Monday, April 23, 2018

Students Make Voices Heard Again - As Communities Around The Country Pass Stricter Gun Laws

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Students packed into New York's Washington Square to make their voices heard again - this time for an anti-gun vote in the November midterms.

Not to be denied their first amendment rights, thousands of students staged another walkout and mass protest Friday in schools across the country - even as assorted communities are taking matters into their own hands re: gun laws.  Here in Colorado, students from Marjorie Stoneman Douglas High in Parkland FL also joined Columbine students to rally Thursday night in Clement Park near Columbine High for a get out the vote message, urging all those of voting age to get signed up.  As one of the kids said:

"The only thing a gun obsessed politician fears is a vote against him or her."

Bingo! He's nailed it. The guntard politicos only fear being displaced from their pseudo reigns. Below is one of the activist Columbine kids:
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This first ever "Vote for our lives rally" drew nearly 500 in Littleton and many thousands more around the nation and preceded the Friday student protests-walkouts, which were tied to the 19th anniversary of the Columbine High School massacre. As if to punctuate student concerns a shooting at Forest High School in Ocala, FL left a 17-year old student injured. Fortunately for those students, the perp misfit (Sky Bouche) wasn't wielding an AK -47, Bushmaster.223, or AR-15. Unfortunately, for 4 slain Waffle House patrons in Tennessee, the degenerate that fired into that establishment did pack an AR.  But the dumb gunnies still insist "more people are killed  each year by fists than guns", yeah right, and pigs fly upside down.

Meanwhile, as reported in the Weekend WSJ (p. A6), NRA honcho Wayne LaPierre told a conservative audience, e.g. at CPAC in February that "current laws" - if vigorously enforced - "are sufficient to curb mass shootings".

Well, hardly  if so many millions of assault type rifles are out there, as well as over 300,000 bump stocks which can easily convert any semi-automatic into an effective automatic (and we saw what that could do last year at the Vega massacre).

So now assorted localities are taking matters into their on hands.  As reported in the WSJ on Friday (p. A6)  Deerfield, IL has now "unanimously  passed an assault weapons ban".  The ban will mandate that all owners of such weapons - residents turn them in by a specific deadline. Failure to do so will result in "violators being fined as much as $1,000 a day from the point the law take effect".  Thus, if any violator delays ten days ditching their AR after the law is enabled, he or she will owe a nice tidy sum of $10,000.

Meanwhile, the city council in Lincoln, Nebraska and the Maryland General Assembly (MD already has an assault weapons ban that has been tested under the 2nd amendment and been preserved) voted to ban all bump stocks.  Then in Coral Springs, FL there is a major push to limit the sale and transfer of large capacity magazines in the city. In addition, Coral Springs, along with two other municipalities is suing the state to be able to do so.  (Many states, like Florida, for some idiotic reason prohibit  municipalities  from drawing up their own legislation.)

Then there is Boulder, CO whose city council has approved an ordinance that would ban the sale and possession of any assault weapons in the city, Infraction may result in a long jail term, possibly up to 2 years.  Predictably, on Saturday a bunch of NRA- backed losers came out to squeal ...errr, protest, about the ordinance - barking the usual false "Nazi" comparisons - which any dumbo that's studied the actual history of the Third Reich knows aren't true,  and carrying fake and real AR-15 rifles as they marched. One bozo quoted in The Sunday Denver Post (p. 2B) whined:

"This demonstration is because of the extremes that the Boulder City Council is going to. If they weren't I wouldn't be here."

Aww. . .boo hoo hoo. This turkey actually believes he has a 2nd amendment right to own an AR. Newsflash,  he doesn't.  He needs to process the words of conservo pundit Joe Scarborough from two months ago:

"If you want to make the argument that the Supreme Court should protect your rights to have military style weapons, that's legitimate.  But if you say it is your God-given constitutional right to have an AR-15 that is not what the second amendment says. And it's not what Justice Scalia says or the Supreme Court says."

 If that Boulder assault weapon ordinance protester doesn't like the ordinance perhaps he needs to move to Texas or Kansas and out of the "People's Republic Of Boulder".

The beauty of all these local actions is there is very little the gunnies (perhaps other than in FL) can do to thwart them. We already know as I've stated at least a half dozen times before, that assault weapons are not protected under the 2nd amendment. This was in the famous  2008 SC case District of Columbia vs. Heller:
http://brane-space.blogspot.com/2018/02/sorry-you-have-no-constitutional-right.html


The majority opinion was written by arch-conservative Justice  Antonin Scalia who - while upholding the right to own arms - adamantly asserted that those weapons "most useful in military service" fall outside the scope of the 2nd amendment.

A recent article in The Wall Street Journal ("Ban On Military  -Style Rifles Upheld", April 7-8, p. A3) notes that earlier SC ruling was once again upheld in a Massachusetts . And I am sure it will be upheld in the more recent Deerfield IL, Boulder CO, etc cases too - for the same reasons.  

As federal judge William G. Young  wrote in the MA  ruling:
"The AR-15 and its analogs - black, semi-automatic rifles with pistol grips and other military features - are simply not weapons within the individual constitutional right to bear arms."

The kids from Parkland and around the nation are now having an effect, with a powerful energy to reclaim gun sanity.  That sanity underscores that there is a higher freedom to live and let live than to be suddenly cut down in a hail of assault rifle bullets as those people at the Waffle House were early yesterday.

The beauty is that the gunnies and guntards will not be able to stop them, or stop the movement now in motion and gaining more steam every day. And that is irrespective of how many photo-shopped images of David Hogg with Hitler, or in a Nazi uniform, they put up on their stupid blogs.

Friday, April 20, 2018

An Ominous Omen For Earth Day 2018

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Earth Day is this Sunday, April 22nd, and the really bad news for climate deniers - as well as the rest of us   -  has arrived. We've now learned the Atlantic Ocean circulation that carries warmth into the Northern Hemisphere’s high latitudes is slowing down because of climate change. This was announced by a team of scientists last Wednesday, indicating one of the most feared consequences of global warming is already coming to pass.

Of course, this was first highlighted in the science fiction film, The Day After Tomorrow, though to be sure the events depicted in that movie were extreme and radically compressed in temporal sequence.  After the film came out, and we watched it at the local cinema, Janice asked my opinion. I basically dismissed it as "pseudo-scientific nonsense."  That was before I investigated the origin of the theory, basically tied to disruption or cessation of the thermohaline circulation - for example, governing  the currents which ensure warmer water (such as in the Gulf of Mexico) is transported to the northern hemisphere.  Hence, it's actually a part of the greater scale ocean circulation.

The  theory basically tracks back to Dr. Wallace Broeker - a geo-scientist at Columbia University-  who originally conjectured that global warming would increase rainfall and river discharge into the North Atlantic. That combination would then lower surface water density (fresh water being less dense than salt water) and the lower density surface water would not sink. 

This would disrupt the thermohaline current (circulation) so that warmer water could no longer be pulled from lower latitudes toward Europe. In the paradoxical result, global warming would plunge Europe into another ice age. To be sure, Dr. Broeker assumed a 50 percent increase in precipitation and increased wetness in Central Asia and North America. (By contrast the IPCC has projected only a 5-10 increase in precipitation).

At the time I perused these results, while I gave Broeker's  hypothesis more credibility, I still didn't believe any major disruption of the THC was plausible. That was before the recent announcement that the Atlantic meridional overturning circulation (AMOC)  has declined in strength by 15 percent since the mid-20th century to a “new record low.”  This was the conclusion of the scientists in a peer-reviewed study published in the journal Nature.

That percentage difference represents a decrease of 3 million cubic meters of water per second, the equivalent of nearly 15 Amazon rivers.

Some of the AMOC’s disruption may be driven by the melting ice sheet of Greenland, and indeed, other new research last week showed that Greenland’s massive ice cap is melting at the fastest rate for at least 450 years. This influx will continue to weaken the Amoc into the future until human-caused climate change is halted.
For an insight into the Thermohaline circulation:

We now have been alerted, based on the research (and in a nod to Broeker) that serious disruption to the ocean current crucial in controlling global climate must be avoided “at all costs”.   THAT is the new message for this Earth Day. The alert follows the revelation last week that the system is at its weakest ever recorded

For those inclined to dismiss these findings as  more climate change "blurtations"  or hype, they ought  to  process that past collapses of the giant network have seen some of the most extreme impacts in climate history, e.g. western Europe particularly vulnerable to a descent into freezing winters. A significantly weakened system is also likely to cause more severe storms in Europe, faster sea level rise on the east coast of the US and increasing drought in the Sahel in Africa.  

This new research  clearly worries  climate scientists because of the huge impact global warming has already had on the currents and the unpredictability of a future “tipping point”.  The currents that bring warm Atlantic water northwards towards the pole, where they cool, sink and return southwards, is the most significant control on northern hemisphere climate outside the atmosphere.

Professor Stefan Rahmstorf,  one of the world's leading oceanographers at the Potsdam Institute for Climate Impact Research, has stated:  

From the study of past climate, we know changes in the Amoc have been some of the most abrupt and impactful events in the history of climate,”

Oceanographer Peter Spooner, at University College London, shares the concern noting: “The extent of the changes we have discovered comes as a surprise to many, including myself, and points to significant changes in the future.”  

He isn't exaggerating. A collapse in the AMOC would mean far less heat reaching western Europe and plunge the region into very severe winters, the kind of scenario depicted (in extreme fashion) in the movie The Day After Tomorrow. A widespread collapse of deep-sea ecosystems has also been seen in the past. 

Another byproduct is that as the AMOC weakens, it might actually increase summer heatwaves. That is because it takes time for the cooling of the northern waters to also cause cooling over the adjacent lands. However, the cooler waters affect the atmosphere in a way that helps warm air to flood into Europe from the south, a situation already seen in 2015

A primary message for this Earth Day is to spread the word about this latest research, to educate citizens worldwide. Because it will impact all of them.

Thursday, April 19, 2018

Tim Cook's Mass Coding Jobs Push Is Misplaced And Dangerous

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Kids are socially dysfnnctional as it is without adding more apps, compliments of 2 million more  app creators!

In his recent (2 weeks ago) interview on the MSNBC special "Revolution' Apple CEO Tim Cook held court before a techie audience at a Chicago high school. Cook made some clearly outlandish claims - at least a sensible person watching would hope they are!- including 2 million coding jobs in the pipeline by 2025.  The other was a push to integrate coding into college science subjects - which has to be the dumbest idea I've heard since some loon proposed teaching creationism along side evolution.

"Wah! Wait, Mr. Copernicus! Coding IS great, it IS science!"

No, it is not. Well, ok, there is computer science - which I also took- but it is generally taken supplementary to actual science courses,. Most college physics, chemistry and biology curricula are packed as it is and many profs are hard pressed to cover all the required material, including labs, without adding coding.   And to make this idiotic plan a reality you'd basically have to double or triple the credit hours for each subject - e.g. for a 4 hour weekly General Physics course- you'd need to expand it to 8 or even 10 hours.  Note this is if Cook's plan of doing coding along side physics (or other subjects) is accepted. If, however, the student already knows programming and can do it - say for a numerical plasma model - it won't encroach on regular class time.

At the University of Alaska- Fairbanks, all science majors - certainly in the upper levels, also took Fortran but as a separate, ancillary course.  The coding (programming) then worked along side the physics topics, without encroaching on teaching time.   If a numerical model, say to replicate Boltzmann's velocity distribution, was assigned, it could be done and enhance class learning of the material. But it didn't compete with class material and detract from it.

Cook's other preposterous claim was to describe for Chris Hayes how 2 million coding jobs are on the horizon. I sincerely hope not! Personally, I believe the coding craze is over-hyped.                             Also we've beheld this sort of emphasis from Apple's CEOs before, e.g. in the person of Wunderkind Steve Jobs.  As the website, "Having the Conversation' reminded us:

"One of the earliest corporate efforts to get computers into schools was Apple’s “Kids Can’t Wait” program in 1982. Apple co-founder Steve Jobs personally lobbied Congress to pass the Computer Equipment Contribution Act, which would have allowed companies that donated computers to schools, libraries and museums to deduct the equipment’s value from their corporate income tax bills. While his efforts in Washington failed, he succeeded in his home state of California, where companies could claim a tax credit for 25 percent of the value of computer donations. The bill was clearly a corporate tax break, but it was framed in terms of educational gaps"
Cook's theme on 'Revolution' is therefore not new, other than that now the creation of "apps" dominates and is said to hold out the promise of more employment opportunity. "Lordy be, we gotta have more apps! We need 2 million more app coders!" No, we do not! The evidence already is ample to show that the proliferation of apps is having a destructive effect on the minds  of younger Americans and the political fabric and relationships of older ones.
But for Cook to suggest  2 million more  app jobs is a nightmare world.Why? Take a look at the recent (April 23) TIME article, 'The Masters of  Mind Control',  wherein we learn  how these app techies in Silicon Valley are turning kids' brains to mush and adults into slaves tethered to their smart phones. (See also the WSJ piece yesterday, 'The Instant Message Generation Gap', on how so many 20 and 30 -something workers are "elated to use apps like Slack so they no longer have to mind spelling or grammar."  It also noted how older bosses and employees disdain IM apps, and prefer email,, but have been pushed into doing IM - which means they are now "on call" at an instant, 24/7.  Pardon me, but this is bullshit insane.

Apart from the tethering there is the addiction aspect which Cook soft soaped in his MSNBC appearance. We learn the average American (not me, I don't own one): 

"Every day checks a smart phone 47 times on average or once every 19 minutes, spending roughly 5 hours peering at screens' silvery glow."


Adding: 

"There's no good consensus yet on what all this means for children's brains, adolescents' moods, and the future of our democratic institutions."


My bet is the consensus will ultimately be that all this screen time and app use is deleterious to mental and physical well being. Most disconcerting, a 2017  University of Texas study found that the mere presence of smart phones, down on the desk in front of users, undercuts the ability to perform cognitive tasks. That is, turning users into veritable dummies.  Then we also learn Silicon Valley's business model is to "keep us in thrall to our screens". 

The longer people are glued to an app - called  eyeball time - "the more money its creators make by selling our attention and access to personal data to advertisers and others."

In other words, we are not really customers or consumers but "products to be sold"

So 2 million more app  creators will likely increase the citizen to "product" mutation by ten fold not to mention the dumbing down and addiction effects. Exaggeration?  Not when former Google employee Tristan Harris, and Facebook investor Roger McNamee, (ibid.)  have flat out accused the tech giants of "deliberately creating addictive products without regard to human or social health."

And then we behold (p. 36)  the likes of Nir Eyal author of 'Hooked: How To Build Habit Forming Products'  who also runs a "Habit Summit" workshop , where participants pay up to $1,700 for the three day conference  where they are given "practical steps to design habit forming products."

THAT is why we don't need or want 2 million more app creators! Especially, as the "market" - devoid of any moral compass -  will almost always veer toward the lowest common denominator. E.g.  cheering the  most socially inimical (but profit generating) products whether video games like Grand Theft Auto  V where users get to  virtual rape assorted females, or the stupefying, zombie-inducing game of Candy crush.

Then there are the other nefarious aspects of apps, related to tracking users, especially kids. A new study by  UC Berkeley showed that of 6.000 apps in the Google Playstore a majority were in likely violation of the Children's  Online Privacy Protection Act.  Also the study found up to 57 percent may collect data without parental permission. This data includes GPS location and email addresses. These are then shared with advertisers.   As one of the study's lead authors noted on an NBC News segment two nights ago, the data is often used to "build dossiers on individuals. "   One of these apps that transmits GPS location is "Fun Kids Racing" which has been DL'd  50 million times.

Tim Cook made very little mention of any of this in his prime time performance, but why would he? If he can get two million more app makers in the pipeline to create two million more apps  - or even one thousand - that is tons of money in Apple's  already bloated pockets.   That leaves it to consumers to put the brakes on and cease allowing the techies to raid and hobble their minds, or render them virtual "coke" junkies always needing the next screen "hit".

On the other hand, if Apple, Google and others can come up with more (non-addictive, non-invasive) math and science apps I am all  for them. Say an app that can predict the result of any given chemical equation, before a student or teacher actually performs the lab experiment.   But hey, it's doubtful such  apps would rake in the profits that the addictive apps do.

See also:

Wednesday, April 18, 2018

Demise Of The Denver Post Has Nada To Do With "Too Much Liberal Content"

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The last gasp of the "Voice of the Rocky Mountain Empire" now appears to be only weeks away, A steady stream of news regarding cuts to reporters, editors, photographers, videographers, page designers and  others, now threatens to end the 125 year run of The Denver Post which has won 9 Pulitzer prizes. For those of us who love to get our news and information from  hardcopy, print papers - this is an unmitigated disaster. Especially as the only alternative here in Colorado Springs is the cartoon paper known as The Gazette, which I take to be the print version of "Fox and Friends".

My love of newspapers probably began when,  as a seven or eight -year old,  I'd take out the "Green Sheet" from The Milwaukee Journal and work its various puzzles and games, and read the science articles.  Thenceforth in every place I lived, whether Miami (Herald), New Orleans (States Item and Times Picayune), Barbados (Nation, Advocate News), Baltimore (Sun, Evening Sun), or Colorado, I'd be sure to have the daily paper delivered.

There was something special about opening any of them up in the mornings to read the news, cup of Java at the ready with a few English muffins and avocado - maybe a hard boiled egg and slice of bacon.  But alas, in each locality, retrenchment often followed - usually preceded by losing the 2nd paper of the day . For Milwaukee,  it was the Sentinel (later folded into the Journal to become the Milwaukee Journal -Sentinel). For Miami it was the demise of The Miami News leaving only the Herald, and for Baltimore it was the folding up of the Evening Sun - - the paper that gave the great H.L. Mencken his start.

In the case of The Denver Post, I began to get worried some ten years ago when a number of liberal reporters like Cindy Rodriguez and Michael Booth were rendered redundant.. At that turning point the paper lost many of its liberal readers, and in truth, I cut my subscription down to 5 days a week.  I confess to being less interested in reading the blabber of conservative mouthpieces like Thomas Sowell, or their many clones hailing from assorted "think tanks" like the Hudson Institute, The American Enterprise Institute and others.

Then, in the last two years the Post's proportion of ads increased significantly while the original reporting - whether on the state's health care woes, the environment, higher education or assorted protests, dwindled. At that point I cut my subscription down to 2 days a week, Wednesdays and Sundays, opting to read The Financial Times online the other days.

Now, that appears to have perhaps been what many others did as well, given The Post now has its "marching orders" to cut the original 250 plus staff to 75  by July 1st.  More humiliating, the remaining core staff has had to move out of its original Denver News bldg. in downtown Denver, to a nondescript,  industrial building in Aurora.  

What hastened the paper's demise? The most immediate reason was that it allowed itself to be purchased by a hedge fund (Alden Global Capital of NYC) and thus was answerable to its shareholders.  As their pickings grew ever more slim, they began to demand the paper make severe cuts.  But as we know, nothing of quality ever comes of cuts. As one wry journalist (Jimmy Cozier)  in Barbados once put it  : "So, you're really gonna cut my legs off at the ankles and expect me to challenge competitors in a 5 K?"

For this reason the Post editorial board issued a plea in its April 8 Perspective section:

"Denver deserves a newspaper owner who supports its newsroom. If Alden isn't willing to do good journalist here it should sell the Post to owners who will."

True, but please, just leave out Philip Anschutz - who owns the rag known as the COS Gazette.

Then there is liberal gadfly Jon Caldara who wrote "many conservatives can't  hide their delight, at the Post being put on a ventilator."

Adding:

"It reinforces our view that papers are dying because we consumers want actual balance in reporting and the market is responding."

Ah yes, the market.  As I noted in my book, The Elements of the Corporatocracy, the market  is an abstraction which embraces the dynamics and exchanges in a money culture, consumptive society. Its priorities are not always benign but are faithfully reflected in the movement of speculative  financial markets. In the end it is nothing to base a culture or civilization on. After all. "the market" may be all agog and favor more apps that keep the hoi polloi addicted to their smartphones, or more tawdry electronic trash to fill up homes and storage units.  The market can never be an arbiter of reliable information, and by extension hedge fund ownership of a newspaper can never ensure its survival.

In Caldara's newspaper universe, every piece that attempts to educate the public about climate change, global warming, is "balanced" by a piece that denies it - or attributes it to a "natural cause" like the Sun.   But as I also observed in my chapter on the media corporatocracy, it is a myth to believe left wing or liberal views dominate the press. I cited a 1997 Nation piece, which read:

""The truth is that genuinely left-wing views rarely get a hearing. Norman Solomon had this confirmed while trying to peddle his column, when editors told him 'We've got progressive views covered - we run Anthony Lewis'.  The same Anthony Lewis who has described himself as a 'pro-capitalist, middle of the road tepid centrist', who supported George Bush Sr.'s Gulf  War."

This also explains why  - until the resurgence of robust liberal magazines like ''The New Republic', so many "leftist" authors, writers, journalists (like Greg Palast, Robert Scheer and others) were forced to go to Larry Flynt's Hustler to get their work published   There simply wasn't a place for them in the regular, "vanilla"  mainstream news papers, because corporate boards rejected what they had to offer. (For more on this see Norman Solomon's and Jeff Cohen's text, 'Wizards of Media Oz: Behind the Curtain of Mainstream News')

So I really don't know what planet Caldara inhabits but it's not the one I'm on where The Denver Post is more a centrist alternative to the extreme Right Colorado Springs Gazette.  The only other actual "left" paper, the COS Independent, is a weekly,  not a daily.  It is also of interest to note that, contrary to popular myths, even left blogs are struggling to sustain funding. See e.g.

http://www.smirkingchimp.com/thread/jeff-tiedrich/78748/even-if-you-cant-or-wont-donate-there-are-other-things-you-can-do-to-help-us-out

And wifey informed me last night that even at "liberal" MSNBC there's a push to have more "Never Trumpers" appear than actual liberals.

Caldara and his whining ilk also bemoan the lack of more conservative intellectual material, which kind of shows me he needs a pair of better glasses.  He's obviously missing the op-ed fare from the toadies of the American Enterprise Institute, Hudson Institute, Stanford's Hoover Institute  etc. 

Besides, there isn't any genuine intellectual fare on the conservative side anyway, at least since William F. Buckley died.  As NY Times columnist and Nobel winning economist Paul Krugman has noted in a recent column:

"As others have pointed out, the real problem here is that media organizations are looking for unicorns: serious, honest, conservative intellectuals with real influence. Forty or fifty years ago, such people did exist. But now they don’t. To understand why, let me talk about what I know: the field of economics. This happens to be a field with a relatively strong conservative presence compared to other social sciences, and as far as I can tell even contains considerably more self-identified conservatives/Republicans than hard science. Even so, trying to find influential conservative economic intellectuals is basically a hopeless task, for two reasons.


First, while there are many conservative economists with appointments at top universities, publications in top journals, and so on, they have no influence on conservative policymaking. What the right wants are charlatans and cranks, in (conservative) Greg Mankiw’s famous phrase. If they use actual economists, they use them the way a drunkard uses a lamppost: for support, not illumination.
The second problem with conservative economic thought is that even aside from its complete lack of policy influence, it’s in an advanced state of both intellectual and moral decadence – something that has been obvious for a while, but became utterly clear after the 2008 crisis."

And I have certainly given examples of this decadence in critiques of assorted  conservo  economists from time to time, e.g.

http://brane-space.blogspot.com/2018/03/americas-debt-disease-prof-marty.html

The ironic aspect of Caldara's rant is that even he admits in the end it is better to have a Denver Post paper than to be without one, i.e.

"From my point of view battling ever expanding government, we have a better chance slowing it down with a vibrant, even if liberal, paper in town."

He's partly right - but the D. Post still isn't a "liberal paper".   It's a centrist leaning paper - especially if you read its editorials, which features some liberal content - mainly in letters to the editor.

See also:

Tuesday, April 17, 2018

Selected Questions- Answers From All Experts Astronomy Forum (Relative Distances of Superior, Inferior Planets)

Question: Can you explain how one can find the relative distance to an inferior or superior planet, i.e. in the solar system?

Answer:  Let's first define geometrically the inferior and superior planet based on the diagram shown below:
















As seen from the diagrams, an inferior planet defines one which is interior to Earth's orbit, relative to the Sun. A superior planet defines one which is exterior to the Earth's orbit.

While  it's easy to apply Kepler's 3rd law to obtain the basic dimensions of an orbit, namely the semi-major axis (a)  of the orbit - or the mean distance from the Sun, things become somewhat more difficult when we seek to find the distance say, of the Earth to the planet.

So, we consider two cases:

(A) Inferior planet (see the diagram A)

(B) Superior planet (Diagram B)

Case (A):

The maximum elongation occurs when the planet's geocentric radius vector (pE in diagram A) is perpendicular to the planet's heliocentric radius vector, pS. 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 therefore the distance of the planet from the Sun in terms of Earth units (or AU, astronomical units, where 1 AU = 1.5 x 1011  m). Let Sp = R and SE = a(E) the semi-major axis for Earth's orbit, then:

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

Example:

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):

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 (from the previous answer) we may write:

Θ = 360 (1/P - 1/P') t

where P and P' are the sidereal periods for the Earth and the planet, respectively.  Then, it follows by the synodic/ sidereal relations seen in previous answer. 

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

or:

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

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



To fix ideas here is a further  example problem:

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


Solution:

The diagram is shown below with the angle of maximum elongation.

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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

then:

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