SDI's plasma-core rocket

In lieu of Cassenti's microfission-catalysis for fusion rocketry, for interplanetary missions Omira and Mourad suggest "plasma core". Interstellar is another matter (heh). So let's look at plasma-core. This is an idea from 1985 to power NERVA/NΘP.

The core is Uranium Hexafluoride, either U-235 or -233. In theory a Curium-247 hexafluoride also can be made. Anyway, UF₆ is a solid at reasonably-warm temps (<56.5°C). As a plasma the fluorine ions are likely more problematic but we're hoping to make a nuclear blast out of it so noöne cares.

In 1985 they were trying to contain a sphere of this plasma, swimming in a mutually-immiscible noble gas; and why not, in microgravity. They picked argon, probably-obviously; they got it running for about two minutes. After that, they lost enough uranium that the critical-mass went subcritical. Also there won't be microgravity during the thrust phase. Before anyone could figure out how to make this practical for a space trip, after January 1986 the launch costs per kilogram hit the Challenger wall.

Spacenerd life is better now. But the middle-1980s flights of fancy have been forgotten... mostly.

Hence such fission pulse engines as in Howe two years ago, which promised 5ks specific-impulse. Or last year centrifugal NERVA... 1.8ks. They'd make it up in thrust though; so if they just wanted to push loads to Deimos or Venus rather than all the way to Jupiter, it might work.

Gerald Marsh seems unhappy with Howe and, more so, with that lumbering 1.8ks solution. Howe's 5ks seems comparable to the 1980s 50km/s exhaust measurement. (We divide that latter by Earth 9.8 to make of that a ratio independent of SI or Freedom units, although now it seems dependent on Earth being that frame-of-reference.)

Marsh proposes to revive Ronnie Raygun's tech: with magnetic confinement, in a spheromak. Marsh seems an expert in magnets, working on them in 1996. Marsh must however conclude that one (not he) must also find a way to generate the plasma with the field configuration chosen, maintain thermal stability, and find a way to turn the rocket engine off; opining these are non-trivial engineering problems.

I counter that turning the rocket off is the least of this rocket's problems. What you do here is to calculate the cooloff of the rocket and let the spacecraft reduce its acceleration naturally. It all gets tested in the field like SpaceX tests its Starship. If you're asking after an abort sequence then whatever, just separate your craft from the engine and push the still-running engine to the side as it makes its own merry way to the outer AU fringe.

BACKDATE 8/5

A proposal for the House of Representatives

Cambridge University is, presently, a disgrace and one excellent reason for its disgrace is politics. So, sigh, let's listen to Cambridge on politics.

Britain (not part of the EU) runs on the DSA system. It has a Parliament. The majority of Parliament votes for a Prime Minister, even if the people didn't want it. Margaret Thatcher was the Prime Minister throughout the 1980s. To her, is attributed the comment "we have an elected dictatorship". However you think of Thatcher or, if you're DSA, Burnham: I don't think Thatcher ever cracked 50% of the popular vote and we jolly know Burnham hasn't.

Similar has happened to Denmark. Frederik Ravn Klausen, who sounds like a Scandinavian, nonetheless works out of Cambridge (he should leave); he has teamed with Sebastian Tim Holdum in Copenhagen. They propose instead "geographically ranked guaranteed proportionality". Buroughs / ridings / precincts / parishes still exist. But the election winners are chosen by popular vote. So if your Albertan ridings (screw it, let's be Canadian) voted for the Tory, and everyone north and east of the Lakes voted for the Grit; the Grit votes override most of you. Some of your Tories will get through however. From the truest-blue ridings.

As they note, regionality is here sacrificed. It rather has to be, because someone Federal (or Royal) is going to have to guard the ballots wherever the score stands to be run-up. Historically the cities.

An expressly-regional second chamber would counter this. Americans have such a body: the Senate, wired into State boundaries and once-upon-a-time appointed by State legislatures. This is why Americans deserve to take Klausen-Holdum seriously where, frankly, I would never recommend the above system for any unicameral state. Fer cryin'-out-loud, Denmark is made of islands (and a peninsula).

Drawing up the constituencies is still up to the States I guess. On the plus side, if their constituencies might get overridden by their neighbo(u)rs anyway, gerrymandering might not be as hot an issue.

The issue wot I see as hot is if these States' voters are overridden by other States' voters. They already have to suck it up when Senators from Delaware and North Dakota dab on 'em.

Pekah, Shalish of Israel

Pulu wrested the throne of Ashur in 745 BC, from a "Shalmaneser V" whom Pulu's family then disavowed. Perhaps similar breaks of memory were had in Israel at the time. So: Carl Lederer, and now youtuber "Dig."

The eretz-Israel had been a united land under Jeroboam II, but as all men do he died. His heir Zechariah was ousted in a coup and that coup - under Shallum - collapsed. Menahem and Pekah picked up the pieces. The Bible says Menahem ruled for ten years and Pekah for twenty.

The maths don't add up under scrutiny from Assyria however. Menahem gave tribute to "Pul"; that emperor claimed he'd had it from Pekah as well. Luckily, we have a local report: from Hosea the northern prophet. His sermons made a point of the twin iniquities of his land. Hosea didn't consider Judah in this calculus, despite that it was starting to matter again; Hosea's twinland was Ephraim-and-Israel.

According to Lederer's reading, Pekah had a base in Gilead and simply slipped over there, keeping that base. The face-saving fiction was that Pekah would hold the title "Shalish" and not "king of Israel". In practice, yeah, Pekah was sulṭan across the water, as it were.

I must inject here that per Rendsburg (pdf), Amos especially Amos 6 is also writ in a nonJehudi Hebrew to be considered northern. Amos didn't preach about Israel/Ephraim's twinship for the simple reason he preached under Jeroboam II when that kingdom was one. His kingdom likely included Judah then; maybe then Edom (so I'm not getting into which "Tekoa" here). So for Amos, Jeroboam's court was the court which mattered.

Pekah would eventually switch to being an ally of Damascus and make a bid to take Judah. Ahaz squealed to Assyria who then attacked and got all of it. Israel, from Samaria, would end up a rump and tributary Assyrian vassal, under Hoshea.

More Trappist-1 constraints

On the (excellent) assumption that Trappist-1's planets are all differentiated, Emeline Bolmont, Alex Revol et al. offer "Estimation of the tidal heating in the TRAPPIST-1 planets". They are admittedly constrained by the uncertainty of what these planets' cores actually be, that Love Number we'd noted here once.

Also they don't know the eccentricities of b or c. Frankly I doubt they're Keplerian, so they need some postLaplacian model. Eccentricity tides would bump up their estimates especially inward.

What Revol (especially) thinks he does know, are the obliquity and the libration of each planetary rotation: less than one degree, each. But Revol does not hold these planets as tidally locked: a slow drift of the substellar point, which therefore leads to a day-night cycle.

I find intriguing this space elevator design for e. However Revol argues that the rotations for all planets are slow such that day/night appears retrograde. GEO is, then, high. Where GEO extend past Hill, all space elevators must be floating tether.

Even with low eccentricity it came out that b and c are superheated like Io (if not technically lava); it's elsewhere been noted they've lost everything volatile by now and are airless like Io. Planets d, e, f get more internal heat than Earth; e, they submit, may have a crust and plate tectonics. And we hear e has air. Although I am still not hopeful for photosynthetic life.

Kleisioti et al. move on to f, g, h asking after ice shells, quite reasonable for these cold planets with, further, lower measured density. Planets f and g might have thin Enceladus-tier ice shells; h's would be thick like Europa's. They think possible for us detecting cryovolcanically generated water vapor on f (maybe g) for which we haven't looked. 20 transits should do for seeing it on f.

The patent for a supercloud server

A patent now exists for the heliosync orbit: US-12679564-B2 at ppubs.uspto.gov, for datacentres which I'd written off two years ago as "cockamamie". Various factors as of 2026 are making this less silly. Sophia Space has press-releases, linked at Zim's place.

Heliosync in theory runs 400-1000 km so, LEO. In practice they don't want drag: superfast atmo, which degrades... everything. They also don't want the congestion which reaches further, maybe to 600 km. So they're thinking 800 km. They must beam the data to a comm array anyway, which may as well be SpaceX' constellation of Starlink v2.

Heliosync around Earth gets about 1.361 kW/m² "flux", more than that most the year because of eccentricity. The patent illo assumes they can drive 1 kW/m² from the solar-cells, which they expect η=.3. They leave the material to others; maybe Perovskite. Anyway I read 400 W/m² available to the computer, not 1000. Also here are transmitters, of data.

Some of that flux is reflected (5% here); less is transmitted. Most that heat needs radiating-off, still maybe 1.3 kW/m². The good news, if they insulate the computer: the computer is wide, flat, and narrow. They think that the shaded darkness will allow "passive" radiation through the shade, into space. More good news: most office CPUs seem to run in the 45-65 W range as long as you are not gaming on them. 400 W/m² might make for a respectable server-farm.

The design is simple if they can stow the volume onto a rocket chassis. Direct 800 km looks like a Starship job.

In addition, if the Lunar south pole gets a superstructure, similar architecture might work there too. For a start. (Later we expect coolant-cycles underground.)

Loanwords in Choltian

In pictographic old Egyptian, loanwords are easy to suss. Not having any indigenous roots, such words are spelt phonetically and never otherwise. Magnus Pharao Hansen has been applying the same principle to classic Choltal inscriptions.

They have a loanglyph too: the Striking Owl. This iconography is Teotihuacano. I think everyone agrees that the Place Of Reeds knocked a lot of head down in the Petén. The empire even installed a prince to rule over Mutul ("Tikal"). But we're talking about intrusive words that haven't a contemporary Maya-family etymology.

This'll be a placeholder. (I am not a mayanist.)

Dr Hansen has been arguing that the loans are in some paraNahua dialect and that, therefore, the Place Of Reeds was, if not called anything like "Teo Huacan" at the time, also paraNahua. Mind: this depends on his ability to reconstruct what that dialect would have sounded like, a thousand years before Catholics came with a Latin alphabet. We can do it for Choltal, precisely because sometimes an author could get phonetic. But not many outsiders were using so good a system, then, for writing.

That central Vale was shared between Nahua and Otomí as of AD ~1500. It may be some sharing had happened already. One does wonder how the Purempecha interposed themselves into Michoacan in the meantime.

Anyway if you want to give Dr Hansen a hearing, try "What Happened When?: Relative Chronology and the state of pre-Nahuan in the Classic Period. Paper presented at the Relative Chronology workshop at the University of Copenhagen, June 30th, 2023".

n-body, near O(n)

After Newton discovered the equations behind Kepler's 2-Body solution, he ran afoul of the n-Body Problem. A limited solution presented itself in the equilibrium point; the full five solutions were offered by Lagrange. Further refinements handled special cases of the 4-body like when Laplace sussed out three of the heaviest (and largest) Jovian moons. So here we are in the computer age, when computers struggle to handle particles numbering more than maybe five. It's O(n*n).

Kepler and Newton assumed that the bodies are rigid points and that we ignore Einstein; so Io's tides and Mercury's depth in the well don't figure. Also computers have to approximate floating point numbers well above Zeno's quantum level (Planck?). That means we have already sold the horse for approximations. And that means we may as well approximate some more. Keyframe Codes has a little primer on the available algos.

Midlevel nerds have been using Barnes-Hut. This method runs on multipoles: it buckets the particles in squares-of-particles, finds the center of gravity, and runs the calc for the centers. The buckets are identified with quad-trees; Barnes-Hut ends up O(n * ln(n)). Leave aside for now if we want to run this 2D or 3D; we'll pretend perfect ecliptic. What if the cluster doesn't behave like a square (or cube). Real astrodynamicists need the particle swarm where most particles would be clustering. They will be looking first at Lagrange's L4 and L5 "Trojan" haloes especially for Jovians. These haloes are elongates.

In 1987 Leslie Greengard came up with something else, the "Fast Multipole Method" - usually FMM. Not only does it claim O(n) but, depending on how often you want to run each n, the error can arbitrarily diminish. This was Greengard's thesis and, it seems, got a refinement under one Vladimir Rokhlin. Discontents exist: Srinivas Aluru in "Greengard’s N-body Algorithm is not order N" (pdf) showed that the choice of precision must depend on n (at least ln n), therefore cf the title - to the tune of O(n ln²n). That extra ln(n) is, then, the price for accuracy Barnes-Hut must pay in the Trojan haloes. Dr Greengard's peers seem to have agreed; he got to keep his PhD and the IEEE considers FMM in the top ten of twentieth-century algos.

This starts by keeping each interaction as a field vector Φ and treating that vector as a number on the complex plane. The vector acting upon particle "i" is the gravitational parameter of counterpart "j", times the natural logarithm of the i-j distance (plus iθ); that's the force. The iθ exists, here, to make it a vector as to place the particle on the coördinate plane; a computer may ignore it now to figure the coörds when it's display-time.

Some might then use "numerical methods", which is mathematician for iteration. The FMM, in the complex plane, may use the Cauchy-Riemann equations. At this point I'm leaving the rest to the nerds.