No Simple Formula for Circumference of an Ellipse

Did you know there is no simple formula for the circumference of an ellipse?

Earlier I wanted to calculate (don't ask) the average speed of each planet in its orbit. So I wanted to calculate the circumference of its elliptical orbit around the Sun. For the Earth the eccentricity is small, 0.0167, so it's almost a circle. But what of the other planets?

This is probably common knowledge, but I don't think I've encountered it before. To my surprise, there is no simple formula for the distance p around the perimeter of an eclipse. The best you can do is an infinite series, which can be quickly truncated in the case of the Earth, but not necessarily for other planets.

 where

where a is the semi-major axis of the ellipse and b the semi-minor axis. (These aren't the orbit's perihelion and aphelion, but those can be easily calculated from a, b (=a*sqrt(1-e²)), and the eccentricity e: perihelion=a(1+e) and aphelion=a(1-e). The function in parentheses behind the sum for p is the combinatorical function, or binomial coefficient

(Here's how to take the factorial of a noninteger.) Anyway, for the Earth e << 1, so h << 1, so

which reduces to the circumference of a circle when e=0 (a=b), as it must.

Nothing so remarkable here -- I just never knew there was no simple formula for the circumference of an ellipse! Or if I did know, I'd forgotten.

PS: But there is a simple formula for the area enclosed by an ellipse:

The Orville, Coming in September

This upcoming TV series looks good, unless all the jokes are in the trailer. Due September 10th.


There's a new Star Trek series coming too, Star Trek Discovery, which somehow doesn't look as good:

GOP Rep Johnson Shows Why Single-Payer Is the Only Solution

Ron Johnson (R-Wisconsin) just demonstrated why private health insurance cannot provide necessary care to all Americans -- and, what's worse, while doing so he doesn't seem to understand that he made the best case for a single-payer system.

During an interview on Meet the Press, host Chuck Todd noted that Republicans in the Senate had held no hearings on their health care bill and so they could not say for sure why insurance companies were abandoning some markets.

Johnson sidestepped the refusal to hold hearings and insisted that he already knows the answer “but nobody wants to talk about it.”

The Wisconsin Republican pointed to Obamacare rules that forbid insurance companies from charging more for people with preexisting conditions.

“We know why those premiums doubled,” he opined. “We’ve done something with our health care system that you would never think about doing, for example, with auto insurance, where you would require auto insurance companies to sell a policy to somebody after they crash their car.”

“States that have… guarantees for preexisting conditions, it crashes their markets,” he continued. “It causes the markets to collapse. It causes premiums to skyrocket.”

Notice that Johnson is more concerned about markets than people. That's the fundamental problem. He likens people to old cars, which are thrown into a scrapyard when no longer userful. And he doesn't even realize what he's saying.

But it's been known for over 50 years that markets cannot provide quality, universal health care to everyone in a society. Nobel Laureate economist Kenneth Arrow showed why in the early '60s:

"Uncertainty and the Welfare Economics of Medical Care," Kenneth J. Arrow, The American Economic Review, Vol. LIII n 5 (Dec 1963)
http://www.aeaweb.org/aer/top20/53.5.941-973.pdf

For a synopsis you can read:

"Why markets can't cure healthcare," Paul Krugman, New York Times, July 25, 2009.
"Patients are not Consumers," Paul Krugman, New York Times, April 21 2011.

In short, markets cannot deliver health care like they deliver bread or shoes, because

(1) you cannot predict when you will need care

(2) or what care you will need (you need to rely on experts)

(3) you usually can't comparison shop, especially for the most expensive costs.

Buying health care is not like buying bread. Thus, you need an insurance system. And private insurance systems demand a profit, and a large administrative staff to analyze and deny claims (NOT paying for care is, after all, how they make their money). Private insurers refuse to insure those they think will be too expensive, and drop clients who have become too expensive. 

You can be sure I am taking this pretty fucking personally -- at my age I need health care. If my government can't help me get it I will seriously need to think about moving abroad to somewhere where it's affordable. And moving away from my family, especially my niece and nephew, who I am very close to and want to watch and help grow up, is one of the major thrusts of my life.

We all know that America has been in decline for some time now. This GOP health care bill -- really a tax cut bill; it's just that healthcare is where they found the money -- will kill people, will cause millions to suffer, will mean hundreds of thousands of the elderly will not be able to live in nursing homes -- and it is so severe it could possibly be what finally sends the U.S. over the edge.

And it won't reduce insurance premiums and deductibles and copays at all. With tens of millions of people lacking health insurance, but still needing care, hospitals will pay for them by charging those with insurance even more, like it was pre-ACA.

Imagine a political party that cares so much for the wealthy and so little for the rest of the country that they are throwing the country into the sewer. Try to imagine the hearts of such men. Because I can't.

The 3 S's of Climate Change: Simple. Serious. Solvable.

I like this, from Scott Denning's Twitter profile (@airscottdenning):

"Tweeting about the 3 S's of Climate Change: Simple. Serious. Solvable."

Al Franken Made a Fool of Rick Perry

Admittedly, it wasn't very difficult. All Perry could do was just dumbly deny what the science says:


I think Franken might be thinking of running for President. He has a new book just out -- why now? -- and yesterday I heard him being interviewed on Oregon Public Radio. There he was sharp and smart and, just in the right amount, funny. But in the video above, he comes off as droll and a little bored. His points are smart -- far smarter than the hopelessly banal Rick Perry has, who can't explain any science to save his life -- so he'd need to work on that. But he could be just the right foil if Trump runs again in 2020 (which I doubt he will; I suspect he'll resign before them, maybe right before then). And Mike Pence would have no idea how to counter Franken's intelligence and humor.

Abdussamatov's Solar Irradiance Prediction is a Total Failure

Deniers like to believe there are reasons why a decline in the Sun's irradiance will lead to another ice age -- it's not true -- and one of their favorite papers is by H. Abdussamatovhttp://www.ccsenet.org/journal/index.php/apr/article/view/14754/10140, which I don't think has even been published anywhere.

I've written about his claims before, and took a look again today. Abdussamatov is even more wrong than he was a year ago.

The vertical blue line on this graph is the present. According to Abdussamatov, the "new Little Ice Age epoch" should already have started.

Nonsense.

Abdussamatov says he used PMOD data for total solar irradiance (TSI).

Here is PMOD's latest data page.

Which link to use for the latest TSI? This, I guess. It's hard to know. Good luck trying to figure that out.

Their FTP site was written as if this was 20 years ago. I can understand how back then the WWW was new, as was expecting scientists to post their data.

But in 2017? No way. Wake up, PMOD, and make your data easily available to the people who are paying for it.

Anyway, here, as best as I can determine, is PMOD's latest TSI data:

This dataset aren't anything like the one above. Abdussamatov predicted that TSI would now be about 1.25 W/m2 below the PMOD 1980-2005 base value of 1365.5 W/m2.

This isn't at all true. Abdussamatov didn't link to his data, so I can't reproduce his actual base values. PMOD's base value is, by my data, 1360.0 W/m2. And it is now nowhere 1.25 W/m2 below that base value.

Conclusion: Abdussamatov's prediction is a total failure.

James Randi

World Coal Production Decreases For Third Straight Year

From Bloomberg News:

However, US coal production is was on a bit of an upswing in recent months.

Temporary, surely. And I don't see that Trump had any role in this whatsoever -- it started almost a year before he took office.

Celilo Falls, Now Gone

Here's a great picture of tribal salmon fishing at Celilo Falls, on the Columbia River, once the fourth largest waterfall in the world by flow rate (over twice the flow over Niagara Falls). It was submerged when the Dalles Dam was built in 1957. From the Oregonian article, "7 wonders of Oregon that no longer exist." Most of the salmon are gone too.

Wikipedia has this picture in color.

And here's a video of this beautiful thing before it disappeared.

When Christopher Monckton Warned about Manmade Greenhouse Gases

He wrote: "...too much carbon dioxide is dangerous."

From the Evening Standard on February 2, 1988.

Via Ed Hawkins on Twitter.

Con Beausang, Rest in Peace

I received the sad news today that one of my officemates in graduate school, Con Beausang, passed away the other day.

Con was an experimental nuclear physicist and held the Robert E. and Lena F. Loving Chair at the University of Richmond. Unfortunately I hadn't kept in touch with him after graduate school, but I have warm and cherished memories of him from our time at Stony Brook. He was unique, that's for sure.

I never, ever saw Con in anything other than a very cheerful mood. He would come into the office each morning to drop off his coat, before going down to Stony Brook's accelerator to work for the day. He'd breeze in with something like "Top of the morning to you, gents! What a fine, lovely day it is," regardless of what the weather actually was. He'd say something about his car, which he named and talked about like another person in his life, but closer than most. Sometimes he'd say something about us theorists (Con was in a research group that worked on the detailed structure of nuclei, while the other three us in the office did theory, which, as he observed, mostly involved just sitting around). Being Irish, he pronounced the word "three" as "tree." He taught me about Brian Boru and the Battle of Clontarf, and surprisingly, that phrase still rolls melodically right off my tongue. Once he and I were going somewhere and were on a sandy, dirt road and something in his engine caught fire; Con stopped and had me help him throw sand on it to put it out, then he got back in the car like nothing had happened. He always served a small scoop of ice cream the few times I went to his place for dinner. He was exceedingly easy to be around.

The administrative assistant at the University of Richmond's physics department told me they have been getting more and more graduate students in recent years, and she thought Con had a big part in that, "taking care of everyone."

I have more information about his death, but don't feel it's appropriate to share it in a public forum. Write me if you knew him and would like to know more. I also have his home address, if you want to send anything in memorial, to his wife Cindy.

I am very happy to have known Con; there was no one else like him. It almost seems like yesterday. How very sad that he is gone, and far, far too early.

US's Progress Towards Meeting Its Paris Commitment (= On Target)

So, most of the US's recent reductions in CO2 emissions are due to fracking, which has produced enough natural gas at a low enough price to outperform coal, leading utility managers to shutter coal plants.

I don't see why this won't continue, Paris Agreement or not -- it's pure economics. I estimated here that 70% of recent US CO2 reductions are due to fracking -- that is, not down to a deliberate shift to renewable energy sources or increases in energy efficiency, but simply due to getting the same amount X of energy from natural gas instead of coal.

This shift can't go on forever. I estimated here that at best this can lead to a US per capita CO2 emissions about 15 metric tons (t) CO2/yr. That's still huge, relative to the world, whose per capita emissions are about 5 t CO2/yr.

Obama got lucky with fracking. It grew during the end of the GW Bush administration, and progressed strongly throughout Obama's two terms. The US committed to a 26-28% reduction in 2005 CO2 emissions by 2025. Fracking has actually put us on that trendline:

Trump can try to affect the 30% of US CO2 reductions that come from nonfracking sources -- better gas mileage, more electric cars, some utilities' shifts towards wind and solar, and what else? -- but I don't really see how he will delay the transition of utility power sources from coal to natural gas. That will remain as long as natural gas is the cheaper source.

And is Trump really going to expect car manufacturers to build cars that get less gas mileage? No -- they're not just designing and building for the US, but for Europe too, and Asia. And to consumers who can afford new cars, who are more smart and level-headed.

It seems to me that at best Trump can delay some CO2 reductions -- though only a fraction of what the US emits. The other reductions are happening because it's finally economical for them to happen.

And because major US states want them to happen, because they see and understand the future in a way that completely eludes Trump.

So I think Trump's decision on the Paris Agreement -- probably based more on his psychological weaknesses, of needing to always play the victim, to think that everyone, everywhere is against him, which he clearly projects onto America -- might not be as bad as is currently feared. But in no way because of him.

Some Good Cartoons

"Let These Cartoonists Illustrate The Horror Of Trump's Climate Change Stance"

http://www.huffingtonpost.com/entry/climate-change-political-cartoons-trump_us_59316488e4b02478cb9a9d62

PS: I don't buy into "horror."

DOWNLOAD_HUFFPOST

Modern Cities: Stuff Goes In, Doesn't Come Out

An interesting through from The World in 2050: Four Forces shaping Civilization's Northern Future, by Laurence C. Smith (2009):

Who's Caused the Most Warming? The British!

At least, per capita, from 1850-2005.

This result is from a 2014 paper by Damon Matthews et al, "National contributions to observed global warming." The US is by far the biggest absolute contributor -- and even up through 2012, the US had emitted 2.4 times more than the Chinese and 9.6 times more than India.

(I used data from another source to estimate these numbers up to 2014, and got 2.1 times more than China and 8.6 times more than India.)

So it's rather ridiculous to complain about China and India when we've already contributed more than both combined.

But per capita, it's actually Great Britain that leads all other countries. All that coal burning in Dickensian London, I suppose. This is from the paper cited above (remember, it's only 1850-2005):

So Canada doesn't look so good, either, per capita. India practically vanishes.

Here's another graphic from that paper, again showing who leads in per capita emissions and who hasn't (yet) become affluent by emitting them: