trump election big lie is likely to fail and dwindle in relevance for the same reason the collusion big lie failed. The latter was not some outsider phenomenon, pushed by people without connection or influence. It was embraced by the establishment and mainstream media, encouraged by leaders of Congress and the executive branch, directly instigated by the Democratic Party’s presidential candidate, the protégée of the then-sitting president—so much so that a CIA chief felt obliged to rush over to the Obama White House and report that the Russians were aware of Hillary Clinton’s plan to paint Mr. Trump as a Russian agent.

This is obviously histrionic horse manure, as anyone with a grain of historical sense and recollection knows.   It was indeed clear from the get go Trump was a Russian agent. a "Manchurian candidate" if you will. What was illegal was the Trump campaign team holding more than 100 meetings - that we now know of -  with Russians, including GRU intelligence agents.  Specifically in "Trump and His Associates Had More Than 100 Contacts With Russians Before the Inauguration,"   The NY Times tracked down "more than 100 in-person meetings, phone calls, text messages, emails and private messages on Twitter," all made by "at least 17 campaign officials and advisers [who] had contacts with Russian nationals and WikiLeaks, or their intermediaries."

Further, foreign intercepts of meetings of Trump cronies, e.g. Carter Page, with Russian  (GRU) agents meant that the U.S.  FBI  had to enter the picture with its own unmasking,  FISA warrants, surveillance, etc. Not to do so would have violated agreements with foreign intel sources, assets, and would have amounted to dereliction of duty.   Hence, there was no evil conspiracy by Hillary, Christopher Steele, Obama, the FBI,  or anyone else but the Trump cabal. It exists only in Holman Jenkins Jr's febrile brain.  Or perhaps in his fervid, MJ-laced dreams?  

Then there are  Robert Mueller's GRU  indictments [Read the indictment here.]   with this partial preface: 

"On or about July 27, 2016, the conspirators attempted after hours to spearphish for the first time email accounts on a domain hosted by a third party provider and used by Clinton's personal office. They also targeted seventy-six email addresses at the domain for the Clinton campaign. '

Most interesting, this happened on the very same day Traitor Trump appeared in front of the media cameras and pleaded with Russia to hack Hillary's emails, e.g.

"I will tell you this, Russia if you're listening, I hope that you're able to find the 30,000 emails that are missing. You will probably be rewarded mightily by our press. Let's see if that happens."

This traitor openly betting that if he made the plea in full public view no one would take it as a serious admission of Russian collusion. Who could be that insane?  Not realizing a psychotic and sociopath would! Well a lot of people have, except of course his defenders like Jenkins Jr.  For all these reasons, Holman's next paragraph emerges as total twaddle:

And nonetheless the big lie was an ignominious flop despite millions of Americans continuing to believe it. It didn’t stop Mr. Trump from being elected, taking office or serving out his term. Tens of millions of voters were willing to disbelieve the media. ... In adherence to their job descriptions and personal integrity, establishment figures like Robert Mueller, Michael Horowitz and John Durham were willing to supply evidence against the collusion narrative.

Of course, what Holman calls the 'big lie' here (the Mueller investigation,  Trump's guilt  etc.) was surely not a "big flop".  Indeed, his very analogy of the Mueller investigation and Trump's Russian collusion with the 'Big Lie' concerning the 2020 election is not only vile, but an abomination. Mueller put all the collusion  evidence together in Vol. I of his report. See also: Of Course There’s Evidence Trump Colluded with Russian Intelligence - Lawfare ( 

For more on those connections and even the methods used and conspiracy to toss the election to Trump, read the Senate Intelligence Committee report final volume, entitled : 

 Volume 5: Counterintelligence Threats and Vulnerabilities,” 

It was Trump-named AG Bill Barr who muddied Mueller's Report findings with his own B.S. spin back in early 2019 e.g.   

As for Michael Horowitz, Holman forgets or ignores (my post of Dec. 10, 2019) The 434-page report issued by Justice Department Inspector General Michael Horowitz concluded the FBI had an “authorized purpose” when it initiated its investigation, known as Crossfire Hurricane, into the Trump campaign. In doing so, Horowitz implicitly rejected GOP assertions that the case was launched out of political animus, or that the FBI broke its own rules on using informants.  

As for John Durham, we know his investigation into the investigators was bogus, e.g.

Watch Out for Bill Barr's Flunky John Durham to Fabricate a Report That Would "Absolve" Russia of 2016 Election Interference

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by Bill Berkowitz | October 31, 2019 - 6:38am

Further it was Trump in cahoots with his toady Barr who concocted the phony Durham probe - to get back at the investigators - who had every right to probe him,  see e.g.

The Durham Indictment Fuels the Real Russia Hoax – Mother Jones

But does any of this faze Jenkins?  How could it, buried as he is in his lies and historical-verbal  manipulations?  I.e. spouting even more balderdash next:

The American experiment remains sturdier than we may realize...

Those Jan. 6 rioters hauled up before judges have belatedly discovered the wisdom of adopting a critical mindset toward their news sources. Also worth remembering is the iron principle that the partisan version of everything is almost always a lie.

This is clever parlance for people, usually the gullible, to ignore the ten thousand a month lies spewed by FOX - especially Tucker Carlson - whether on Covid, the vaccines, the economy (inflation),  Orban's Hungary or any other poppycock he can come up with.   As for the American experiment "remaining sturdier than ever" the work of Barbara Walter shows it is not. From her analysis of the Trump years, by the  end of his presidency, the U.S. score on the democracy scale  had fallen to a 5, making the country a partial democracy for the first time since 1800.  

According to Walter from her text:

We are no longer the world’s oldest continuous democracy.  That honor is now held by Switzerland, followed by New Zealand, and then Canada.

 Our democracy - despite Jenkins' ignorance -  is on a knife edge between a marginal democracy and autocracy. Indeed, as Barton Gelman points out:  'Trump's Next Coup Has Already Begun'.   E.g.

How Donald Trump Could Subvert the 2024 Election - The Atlantic

But is Jenkins Jr. bothered? No way, as we see him going on to bloviate:

Worry porn, among its many self-deceiving tricks, telescopes time in order to ignore its healing effect. Thus a New York Times editorial last week revealingly insisted (and pleaded), “Jan. 6 is not in the past. It is every day.”...... and points to perhaps the biggest Jan. 6 worry-porn fallacy—the assumption that a few hundred of the worst Capitol Hill rioters are representative of 75 million Trump voters.

This is also glib bollocks. What Jenkins Jr. is missing is that to the extent those 75 million Trump voters (even a solid majority) accept the 'Big Lie' they are representative of the hundreds of lawless renegades that assaulted the Capitol.   This goes back to William Davies' arguments (see above) on how the manipulation of reality (via Trump lies) triggers emotional upheaval and mob behavior out of all proportion to the stimulus.  So long as Trump lives and has the potential to lie to the nation and especially to his MAGA mob this will be the case.  And the sooner little Holman absorbs it and stops pumping out his codswallop columns defending Trump,  Trumpers, and glossing over the insurrection -  the better. As Barbara Walter writes in her book,  “How Civil Wars Start,"  :

"We are closer to civil war than any of us would like to believe.  No one wants to believe that their beloved democracy is in decline, or headed toward war.   But if you were an analyst in a foreign country looking at events in America — the same way you’d look at events in Ukraine or the Ivory Coast or Venezuela — you would go down a checklist, assessing each of the conditions that make civil war likely. And what you would find is that the United States, a democracy founded more than two centuries ago, has entered very dangerous territory."

Asswit and troll Holman Jenkins Jr. needs to read it.

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