Betelgeuse is a red supergiant star evolving rapidly to an expected supernova. It has dimmed dramatically in recent months, and I’ve seen estimates of thousands to hundreds of thousands of years until it explodes catastrophically in a surge of **neutrinos**, but 10^{4\pm1} years is so soon astronomically. (In physics, the uncertainty is in the mantissa, but in astrophysics, the uncertainty is in the exponent.)

While a Betelgeuse supernova would irrevocably scar my favorite constellation, it would be the most dramatic astronomical event of my lifetime, outshining Earth’s moon for months before dimming to dark. For a minute or two I seriously contemplate losing Betelgeuse — and gaining a spectacular naked-eye supernova. I frantically search online for more information. Betelgeuse seems safe, but at least one astronomer walks outside to visually check. My breathing returns to normal. More time to prepare the next generation **neutrino detectors**.

Enjoy Orion while you can, because sometime soon, Betelgeuse is gonna blow.

]]>Last week I was in **Iceland** for the **winter solstice** in search of **aurora**. Came for **astronomy**; stayed for **geology**.

Iceland is a **hot spot**, probably the expression of an entrenched **mantle plume**, straddling the boundary between the North American and Eurasian tectonic plates. In southwest Iceland, on the lava-scarred Reykjanes peninsula, the Mid Atlantic Ridge is above ground. As the plates drift apart, several centimeters each year, a **rift valley** widens. Although the rift itself is several kilometers across, at Sandvik a small footbridge over a fissure in the rift symbolizes the connection between the continents.

The start of my version of the table of nuclides is below, where number of protons *Z* increases toward 2 o’clock, number of neutrons *N* increases toward 11 o’clock, and atomic mass *A* = *Z* + *N* increases toward 12 o’clock on average (because more neutrons than protons are needed to bind large nuclei). Rainbow colors code lifetimes *t* from short (violet) to long (red). For example, the heavy hydrogens are *very* short lived. The whole chart is a very tall 880 KB PDF table of nuclides. Enjoy!

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“Cubum autem in duos cubos, aut quadratoquadratum in duos quadratoquadratos & generaliter nullam in infinitum ultra quadratum potestatem in duos eiusdem nominis fas est dividere cuius rei demonstrationem mirabilem sane detexi. Hanc marginis exiguitas non caperet.”

which roughly translates to

“It is impossible to separate a cube into two cubes, or a quartic into two quartics, or in general, a power higher than the second into two like powers. I have discovered a truly marvelous proof of this, which this margin is too narrow to contain.”

In modern notation, the equation

x^n + y^n = z^nhas no positive integer solutions for exponents n > 2. Although Fermat did leave a proof for the case n = 4, 358 years past before **Andrew Wiles** published his proof of the general case in 1995.

Relaxing Fermat’s constraints to allow non-integers greatly expands the number of solutions. The looping animation shows all solutions for 1 \le n < \infty and 1 \le \{x,y,z\} \le 11. All points on the arcs

y_{z,n}[x] = (z^n - x^n)^{1/n}are solutions, and red dots indicate integer solutions. Watch the the famous **Pythagorean triple** \{3,4,5\} flash by for n = 2. Integer solutions are visibly harder for large finite n. Many more solutions exist for n < 1.

**Starship** is a prototype upper stage for a next-generation, fully reusable, two-stage-to-orbit launch vehicle designed to enable the human exploration of the solar system and the colonization of Mars. It’s made from stainless steel. (A little **carbon** converts **iron** to hard **steel**; a little **chromium** converts steel to corrosion-resistant **stainless steel**.) At **cryogenic** temperatures, grade 301 stainless steel has higher strength-to-weight and strength-to-cost ratios than **carbon fiber **reinforced polymer, and it has a higher melting temperature.

Starship will dissipate orbital energy by entering a planetary atmosphere like a **sky diver**, belly first, its fore and aft fins rapidly moving to control its descent prior to a tail-first rocket-powered landing. Strong electric motors powered by **Tesla** batteries will flap the fins.

Starship is powered by next-generation **Raptor **engines, the first **full-flow staged combustion** rocket engines to fly. In these efficient** closed cycle** engines, no propellant is wasted: all the oxidizer (and some fuel) power the oxidizer turbopump and all the fuel (and some oxidizer) power the fuel turbopump, which together pump gaseous oxidizer and fuel into the combustion chamber to combust and thrust. The oxidizer is liquid **oxygen**; the fuel is liquid **methane**, the primary component of natural gas, which can be manufactured from the martian (or terrestrial) atmosphere.

The tension is palpable. The cartoon lander reaches the surface at the expected time, but Aldrin’s monotone readouts continue. Absence of video heightens the audio. Mission control radios “60 seconds” of fuel remaining. Then “30 seconds”. I hold my breath. At last, Aldrin reports “Contact light” — we have touched the moon — followed by Armstrong’s famous, “Houston … Tranquility Base here, the Eagle has landed”. Of the landing site, my mother observes, “They’ve already named it”.

No one wants to cook, so we go to McDonald’s for dinner. As we drive, I see a small shop with photos of the three astronauts in its window. The streets are still. The world seems stopped.

As Collins orbits the moon solo, Armstrong and Aldrin forgo a scheduled sleep period, moving forward the moonwalk. Finally video — live from the surface of the moon — shows a LEM landing leg, first inverted but quickly rectified. Armstrong describes the surface as “almost like a powder”. Again I hold my breath, a lump in my throat. “Okay. I’m going to step off the LEM now … that’s one small step for [a] man, one giant leap for mankind.” I don’t hear the indefinite article, but I immediately grasp the meaning. Armstrong reads the plaque, “We came in peace for all mankind”. Aldrin practices locomotion, which “would get rather tiring”. The president phones. We leave Aunt Nora’s as the astronauts prepare to return to the LEM.

The next morning I sit on my living room floor reading two newspapers: The New York Times, with its simple banner headline “Men Walk on Moon” — which still brings me tears of joy, triumph, and wonder as I write this 50 years later — and the local newspaper, with its astonished “Now Do You Believe!”.

]]>The animation below traces the Wooster **W** in epicycles of 100 circles-moving-on-circles in the complex plane. Algebraically, the trace is a complex discrete Fourier series \sum c_n e^{i n \omega t} =\sum r_n e^{i (n\omega t + \theta_n)}, where r_n are the circle radii, \theta_n are carefully chosen phase shifts, \omega is the fundamental angular frequency, and t is time.

Cs-133 transition frequency constant Δν_{\text{Cs}} = 9\,192\,631\,770~\text{s}^{−1} defines the **second**.

Then light speed constant c = 299\,792\,458~\text{m}\cdot\text{s}^{−1} defines the **meter**.

Then Planck’s constant h = 6.626\,070\,15\times 10^{−34}~\text{kg}\cdot\text{m}^{2}\cdot\text{s}^{−1} defines the **kilogram**.

Then electron charge constant e = 1.602\,176\,634\times 10^{−19}~\text{A}\cdot{\text{s}} defines the **Ampere**.

Then Boltzmann’s constant k = 1.380\,649\times 10^{−23}~\text{kg}\cdot\text{m}^{2}\cdot\text{K}^{−1}⋅\text{s}^{−2} defines the **Kelvin**.

And Avogadro’s constant N_{\text{A}} = 6.022\,140\,76\times 10^{23}~\text{mol}^{−1} defines the **mole**.

And luminous efficacy constant K_{\text{cd}} = 683~\text{cd}\cdot\text{sr}\cdot\text{s}^{3}\cdot\text{kg}^{−1}\cdot\text{m}^{−2} defines the **candela**.

(Where “sr” is the steradian or square radian, the 3D analogue of the 2D radian.) Discussion continues about the mole and the candela, including whether they should even *be* base units. The new definitions break the relationship between the C-12 mass, the dalton, the kilogram, and Avogadro’s constant, and the candela is arguably a photo-biological quantity.

I wish my phone number were 919-263-1770.

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