The occulted Shi'ite Quran

Nebil Husayn reviews Seyfuddin Kara, In Search of 'Ali Ibn Abi Talib's Codex. Kara has endorsed it on academia.edu, so I assume it a fair summary of Kara's text.

Husayn and Kara before him share the same problem of most literature since Behnam Sadeghi first published the Sanaa 1, aka 27.1 DAM. It is commonly assumed that the Sanaa 1 is just about the archangel Gabriel's own autograph, and that radiocarbon proves its ancient date.

The grey-eminence behind Kara is modern Shi'i scholar Ma'rifat on Shi'i doctrine concerning Quran. The Shi'a today hold to the same rasm as do the Sunnis. In fact they make something of a point of that. They believe, also, however, in a parallel interpretation vouchsafed to the Imams, accessible mainly to the initiated. Every now and again a text has come out into scholars' attention collecting these interpretations, most dramatically that of Sayyari although 'Ayyashi also shares a lot of these.

Pace Ma'rifat, suppose that these "interpretations" were early. If early enough, they may have preserved qirâât from before the great Umayyad standardisation(s). Literally "recitation", qirâa incorporates "reading", "interpretation", "vocalisation", and - at the extreme - "alternative". You will find "'Ali read -" across all the books which Arthur Jeffery cites in Materials, that magisterial collection of variants against the text. Usually, in al-Kufa, it was Ibn Mas'ûd held responsible for these changes; when Shi'ites waxed in al-Kufa, and where they debated Sunnis, these preferred to ascribe 'Ali readings to him. It seems that Marandi over in Spain tended to foist such upon Ibn Khuthaym.

Etan Kohlberg and Mohammad Ali Amir-Moezzi argue for a difference between modern Shi'ite dogma and the Shi'ites of the latest first century, when Shi'ism was first being formed (per Najam Haider). The first Shi'ism was a sectarian cult. As such, the full range of its dogmas were opaque to outsiders. Sayyari and 'Ayyashi, then, were not "extremists" but insiders holding to the dogmas of their time. Husayn and (I think) Kara are fair enough to note this perspective.

Kara's main aim was to trace some Imami ahadith about 'Ali's codex. He does so to the late Umayyad era. This shouldn't surprise, because that's when the sect started shuttering its windows.

Overall I am unsure that any of the scholars noted here have made their case for a Quran earlier than, oh, 'Abd al-Rahman's seizure of al-Kufa circa AD 701. I don't think they need to, given that their isnad-chains peter out a decade or more after that.

The efficient ballistic

I am pondering the errata. Never mind the porkchops, those are a dodge. And yes, sticking with inclination-dominant cyclers, like I did with Earth-Venus, lies in that subset of "dodge".

The cyclers' maths were designed for Earth-return. There is only one run by Mars before cycler-repeat. (If that: cf. 5S8.) Something may do plenty of runs past 1.53 AU or wherever, but no more than one run by the red planet - per synod. Hence my assumption that the second visit to Mars would be at the same place at the same angle. I question here if the cycler is headed on that same angle.

The whole point of Russell-Ocampo '04 was to provide an array of angles running past Earth.

Why is V_∞ at Earth not an array? I mean, maximum angle makes the turnratio, but shouldn't we have their lower V_∞s too? Leaving aside that I personally don't yet know what those are for h>3 cyclers.

And wouldn't this be a fine place to consider Earth eccentricity and inclination on return?

I would set for each cycler a table of seven rows. Each seventh corresponds to the 51° angle-increment Earth has proceeded over the 15/7 years of the Earth/Mars synod. The row has a pair of vectors for Earth: position and velocity. Any return to Earth will hit one of these rows, depending on how many synodic periods p have elapsed. For Aldrin's 1-0-1-6 it's just the next one, for backflip's 2-1-1-5 skip to two and so on. The 7- series are, like VISIT, often "degenerate" but, not all of them; they stay on the same row.

This multiplies complexity such as to explain why Russell and Ocampo didn't want it. I insist on Martian eccentricity but, yeah, what I've just outlined seems like porkchop.

Subluminal warp

Alexey Bobrick and Gianni Martire propose a warp-bubble drive. It's Alcubierre without the silly. It's Lentz but better explained.

The ship still takes a generation (from our perspective) to get anywhere good, like Gliese 876. But time slows down inside the bubble, so it's not a Generation Ship mess like Kim Robinson's Aurora or that Aniara poem. And it doesn't need dangerously relativistic speed like Tau Zero. The travellers' relatives on Earth still have to wait it out. The travellers won't.

This will be nice to have closer home for interplanetary transfers as well. Although, as Lentz, the spacetime-bending physics here look to require some hardcore energy in-system.

FOLLOWUP 1/16/22: Sabine says that Jessica Santiago rules out everybody except Bobrick-Martire. Lentz, last we looked, won't give up yet. I didn't pay attention to the Santiago paper because, drrrp, causality; intuitively any FTL is bollocks. As for Martire, whose warp escapes Santiago; Sabine relays that he is hiring.

In hot water

Earth's mantle has an extra ocean in it. Back in the 3000s Mya, the lowest third was still Basal Magma Ocean, in effect more core. But the outer two thirds had gone rockier. If still very hot. Too hot to hold water in fact.

Conclusion: after the Moon broke off and the various bombardments leveled out, which they're positing 4 billion years ago, Earth was a water-world and the water would scald you. As the [outer] mantle was left to cool, it sucked more water down, leaving about the volume of ocean we got today. SEQUEL 5/16: And come 3.6 Bya, the plates moved.

The Sun was cooler then, tho' maybe more prone to flare. I think they assume Earth had some magnetic-field, and an ozone layer - not from plants of course but from oxygen ions direct from (at least) atmospheric water vapour. So the vapour wasn't boiled so far as into space.

Although: maybe some excess was. Before 541 Mya (they say) it's hard to tell. They seem to have pulled that date out of the Cambrian; maybe because there aren't trilobites before then, for dating proxies. I'd honestly turn that dial to 565 Mya when we know we had magnets. I don't know this for 4-3.2 Bya, liquid lower mantle or no.

Options

Mrs Helen née-Smith Reynolds has a page.

I have to say, it's tempting. Although - once upon a time, your own humble blogger was tempted to move a prior blog to another female-run page. That female, who had not at that time changed her own maiden name, turned out... different; turned out anti#gamergate, turned out antimale. But Smith is the devil we don't know.

Amazon is the devil I do know. Amazon is playing the mafia toward us CreateSpace legacies. As of now, if you self-publish on the Amazon platform, Amazon will bury your book in its listings. If you are published through a "real" publishing house, obviously your publisher will promote your work. But Amazon does not promote Amazon-published work. Why not?

Because Amazon also "offers" an advertising service. Conflict-of-interest much?

Amazon bets that it can make more money from taking your money than from getting a cut from your customers.

Fauci is not Pharaoh

Howard Schneider would like five minutes of your time to understand how U.S. COVID response could have avoided hundreds of thousands of deaths.

Keep that in mind as Tablet angles for conservative funds by poasting this, at Moldbuggian levels of loquacity without providing Moldbuggian levels of content. In it, I find this:

Boldly dismissing without argument the fact that viral infections cannot be stopped from running their course once they have taken root in a population, they asserted that acquiescing to indefinite cessation of social and economic activities they deemed to be nonessential would stop the disease’s progression. The ensuing lockdowns, mask mandates, and other measures made life for most Americans worse in every way.

If that viral infections cannot be stopped from running their course once they have taken root in a population is a fact, this poast itself boldly states it without argument. We're just shouting slogans at each other.

At least the latter uses the word most. Although the masks were a trivial inconvenience compared to the alternative, SARS-2, which absolutely made life worse for anyone who contracted it. But then the Julie Kelly set would have you understand that Long CoVID doesn't exist.

We cannot even argue the point, because the whole well has been poisoned. This claim is buried in a larger article against The Oligarchy. If counterinformation comes from The Oligarchy, it is invalid.

They even dare cite the Exodus. All I can say to that is, get over yourself. Unlike Pharaoh the Oligarchy was not trying to ruin lives, at least not with the CoVID measures, but to save them. Here is the Jewish way to Godwin. Funny how the people who claim they want an honest conversation kick it off like this. SHUT IT DOWN

Perhaps the "vaccine passport" is an idea whose time has not come and should not come. The people arguing against it are selfish people, dishonest people; people who have abrogated their moral right to the franchise, and are too epistemically-closed to contribute to so much as a conversation.

It is difficult to argue against the "vaccine passport" or against the Oligarchy generally when the opposition thereto was, in its former iteration, a death-cult.

UPDATE: I mean, also, there's Matt Gaetz. Victim. I suppose... yeah, it's a curse.

UPDATE 2: Donate NAO. Trump will be President any month now.

UPDATE 4/1: Fool's Day. Sarah Palin isn't joking.

On the next generation of failboats

I avoided the saga of Boatplug McWedgie in the Suez. Now that the ship is free, David Fickling posts a thread about future shipping. I don't know squat about this topic myself so I'll mostly just summarise him.

Although Suez might be done heaving this stuff through its colon (at present size), ships are only going to get bigger in future. Bigger boats carry more cargo at once. Which means Suez will have to get bigger. But other straits like Singapore really can't get bigger - they're natural, so the very tides are conspiring to keep them the way they are. So the bigger boats out in Asia are going to have to accept longer trip-times through such natural straits as are deeper and wider.

Some tie-in engineering projects being noted are that Indonesia wants to move its capital over to eastern Borneo; and that Australia and New Guinea are up for restoring the Sundaland via bridge. A mighty bridge at 500 meters over the seafloor would keep the ferries out of the way, so the shipping can continue. Although I am unfamiliar with the typhoon situation down under.

Nuclear power is being mooted to run these monsters, as well. Of course private corporations can't have them, only sovereign ones - that is, governments. Fickling floats the public / private mix of international trade common to the Age of Sail. I'd have brought up the pochteca. I will say that if an international port doesn't want the RFS Chernobyl docking nearby, she can float out in a calm spot of sea and let lower-capacity chemical shuttles take the freight. Any fine spot for this sort of thing would be some submerged old Pleistocene lemuria - like the Dogger Bank, or the Zealandia. Should be shallow enough to drop anchor(s) whilst still deep enough not to get SHOALED.

Don't be a forger

Guest post at History For Atheists: Lee Clarke, on literalism. I am here for that Alexandria / Antioch dustup, which cities birthed the Miaphysite / Dyothelete schism.

Clarke claims here that the Alexandrine school held to the spiritual interpretation of Scripture; the Antiochenes, more moral. We could say that Alexandria held to the Gospel of John against Antioch's Matthew. Clarke's argument is that neither of them were literal - both schools made use of qiyas, as the Muslims would say.

From that common ground, in where they chose different emphases: I am not seeing a schism. There is room in our Father's mansions for a Christianity both spiritual and moral. I cannot but see that the third century Christians saw it the same.

Where there may have been openings for schism is where either side fell into writing new scriptures of their own. The Egyptians were infamous for composing new Coptic "gospels", often gnostic. West Syria bequeathed to the world the Pseudo-Clementines.

It was in literature that schisms could be forged.

Errata for Mars missions

I "took a break from" (not) figuring out h>3 and looked into using Kepler, rather than Newton, in finding time-of-flight - Newton was a time-waster and (at float-point δT) increasingly inaccurate as T rises. I also strongly suspected that we actually need eccentricity in getting to the next planet over. And that Earth/Mars wouldn't need those Pork Chop Plots which admittedly we do need for Earth/Venus, and for the Belt.

After banging at this, last weekend - I think I'm done. Here is "On reaching an eccentric orbit by a ballistic route". In the process this un-messes Mars; so, if you've read Russell-Ocampo 2004, use this chart instead.

One nice knock-on effect is that if you time your departure right, you can hit your desired point in Mars' orbit, and shave off V_∞ or time-of-flight. Probably not both unfortunately. And the s[h]avings are light enough that it might be Pork Chop Night anyway.

The latest Aurora psycho

Ahmad al-Issa whose family lives in Aurora crossed the Denver metro and did some damage here. You may have heard.

The FBI was looking at this monster for some time but, as usual, let it happen - because, whenever something bad happens under an agency's watch, that just means the agency needs proper funding. Par for the course.

Also noted at one of these newslike outfits was that al-Issa's politics were mixed. Anti-Islamophobia but also anti-LGBT. Gee, wonder what ideology fits all THAT! Likewise a lot of politicals around here remain flummoxed about motive after many man-hours of interviewing. The "counter jihad" community has come to its own conclusions: JIHAAAD

I'll post here my lack of interest with all the options. Jihâd terror does exist. But... it is done for a struggle. Random jihâd is, believe it or not, condemned in Qurân. It is only good for G-d if fî sabîli'llâh - in G-d's path. Doubly so if qitâl.

In that light, conquering northern Mozambique is (by Islam) lawful qitâl. Maybe attacking a gay nightclub. Certainly shooting up an art-exhibit where the Prophet's image is to be drawn. I don't approve any of these actions but they do spread the rule and the fear of that religion and its god.

Some pudgy prematurely-balding khâsir driving 20 miles to shoot random whitoids who, in their spare time, also shun "Islamophobia" is to be filed as a hate-filled loser. Al-Issa did not aid the cause of submission to G-d. He did the opposite. The Islamic god will not reward him.

As to whether the Divine ideology inspired him - well, maybe. But he was a loser. He was going to be inspired by something horrible if his family had tried to raise him in Syrian Jacobite Christianity. He should have shaved his head, lifted weights, and inspired others by example. I'd say he should have converted to Catholicism as well but, we cannot have everything.

PS raḥima Allāhu, Mohammad Anwar. And requiescat impacem, Eric Talley.

John Damascene was a Monothelete

Jacob Tate raises, at OnePeterFive, John Damascene. This lesser blog hasn't spent much time on John's theology ... for its own sake. (A previous blog had spent more time on how John handled [an outdated form of] a different theology.) Tate points out mainly John's support of icons, but in the process cites John's (ostentatious) veneration of the Virgin Mother. In that light: Zachary Keith.

The Christian focus on this Mary has, historically, been a Monothelete concern. By saying Mary was the Mother of God, late-antique politicians like Cyril of Alexandria identified Christ with the Father In Heaven. With the failure of Constantine's and Arius' "Eunomian" project, the next generation of Constantinopolitan Emperors - particularly Theodosius II - could use this Marian formula to identify Christianity with the "well ordered" Christian State. So it was when Cyril ousted Nestorius. It is in Cyril's footsteps John will tread.

Keith notes that John set out his "Fount of Knowledge" as a middle-way between the "Eutychians" and the "Nestorians". In practice John addressed the Miaphysite organisation out in Egypt and in his own west-Syria much as Pope Benedict used to address the Pius X Society. For John they are in schism but not in heresy.

Note that John lived in an Arab-run west-Syria. The Marwânid régime in Damascus, up to the AD 710s / AH 90s, favoured the Miaphysites. The Roman emperors at the time were Constantine IV, Justinian II, and finally Leo III the Isaurian; these were dyotheletes. And Leo III and more-forcefully Constantine V were not just Dyotheletes. They were against icons and, under that Constantine, full-bore iconoclasts. This tendency traveled over to the Caliphate when, in the 100s/720s, Yazid II tore down statuary from Egypt to Syria.

I see in John's career first an attempt at rapprochement between the Miaphysites and his own Constantinople-loyal(ish) Melkites, mediated by the Virgin. John I doubt was ever that much loyal to the Rhomanía - as a Syrian, why would he be. Leo's turn against icons gave John that one more excuse to disassociate himself from Rome in writing.

In sum: John was a Monothelete, at least in the Constans II "Maroni" tradition. File him with the Maronite Chronicler and with George of Resh-'Ayné. (To the extent our Orientalists don't already.)

As to John's infamous rant against that different theology, to which the caliphate adhered: perhaps John sketched this text under 'Abd al-Malik, early on. John suppressed his own work - as long as that caliph was tolerating the Monotheletes, and the icons they venerated. Under that caliph's heir Yazid, those bets went off.

Everyone messed up Mars

Russell and Ocampo's 2.0 km/s for V_∞ insertion to Mars at 2-1-1-5 aphelion is, frankly, a joke.

For vinf: the cycler at the outer planet needs to target that ones' speed at that distance from the Sun, not a fictional planet's circular speed at its semimajor (possibly) millions of kilometers thence. And the cycler needs that angle - which, where the planet isn't himself at peri', is never circular 0°. (Tho' 'tis a sight closer than is the cycler's - obviously, or Mars would be a cycler...)

Mars, coming off his own 1.385 AU peri', is going faster than he will at 1.54 AU. At 1.45 AU that factor is 1.09775756.

We next have to consider cycler/Mars γ-angle. The cycler at aphelion is, itself, γ=0 with respect to the circle. So the angle we want is that angle Mars is going with respect to that circle. It's actually not so different from circular, especially this close in: only 0.00350 radians. And he's tilting for us.

It's the destination planet's speed which is killing us: where 2-1-1-5 and Mars meet, Mars is going 26475 m/s. This is decidedly midway semimajor-Mars : Earth 24.07 : 29.78 km/s. So 2-1-1-5 V_∞ @Mars = 1788 m/s.

For McConaghy et al. 1L1, 2L2, and 3L4 still check out. But... 2L3 is V_∞ 2678 m/s at aphelion (290 days), against McConaghy's 3.05 km/s. Sorry to say, we'd all got the cycler-Mars vinfs wrong for Mars where the cycler doesn't reach semimajor.

Heavy planet biota

Chang Liu et al. nine days ago found bone density genes in the African giraffe. It strikes me (belatedly) that this will help human-sized biota on higher-gravity planets.

I could easily see these being evolved in Permian-era "Mammal Like Reptiles". As soon as they get out of the swamps and evolve that ability to hoist their bellies off the ground.

In this scenario, I wonder if the Barbados flying fish, without those enhancements, evolves into a flying amphibian that roosts in island and lagoon trees and cliffsides. The atmosphere will be denser in such a planet, remember.

Some planets, you just cain't reach

I am reconsidering Earth-Mars backflip, Russell-Ocampo 2-1-1-5. Alongside other cyclers as don't reach Mars' semimajor.

They floated 2-1-1-5 (r 2) 1.45 AU, and 3-5-1-11 (r 2): 1.45 and 1.42 AU for (on their Table 4) 0.94-5 ratio. As for what Martian orbit the cycler hits, it can get anything from Mars' perihelion up to its own aphelion. R-O were, I believe, targeting cycler-aphelion: since my Newton simulator for 2-1-1-5 takes 203 days against their 207; for 3-5-1-11, 222.5 days against their 231. I expect flight-time and V_∞ both be worst at cycler aphelion but, at least the cycler has the best hope of actually meeting the planet up there.

Aphelion for <1.53 AU cyclers was explicit in McConaghy so I gather that R-O is just passing that along.

For vinf: the cycler at the red planet is hitting a fictional planet's circular 1.524 AU speed. Since not-Mars is himself at peri', the R-O paper assumes circular 0°. So they get 2 km/s for 2-1-1-5 which I verify 2021 m/s. Based on that logic.

Flying inside a Tesla battery

Via the Ineffable Island - Leif Asp et al., "Structural Battery and its Multifunctional Performance". From January.

Last I looked I was looking to Liceron's 650 Wh/kg; this article is boasting 24. But they say - (quietly) - that's not entirely the point.

Leif Asp's team are promising to store that energy in "structural load paths". So: they're taking mass that would otherwise be used only to hold a Tesla car together, and using some of that to store energy as well. They project a "stiffness" of 75 GPa, like aluminium. Which element is itself a battery-cell candidate.

Imagine if that Cessna (also) was a battery, rather than having to lug 'em around, taking up cargo space.

The higher they climb

Step back a moment to single symmetric returns: like, oh, 1-0-1-6 for Mars or 2-0-1-6 for Venus. I am looking here at high h. I am beating my head against the Earth-Mars cycler, 3-9-1-7.

This means the array of "s_j", as the Society Of Russell And Ocampo puts it, should itself be a single-member society. h_j = {9}. Fracking f_j = {6}. Am I missing anything here? No flippin' returns. Just six flies by Earth over three synodic periods.

That h means, half-years "allotted" to the returns.

As long as h doesn't barf up five or six returns, as long as it stays under 8, I'm good. Then 3-9-1-7 says { 72 45 45 45 45 72 }. 4-9-1-12, 4-9-1-14, 4-11-1-10, 4-13-1-6 are similar. Then there's 4-9-2-8: {83 45 45 45 45 83 24}. Their Table 4 consistently brackets six f_j's for that first symmetric-return.

I do not know how this is even possible. This cycler should have six angles, yes. Those angles should all be identical. Nu?

(Apart from that, I see that 4-8-1-8 broke Newton; but, Russell and Ocampo didn't use that cycler themselves, so whatevs.) UPDATE 3/25: nah, I had failed to cast an int into a double where f_j was odd. I have solutions now for all of it.

I see it again 5-9-2-8, 5-9-3-6, 5-10-3-7. 6-8-3-11. So: the problems kick in h ≥ 9 and, as the synods get higher, the walls close in on us.

It's not about my maths nor even their maths - those work great. It's about the iterations. Somehow in the Russell / Ocampo universe, {6} is {1,4,1}.

It may all be moot for me anyway.

Must be solved iteratively

One annoyance with h>3 is that Russell and Ocampo dumped a must be solved iteratively function on me. Find λ where f(λ) = 0. Ick!

But there was good news. f(λ) was differentiable! That meant I could call ol' Isaac to my rescue. I just had to differentiate that f(λ) monster on λ. And to turn both f(λ) and my new f'(λ) into anonymous functions of course. Anyway, for your perusal:

private delegate double SolveForL(double l);
private static double IterateNewtonRaphson(
SolveForL fun, 
SolveForL dfun, 
double startguess, 
double epsilon) {
 double l;
 double lNext = startguess;
 int iter = 0;
 do {
  l = lNext;
  lNext = l - fun(l) / dfun(l);
  iter++;
  if (iter > 1000) throw new ApplicationException("won't halt");
 } while (Math.Abs(lNext - l) > epsilon);
 return l;
}

My initial guess could fail, famously with sinusoidals; Mars/Earth 2-4-1-4 failed with initial zero. To that: more good news! These guys assured me that lambda would be bound, here between zero and right-angles. So I wrote this wrapper, to find (hopefully) the first real solution, and leave with it:

private static double IterateBoundedNewtonRaphson(
SolveForL fun, 
SolveForL dfun, 
double lower,
double upper,
double epsilon) {
 double l = 0; //dummy for now
 double guess = lower + double.Epsilon;
 do {
   try {
   l = IterateNewtonRaphson(fun, dfun, guess, epsilon);
   } catch(ApplicationException) {
                    //do nothing, it's a nonsolution
   }
   guess += 0.1;
 } while ((l <= lower || l > upper) && guess < upper);
 if (guess >= upper) throw new ApplicationException("No Solution");
 return l;
}

Just var inr = IterateBoundedNewtonRaphson(fun, dfun, 0, Math.PI / 2.0, epsilon); and we're off. 2-4-1-4 has lambda 0.9960 radians, turns out.

I did a sanity-check thingy after sending these functions over there, something like if (Math.Abs(eq8(inr)) > 10F * epsilon) throw new ApplicationException("you goofed");.

Still not saying I've totally sussed the h > 3 problem set. Certainly not saying the above is the efficient way to go about all of this. I wasn't even sure I was doing it right which is why I had that sanity-check.

But it is looking better.

The new Venus/Earth cycler: 3-0-2-9

My 2L4 has been the "Buzzin' Earth" -cycler of Venus for too long. Let us graduate from McConaghy's Aldrinlikes to Russell-Ocampo.

After much sweat an' tears, I figured out the R-O algorithm (for h ≤ 3 mostly). More: their maths work for Venus / Earth; as I can verify with 2-0-1-6 which is that 2L4.

I am here to beat 2L4's record of 3864 m/s V_∞ @Venus. I am also here: as in, on Earth; not on a station at STL1. Past time we had cyclers to run by this marble proper.

To that end 3-0-2-9 runs three synods before cycle-repeat. The difference between this guy and 3S6 is s=2 rather than =1. This means two symmetric returns - to Venus - over those three synods, before its next run to Earth. Another way to look at it is: 1.5-0-1-9. Or: it's a mirror to the Earth-Venus Hohmann run which makes two symmetric returns to Earth per one to Venus.

Per orbit, aphelion 1.032 AU; back on Venus, 1.5 synods and three orbits later, angle 64.89°. This is not only Earth-crossing but, at home, ballistic! - and Newton tells me that time to Earth will be 103.35 days.

There are always tradeoffs. 3-0-2-9 V_∞ at Venus is 3387 m/s but let's allow 3404.7 given the precession. This is better than 2L4, not so much better; but it's about as good as it gets down there. V_∞ on its whip-by Earth will be 3858 3866 3863 3489 m/s and, I admit, that might suck for passengers.

By i=9: if this cycler was s=1, it runs two revolutions rightbranch. But we're now looking at s=2. Three runs in this orbit come to 897 days. There the cycler uses the inner planet to patch orbit.

"Oh you cheater", I hear you saying; "what about h>3 - what about any h". Sad thing is... I didn't actually cheat; or else I'd have posted this post yesterday. The first cyclers h>0 which don't totally kill Venus' shuttles with V_∞ are 4-3-1-21 then 4-5-1-19. FOOOUUURR SYYNNOOODDDSS. Why even.

Ocampo-Russell's cutting-room

On topic of the Ocampo / Russell Earth-Mars p-h-s-i cyclers, I am still working on those. I believe I have nailed down the set of h up to 3. But. I could not help but notice some cyclers as did NOT make it into Table 4:

4-2-2-5 (r 2): 1.45 AU; 1.12 turnratio; vinf 4147 m/s. angles 92 x 4

Unsure what the authors' dealio was, with 4-2-2-5. This 'un weren't pounding a new one into the planet. Mars at 1.38 AU should be seeing this guy.

UPDATE 6:40 PM MST: Deleted that dumb poast where I'd picked the wrong angle for my turnratio. Gotta pick the longest one(s) or they'll mislead 'ja.

UPDATE 3/26: I should delete this dumberer poast. 4-2-2-i was already handled: it was 2-1-1-i. Whose fifth solution is just Uphoff's backflip.

At least it's an opportunity to improve the R-O algorithm. To whit: if (s > 1 && p % s == 0 && h % s == 0) continue;.

And yet... 3-1-1-19 (r 2): 2.18 AU for 1.43 ratio; 0.9 turnratio; vinf 5434.24 m/s. angles 94.82 x 2. Turnratio a bit low?

Progress update

My job today was to follow Russell-Ocampo such as to wean myself off McConaghy. Aphelia, turnratios and (especially) v_∞s look okay. For h=0.

I'll pause to complain about the algorithm. This is a 3-D loop on p, h, s to calculate time-of-flight. ToF is (S * p - h / 2.0) / s, where S is 15/7 for Earth-to-Mars. If ToF is negative, skip it. If not, carry on to collect that array of vectors on i.

Russell and Ocampo claim they are looping h from 1 to arbitrary hmax. h needs to start at zero, and to max out at 2*S*p. I know they were doing the former because those results are in their tables. C'mon, men! Likewise, s is never more than p.

I'd add other skip-conditions: like the degenerate "solutions" for Earth-Mars VISIT or, for Venus-Earth, Hohmann. Once we get into the -i part of p-h-s-i, I'd start i's count from s since s is never ever more than i.

I am doing h in {1,2,3} next. Here my results aren't as consistent as I'd like. The vital statistics noted above are okay but I'm concerned about the angles-plural of approach.

Arcadia

Elon Musk is looking at the Arcadia plain of Mars. This is in the northern depression. His landing sites are all around 40°N: AP1 and AP9 northwest of Olympus; EM16 in the Erebus hills west of these; PM1 in the Phlegra range west of that. h/t Zimmerman (pdf).

Arcadia is a vast plain not unduly molested by craters (although, keep reading). Elon wants solar power, already on a budget 1.5 AU out. North is overall milder in winter than is the highland south. And it's just easier to land something at a non-polar latitude when approaching from the ecliptic. These particular four sites are better for ice, than other Arcadian sites; as Zimmerman notes however, it would suck to land on a glacier that then gets all slushy below you. Likely a third reason not to land north of 40°.

I ask why nobody considers the Hellas basin 40° south, that great exception to the whole "highland" thing. Wrong side of the ellipse, I guess; bad winters.

As to Erebus: is it just me, or was this a massive debris field from a strike coming in south-to-northeast? Looks quite orthogonal to ecliptic. Comet?

The Russell-Ocampo superset

We missed the Venerean midsummer 17 March - sorry, lads. To make up for it, on this the first day of spring here on Earth...

As sequel to McConaghy et al., Ryan Russell and Cesar Ocampo sketched out an algorithm for finding these and more. "And more" means:

the naming convention for the cycler orbits are of the form p-h-s-i, where the letters represent four numbers that uniquely identify a class of cyclers. For example, a cycler of the class 4-3-2-12 has a period of 4 synodic periods, includes 3 half-years allotted for full or half-rev returns, and includes 2 symmetric returns using the 12th solution, by ascending semi-major axis, from the multiple revolution Lambert problem.

Clearly the McConaghy-Longuski-Byrnes nPr formula is just pPr in the above, inversely n-0-1-i. Here they use i as the ith intersection of all the Lambert curves against the line of time-o'-flight, which time for Buzz was 15/7 start-planet (Earth) years. So for Mars: 1-0-1-6 is 1L1, the Aldrin. 1-0-1-5 would have been 1S1, -4 1L2, -2 1L3 and Lambert has no 1P4+. S is odd and L, even; i_MAX = 2r_MAX + 1. 1-0-1-7 is 1U0, for what that is worth.

For 4Pr, r taps out at 9. Again we count up: 4S8 for 4-0-1-1, and 4L1 will be 4-0-1-16. McConaghy suggested 4S6 (4-0-1-5) and 4S5 (4-0-1-7). Russell and Ocampo like any of that a good deal less than McConaghy did; instead, that duo offer 4-0-3-7. At the 6Pr level: 6-0-1-23, 6-0-1-25, 6-0-1-27, 6-0-1-29 are 6S9, 6S8, 6S7, 6S6 respectively. I extrapolate -1 would be 6S20 so, Lambert solutions start comin' hard-n'-fast up here. Another point is that when h>0, i isn't bounded by p even that much.

Venus-Earth dual-synod solutions count up from 2S76 as 2-0-1-1. My 2L4 is, then, 2-0-1-6.

OOPSIE 3/23: On further investigation, 2S7 has no solution; 2S6 was the 2-0-1-1.

Compartments

Last month this site pondered spinning molten power for the Tory IV.

The idea was to keep the heat evenly distributed around the jet even if the power-supply was superheated such that it would liquify, thus sinking to the bottom in a constantly-moving aircraft. My idea (which, yea, I stole) was to rotate the metal. But that spinning fan will steal energy from the jet. It occurs to me tonight that I could mitigate the rotation if I compartmentalised the heated metals. Say, into thirds.

Now I have a new problem. Each compartment's wall needs not to melt, itself. So the compartments are probably some dense ceramic. That will, I think, keep the neutrons and all the other stuff from inter-reacting across compartments. It will depend on how fast the neutrons are going, I'm sure; but if a neutron is too fast for a ceramic wall it's also too fast for the next compartment over. Critical mass no longer critical, no longer melted.

I wasn't on the Tory II (or III) team so I don't know what they had in mind for the metals. But I can guess: PLUTOnium (239). They wanted lower critical-masses, and that's 10 kg. Curium, at 7 kg, is better but, I think, pricier.

Californium-252 (2.73 kg) might be the best substance to ensure liquid heat at the same time I've assigned it into compartments to keep it distributed.

UPDATE 7/27: Yeah, I know, this whole idea was completely dumb; thought-experiments usually are. Good thing this is a blog and not a university thesis. Tho': now I am pondering vapour Pluto...

Twin tanks

It strikes me that any transport that leaves point A and arrives at B should have two tanks of propellant: one for A and the other for B. This isn't really new; we're already looking at re-purposing old boosters in LEO.

Even the flip-n-burn option might do this. Disconnect old tank; rotate engine and nozzle exactly π radians; attach new tank.

As for what the crew does with the old tank, that will depend on a few things. How much volume of propellant did it have? Was the propellant toxic (probably not terribly, it's likely just oxygen / hydrogen maybe methane)? If it was pumping to a radioactive chamber, how close were the two and how energetic?

I expect NERVA-to-transfer-orbit, as a general rule, like how those old "Hohmann" Venus missions tended to be rather shorter than the idealised 146 days. Also the tanks take in some rads and protons from the Sun and cosmic-rays. Nobody is wasting shielding on propellant tanks.

So the used tanks get used for the rubbish stored up to the tank switchover, where "rubbish" is "solids what doesn't get recycled and doesn't go outside". Broken plastics, unsalvageable clothes. Maybe someone can recycle them at the destination.

Milli-g flip-n-burn

Let's talk Nyrath Nomograms. These are slide-rule type charts where you stick a pin in your [Tsiolkovsky] mission, whip out your ruler, and estimate what magnitude of power you need to lower your mass ratio.

For instance Princeton was promising I_sp 50,000 (N/N)s, if you could come up with 10 MW energy. I thought if I stuck around Venus' halo and harvested hydrogen, I could do that. Fatima Ebrahimi's not on Chung's chart but you can put 'er up on the right above VASIMR.

The slight issue I saw (and why I stuck the poor lady with station-keeping) is that specific-impulse isn't everything. First off (more so for Ebrahimi) where're those megawatts coming from. You often need thrust, too - dependent on cargo. And apparent delta-V isn't everything if we can do a Crazy Hermann. All this stuff I see about liftoff and, for that matter, Hohmann - or any other transfer mission - has that Barrier To Entry, which is thrust / weight / mass. If your thrust is only good enough to get your delta-V to Hohmann at the moment you need to get out, you've gained nothing. Ebrahimi's piddling 100 N will just hose down your lab with propellant.

Here is another option, for those hoping to economise on thrust: the flip-n-burn, which the nerds call "brachistochrone". Suppose I wanted a 0.098 ms^-2 acceleration then deceleration. That is microgravity which I'd not ask of any crewmen - but it may be good for cargo. Also I am in space so I'm unworried about irradiating Canada.

Hence the interest in UltraSafe's low-grade solid NTR. Say the AEC lets us use NTR-liquid in space at what, 15 km/s. Pity: for 0.098 ms^-2 its mass ratio is horrible. NTR-liquid turns out not to work either. You're just lugging a radioactive propellant tank from Earth to Venus (but quickly!).

I think, though, the chart also implies 9.8 millimeters per square-second. Why isn't it there? Partly because the Sun interferes in the mm s^-2 range, 6 of these near Earth. On any transfer orbit, apo' and peri', acceleration orthogonal to direction is highest, more so on peri'; and the speed is least. That much, UltraSafe can give us... to outward planets like Mars, anyway. That much and more, Princeton's other fusion-reaction team can certainly give us.

Breathe in, breathe out

In global-warming news, focus has moved to our planet's lungs - the oceans.

The Zealandia Bank is implicated in the absorption and then emission of carbon. New Zealand's "alps" are much like Ethiopia's, in that respect.

The oceans are supposed to go peak CFC in 2075, emitting them in 2130. We're also supposed to have sharper winter/summer divisions.

I'd ask if there be some proxy for ozone in southern-hemisphere strata: old Patagon pine or Antarctic ice-cores. Extracting all that from the Pleistocene may be difficult. But they're doing it for Grønland. Maybe the Greenlanders can tell us about how the seasons worked during the Eemian behind "warmer".

Solving a water theft

The Expanse (which I'm watching again, in light of what I've learnt last year) posits an Earth with more water than it needs, with New York under seawalls; whilst her U.N. has stripped the asteroid Ceres of the best of her water. I'd like some idea why.

I accept that Earth doesn't use (much) of its hydrogen to boost shuttles (mainly) to Luna - because a fusion drive, especially on this precious marble, will be commanded VERY light on neutron emissions. That means: we're burning only deuterium (and helium-3). That means: we get to keep our protonic hydrogen. Maybe Earth demands every now and again that someone drop an ice cube into the sea like Futurama? whuuut.

I suppose chemical hydrogen propellant might still be in use, but the first stage mostly burns that near the surface where it just joins the clouds. Anyway, the U.N. took none of Ceres' water for Earth.

Out in the Belt: wouldn't runaway water be easier to get back, beyond 2.5 AU? I doubt the fusion drives are burning away their protons, either. Chemical propellant is possible in small bounces from place to place, or if they really wanna Hohmann their way from rock to rock - but the big missions are flip-n'-burn brachie trajectories, that is with that fusion engine again.

Propose that the looters of Ceres' easiest-extracted water, were the [Earth-run] mines at Vesta and Psyche (not Phoebe).

Martian deuterium

On topic of the well-walla water, when planets lose gas they tend to lose the lighter stuff first. We've seen over Venus that they have a lot more deuterium than we got - proportionate to lone protons. So: Martian deuterium. Turns out they're more like us than like Venus.

The scientists think the protons have hydrated the rocks and become clays.

Green land

"Greenland" isn't very green today. But it used to be. It seems that during interglacials, sometimes it melts and attracts a pine taiga.

The warning is that it might melt again.

If it all melts, that is well within bounds of how the Pleistocene works. I am, further, unsure that the sea levels will rise to a significant extent. (So are the Clintons, with all the beachfront they own.) Warmer Atlantic often translates to a wetter Sahara which, by definition, locks water inland.

FLIPSIDE 3/17: On the flip side what Greenland is, 30s kBC Ethiopia was and then Te Waipounamu (unnamed, then).

Potočani's class war

I would have been more excited about Potočani three years ago when I was reading about 4200 BC "Old Europe" and the various feminist interpretations of same. But anyway. Anthro Twitter and what's left of the anthro blogosphere is on it soooo....

Potočani is a site now in Croatia that overlooks the Pannonian Plain. So, Balkans. 4200 BC is before The Rise Of The Sons Of Aryas; their fathers were G2, I2, C-V20 and not R1a/b (nor E). So: Lasinja, Copper-Age. These servants of the Goddess got into a fight with other servants of the Goddess and, well, created those remains.

It was a massacre. The authors don't say genocide: only 41 victims are registered (so far) and they're only distantly (but mutually) related (they estimate 20,100–75,600 breeders). Also there was no "population turnover", such as found in the British Isles in the Bell Beaker wake.

One difference: generally consuming more animal products than their neighbors. They also had better teeth - but there was scurvy. So their diet was more meat, less milled grain. I don't find them to have been particularly wealthy.

Farmers against herders. First they shut off the herders' vitamin C. Then came the murder.

The canon within Paul's canon

The New Testament includes three documents called "Pastorals", 1-2 Timothy and Titus. They present themselves as from the Apostle Paul. Nineteenth-century German and English textual-critics ruled them out, for various reasons (like, why isn't Ignatius citing them in his own eminently pastoral letters?) but usually stylistic. Bart Ehrman has been offering some of these findings to the public. They might not all be good reasons. [h/t Tapscott.]

Here is a decent masters-thesis sort of status-quaestionis.

As these things go, my faith in Christ is based on... Christ, as presented by the Tradition. I treat the Pastorals as "sus". At the same time my faith does not depend on the Pastorals, one lacking in such faith must be warned not to base that unbelief on the absence of the Pastorals.

One factor here I did not know until now is that the saint Polycarp, correspondent with Ignatius, quotes Paul as teaching content with some 1 Timothy 6 parallels in it. William of Ockham, famously not a credulous sort with respect to Christianity, would have to admit that his Razor should be applied here. If Polycarp did not quote from 1 Timothy then ... where's the other Pauline papyrus?

Propose here that there was a Pauline tradition that brought the Pastorals to Polycarp. Our Youtuber linked above noted the Didache, also, paralleling the Pastorals. This is the sort of edifying material that would have circulated around the same sorts of Christian. We can throw in Hermas and 2 Clement.

That would explain why P46 didn't bother with the Pastorals: the editor may have accepted that triad as authentic (like Ephesians) but not fit for P46. There were plenty of booklets containing just the Gospels or (in Judaism) just the Torah; you can buy such excerpts to this very day. In the olden times they didn't have paper, and writing-tech was expensive. This collection goes out to this group of theologians; that collection to those Didache and Hermas lads. It was only much later that the Church cobbled them all together and shut out Didache and Hermas (and, note, if you're Catholic, they never wholly did shut out Didache).

If Marcion and the Gnostics didn't accept the Pastorals at all, that is - in this line of thought - because they were heretics who didn't understand.

Closest approach

With a 109° angle and V_∞ 3864.1549 m/s, the 2L4 "closest approach" to Venus is 0.2290354646802355 / (3864.1549 * 3864.1549) * 3.24859E14. That is 4983 km. It's... better than Aldrin to Mars, at 4640 km over - rather into - Earth. Still, our girl has a 6050 km radius herself. Unless you are piloting the Pegasus from TNG I'd really not advise this. If it wasn't a ghost ship before . . .

Yeah, I knew it was going to be a "Powered Cycler", to be polite; nonballistic. So let's look at doi 10.2514/3.25519 to see what Aldrin, Byrnes, and Longuski did about it in 1993; back before S1L1 was a twinkle in the latter two's eyes.

For that 1L1 cycler, a relatively small maneuver of about 230 m/s performed at aphelion of the cycler orbit can rotate the argument of periapsis by an amount sufficient to make the flyby of Earth occur at 1000 km above the surface. What the three did was to look at the 15 (Earth) year cycle, which is 7 Mars years, to see what would happen to v_∞ and closest-approach both over at Earth and Mars on each flyby.

For us that would be 13 Venus years... 8 Earth. In our case 2L4 aphelion is, at first turn, where it is closest to Earth. It then hits aphelion thrice more before its journey down to perihelion, and up to Venus.

So what we do, I guess, is list all the maneuvres for a Synod A outbound in its four revolutions. Then the next four, and so on, until twenty are complete (equivalent to 20 Hohmann orbits: 10 synods, 16 Earth years &c.). Synod B likewise. Repeat for inbound.

Crazy Hermann

Let's work with vinf. I found a paper on that (pdf) last week.

My highest stable orbit over Venus is 536412 km. For Earth-serving sats I'll actually be orbiting a bit lower, say 530567 km (and 782.5 m/s). Per Hop David, v_∞ to Hohmann Earthbound is 2706.7 m/s. To 2L4 it's 3864 m/s and, unlike Hohmann, it's not ballistic. With 2L4, I'm needing to blow off some steam no matter what. Can I blow off... LESS steam?

Hermann Oberth has a delta-V for this. If I do a big reverse thrust against my orbit, I fall down to say 950 km altitude. That is semimajor 7000000 m. I then use that kinetic energy and another thrust to shoot off whitherever.

Probably best, for Microsoft, if we separate its concerns. Let X = (v_∞/v₀)²; let Y = 2 * r₀/r_in.

For Hohmann: X = 11.965; for that 530567 km semimajor / 950 km altitude ratio, Y = 151.59. So, 782.5 * (1 + Math.Sqrt(11.965 + 151.59) - Math.Sqrt(2 + 151.59)) ends up 1092 m/s.

If I wasn't doing pulsed thrust, Y is just 2. I'd have this much delta-V to make up: 782.5 * ( Math.Sqrt(2 + 11.965) - 1) = 2141.7 m/s. I'm Crazy Hermann and our savings are iiinsaaaane!

Off to 2L4 (again, 3864 m/s), my delta-V on an ion drive would be 3236.8 m/s. Crazy Hermann does even better: 1465 m/s. Theodore Edelbaum in 1959 made tell of a three-pulser, first jumping out to like 795850 km before that big turn planetward - which smacks of the biëlliptic. But let's not get too crazy just yet.

Note that although I've used less total energy, I've told my ship engineers never to mind about a high-impulse rocket, but to use a high-thrust one. And 1092 m/s is a lot of delta-V for thrust. You should see what it's like to use the solar well for Oberth, starting from Earth v₀ = 30000 and, of course, constraining r_in so's you don't get a bad tan (Y ≤ 10). Nobody's ever tried that UPDATE 10/8/22 ...yet.

But anyway - back to planetary orbits. I've also careened my runaway sat down every damn orbit that planet's other sats are using. That might not matter for the wide-period sats, each likely angled away and on some other angle on its orbit. The inner sats, for Venus, I want for scooping oxygen and firing it off to my higher sats, or for catching tourists off Landisopolis - they're important and there will be a crowd of them. Even if I convince their operators I'm not going to hit one, they're still going to ban me from using the Orion down there. Just like... over Earth! I don't recall many satops using Oberth locally, either.

THRUST 5/17/21: Chemical detonations in lieu of Boom Boom.

The Venus / STL1 paper

I figured I'd done enough work on the cycler between Venus and Sol/Terra L1 that I'd write a formal paper on it.

My paper is on the same model as McConaghy, Longuski, and Byrnes' "Analysis of a Broad Class of Earth-Mars Cycler Trajectories" 2002 and, in fact, part of my paper's job is to follow that paper's method to duplicate its results for the Aldrin "1L1". My paper dilates a little more than theirs on some of the assumptions they'd left unstated.

I couldn't quite follow them on S1L1, which is the ballistic trajectory superior to Aldrin's, so I don't moot a "S1L3" or whatever. For what I do have, which is 2L4, I come up with a year-1999 launch date, whence anyone can count forward to track launch days for the future.

Molten world

Gliese 1132, 41 light years away, has two planets of which we know. The innermost one transits with respect to Earth line-of-sight. Now, there's news of its atmosphere.

The planet is on an ellipse so endures tides... in its rock. Its temperature is conjectured 256 C.

The atmo is hydrogen, hydrogen cyanide, methane, and smog. They think it used to be a Neptune but, being close to the star, lost its original atmosphere both outward and inward. That hydrogen is thought to be from its original atmosphere, sucked into the magma and now being outgassed again.

The gravity and the heat of its interior are such that it likely doesn't have mountains. Cracked plains and lava-pools, here. If this was attainable from the game Starflight it would be a Molten World.

Lovely place. All the worst features of Neptune, Titan, Io, and Venus.

UPDATE 3/15: Edwin Kite and Laura Schaefer, “Water on hot rocky exoplanets”, Astrophysical Journal Letters, (11 March 2021).

The queen of Tarshish

Classical Antiquity believed that Tartessos, from the Pillars of Hercules over to the Algarve, was the most ancient European society - older than Greece herself. The Bible mentions a far-west "Tarshish" which most scholars assume is the same. This culture never quite made it to the Punic Age let alone to the Romans.

I was intrigued by this because Iron Age Tarshish didn't really look all that special in context. I mean, sure: they had monumental literacy (in a language-isolate), wealth, trade. But we get the same Early Iron vibe from the Philistines. Even the Etruscans passed down that linen wrap with all that magickal silliness.

So now we find, not from the southwest of Spain, but its southeast in Murcia: 2200-1550 BC grave goods. Comparing volcanoes - the culture spans Avellino and may even survive Thera.

Third from the top Roberto Risch from Barcelona is head of this dig, I'm guessing a German-ancestral Jew, maybe by way of the Americas. Cristina Rihuete Herrada is another headsperson on the paper.

Interesting title on this one - Bronze age burial site in Spain suggests women were among rulers. Read on and Risch says shortly after the woman dies, the whole settlement is burned down. Before we let /pol/ handle this one (or /r9k/) . . .

By the way 1550 BC isn't EBA, it's MBA even LBA. Bio-females could be excellent kings [male gender] in the Middle Bronze Age. Pharaoh Hatshepsut might have been the best ruler Egypt ever had. As for the Murcian Queen, I think this one - like Isabella - ruled Spain as a woman. But she was no Hatshepshut.

The likeliest (final) cause of death was tuberculosis. If a plague caused a succession crisis, sometimes a monarchy will pick what they got. And if she dies too, well... they're basically screwed. But she was ailing before that. She was born a mutant with a bad back and a short thumb. Looks like an inbred. She had a child: they found that infant's remains too. It all looks like the last days of Sasanian Iran. Or the last Eighteenth Dynasty princes in Egypt.

As for what came next, well, it's not Sea People Time yet, but there could have been some Lusitanians and Celts roaming the place, because that's what the Carthaginians will be seeing in the Age Of Iron. Did the Murcian survivors pack up and move west?

Greg Abbott: Andrew Cuomo with a cowboy hat

The governor of Texas, one Greg Abbott, recently stuck his citizens with a five figure power bill. Apiece.

There are various excuses for that: oh, we had to choose between power-using citizens and the urban areas. Oh these are Variable Plans!

Unless there's a freeze or something. Then, by Variable Plan, the power company can boost your rate to whatever. You gambled - you lost! Except that it is poor people "gambling" just to eke out that extra bit to pay off the creditors. This is exactly the stupidity which got us Enron, and then the garbage variable-mortgages which sparked 2008.

To all that I say: the purpose of the Crown is to guard the Wall against the Others. There are plenty of bilkers out there, and some work in companies with Diversity Departments. (I know Shell had one.) Abbott has one job and it is to protect his citizens from the bilkers.

To the libertarians out there - the whole mess started because, oh, we had to choose between nuclear power (or natural gas), and being Green. So many photo-ops where Abbott pandered to Texas Monthly and the rest of The Great And Good over how awesome those turbines were gonna be.

Another little fatwa Abbott let loose was that Texans shouldn't use Gab. They have antiSemites on there, you see. Just to really make that point Abbott made sure to have the Israeli flag cover the US flag, with the Texas flag off to its right (facing the podium). There are, of course, plenty of antiSemites on Twitter and indeed right here on Blogger. Few of these voted Trump last year (which I did and, yes, I am legally Jewish). But hey. Alt Right!!

This man is not your hero for freeedommm.

But don't you worry, Tejanos and Tejanas: Abbott has got your back at least against masks. The capital city Austin (which as noted doesn't always get it right statewide) has this strange notion that Texas hasn't done vaccinating all those who need it, yet; they want to stave off lockdowns in their own city. You know, the lockdowns that only really work if you're on an island? If you can't do lockdowns you need to do masking (pdf). But srrrvatives think masks are Satanic and mooooslim.

What Abbott and that (other) murderer Cuomo have in common is that they don't care. There is a solid inverse correlation between general patriotism - which is just love of your fellow citizen - and CoVID. Cuomo isn't a real New Yorker and - as has just been proven - Abbott is no loyal American, and might not even be a Texan. As long as they get to stay in a mansion and have you pay their electric-bill, they're good.

HE GOT HIS MST 6:35 PM: Battle Swarm Blog cares a lot. Just not about you - Also, I got my electric bill for February and…it’s a totally normal February electric bill. It helps to have natural gas heat…

Keplerian number-theory

If you are of a mathematical bent, the first thing you'll likely notice about the Earth-Venus Hohmann orbit is that it looks, also, resonant with the already-near-resonant Earth:Venus orbits. Namely, 8:13 with 10 shuttling in between. I wonder what other orbital resonances a:c where a and c are natural numbers (or near-enough) can have natural Hohmann b between them.

At stake here is how we can float two satellites in a high orbit and a low orbit, with some service to both - without stopping. Ballistic cyclers, baby! Not every satellite-pair lets you have one. Earth/Mars doesn't - unless you're like McConaghy and Longuski, a genius (S1L1).

There are a couple of equations we're dealing with. One is Bronze Age aphelion-to-perihelion. That's from the highest height at one end (say, Earth); to its other height at its other end, opposite (Venus). Add these values together and that is semi-major axis, doubled. Diameter if a circle which obviously Hohmann is not. Major Axis, perhaps.

The other equation is Kepler's Ratio of time² and semimajor³. We are all sharing the same centre of orbit and Newton's gravitational constant - so this ratio is unity. Time will be based on the innermost body in orbit, here Venus. So Earth will be 8/13 and Hohmann, 10/13, after a single Venus year.

What I get are (8/13)^-2/3 + 1 against 2 * (10/13)^-2/3. In C#: 0.25 * Math.Pow(169, 1.0/3) - 2 * Math.Pow(1.69, 1.0/3) + 1. This is -8.3E-05.

I was doing double-precision, not 32-bit "float". This is not Microsoft failing to do a zero. Too bad for number-theorists: if Kepler does have a Ratio to beat out Pythagoras' 3-4-5, 8-10-13 ain't it. Too bad for orbital planners also. But orbital planners between Venus and Earth were already having to put up with those orbits not being perfect 8:13. They were already pondering solar sails (and, in my case, different cyclers). An error below the myriadth range is zero enough, for them.

To be looked for: natural {a,b,c} such that a<b<c and (c/a)^2/3 + 1 - 2 * (c/b)^2/3 between (-0.0001 , 0.0001). If anyone can surpass {8, 10, 13}, tell me.

Low temperature capacitor

This release, in Fahrenheit, is suggesting how to store energy when it is cold. They are looking at Mars, to reduce rover heating (and energy) requirements at night.

DOI 10.1021/acs.nanolett.0c04780 has an abstract that gives the Centigrade. But I prefer Kelvin: 200 K.

As anywhere else goes, I am unsure. Most space craft are rarely in shade for long, so don't need much in capacitance anyway. Statites in umbra (like Venus') will get this low; so would craft beyond that 2.5 AU snowline (e.g. Ceres).

However any craft in vacuum is also a candidate for nuclear power, whose energy becomes heat by thermodynamics. In vacuum is no atmosphere to carry heat away: see all those radiators on the Space Station? And don't talk to me about wormholes.

As for the (few) atmospheric worlds near here, Titan (which really is not near here) might still be too cold at 90 K. I more wonder about high-atmo floaters on Venus' night side. Also the Moon: power storage for rovers on night-missions.

Ludicrous speed

The Well of Souls is op'ed and all the devils are... being posted about, here.

Our first bit of silly comes from Göttingen where Dr Lentz is talking "solitons". Apparently with conventional sources of energy (as in: not Alcubierre's negative mass) we can create a Warp Bubble, keeping the ship aging in normal time as it carries on to Alpha Centauri. The "twin paradox" is no longer in place. The press-release is less clear about the causality paradox. And the conventional mass we need to burn is a red dwarf star hundreds of times Jupiter mass. Oooookay then. UPDATE 3/31: Martire-Bobrick.

Then there is this from Portugal: traversible wormholes. They are not very big wormholes... yet. The Portuguese think they can use them to deliver FTL messages. Also (I'd add) one might use such to drain heat from a ship toward, well, nowhere and thereby create a cloaking-device. But again I ask - what about causality.

I don't wish to waste more time on all this than I have to, but maybe some science fiction authors might get a kick out of it, if they are not very good authors.

NAH IT'S SHITE 1/16/22: Give it up, dude.

Microgravity crops

On the way Arizona (not Thanga) posted another note on microgravity crops. THAT, I'll take seriously.

I expect us monkeys will be living on the outer edge of the tin cans. Suppose, though, our cans aren't the rim of a wheel; suppose they're a big cylinder. We'll have lower gravity hubward. Be nice to use the space for something since we're not living there. I mean other than the sort of fun monkeys might get up to in low gravity for ten minutes at a time . . .

Also what if we have tied these spinning habitats onto an asteroid. Maybe the asteroid's surface could be purposed for farming - again, because we're not living there.

Food in microgravity (or an asteroid's milligravity) also may get bacteria.

Loony

Jekan Thanga has got his Arizona uni into space science news twice this week. Mostly he's looking into the Moon. One article has something on prospecting for water, inoffensive enough.

In the meantime Thanga wants to use the lava-tunnels as a DNA museum for species from Earth. Powered by solar. Not considering that solar panels degrade especially when exposed to micrometeors on the Lunar surface.

Sigh.

Doctors of the other two churches

Jacob Tate over at OnePeterFive is reminding us Latins of Thomas Aquinas. I am considering if the non-Chalcedonians own anyone close to him.

To start with the Miaphysites, I shall expand the net to the early Maronites also. This, then, starts with Cyril of Alexandria (not one of us!). The two councils of Ephesus were a great victory for that side. Following the Chalcedon reaction, officially Severus and Jacob bar Addai are credited with founding the independent Ephesian church. Among the west-Syrians (using Andrew Palmer's hyphen): Bar Salibi, Michael the Syrian, Bar Hebraeus. Jacob of Edessa's correspondence amounts to an excellent practical guide for a Christianity under alien rule. And there was Dionysius of Tel Mahré among the historians.

I am less familiar with the rest, but the Coptic tradition can certainly look to Severus ibn al-Muqaffa', and of course the Copts are persistent to the present (writing mostly in English). The Tawahedo in Ethiopia was heroic at least to preserve this line of work. Then there's the Caucasus, although over the Middle Ages they have inclined to the Greeks and then to the Russians.

Over the centuries, then, the Miaphysites mustered a formidable intellectual defence against our Church and then against Islam.

Looking at the Church of the East, I cannot think of as many great names offhand. Here it should start with the Antiochene tradition, Theodore of Mopsuestia (less so Nestorius himself); Aphrahat, perhaps, among the para-Nicenes. The "catholicoi" popes Babai the Great, Isho'yahb III, and Timothy II produced impressive literatures. The school of Nisibin was also productive, partly as countervail. Among their historians were Elias bar Shenaye and all the contributors to Siʿrt.

The Orient suffered by contrast with the nearest East. This is not entirely their fault: there was always something of an iron-curtain keeping their literature even from crossing the Euphrates, much less into Greek and Latin. Over there, first the Iranians and then the Muslims sporadically suppressed their libraries. And the Portuguese did no favours for the native Christianity in India.

Also, though, I find the Eastern Church to be riven with schism of its own. Isho'yahb III exerted much more energy against heretics and the breakaway provinces than he did against (pre?-)Islam right under his nose. Other churchmen had Henana's Origenism with which to deal, and various strange ideas seeping out of Nisibin.

The Eastern Church had trouble even defining what it was, beyond "not Ephesian" and, later, "not Islamic". Should they accept a subordinative Christology, like Arius and their own Aphrahat? (Once the Muslims came along, that proposal was an embarrassment.) To revive Origen, like Henana? (Babai killed this one dead.) What of Bar Sauma's "Baptist Convention" theory of a seminary-run Church? Above all, what to make of Chalcedon?

Where do we put the tethers?

2L4 is not a Hohmann free-return cycler so needs to adjust its angle, by 108°.

That 2L4's aphelion rose as the angle decreased means the angle spans that line between the Sun, SVL1, Venus, and SVL2. On its first trip, it starts like SVL1 ahead of Venus heading to perihelion. On return its angle must return to that first angle - to bend that 108°, forward. (Earth's L1 is forward, to which the cycler must catch up.)

Cycler perihelion is 1,586,931,492 km toward the Sun, usually. Given Venus' own 0.007 eccentricity, the cycler always runs by that one's own L1 halo (if aimed right). Also the cycler starts angled to perihelion. SVL1 is a fine place to park the cycler before it starts on its way. Or, park a tether up there so a craft in orbit or in Hohmann can access it, and become that cycler.

Between any L1 and L2 there's a planet. We'd like to use the planet to boost us and, hey, that's where we're reloading outbound cargo.

After its full orbit - hitting a moving target, understand - the angle is called "gamma" (γ) and is -3.57° where 0° is the direction of Venus' orbit. We expect that low value, so close to perihelion: note, it's just Math.Acos(Vector3.Dot( Vector3.Normalize( velocities.Vf) , r2)) * 180 / Math.PI - 90.

That low gamma means that either Libration Point's tether, once initially used, is not of use twice. Stations at either might be available to focus more Solar radiation at the cycler's sails.

Vinf

I've been talking about v_inf, or v_∞, or hyperbolic excess velocity despite not knowing what the heck I've been talking about.

I admit I still don't. But I did find something I can understand: black-box equations.

Erik Francis explains it all: from any orbit, which goes at v_cir velocity, you want into some other orbit... Hohmann, probably; then off-Hohmann. What's the delta-V? And no, you don't get just to subtract one from the other; we're doing astrophysics here. We're not sailing around interstellar space. We're in a solar system, probably a planetary system. We're locked in an orbit.

Where escape-velocity is the velocity just to get off that first orbit (if angled directly away), you're in orbit - and if it's a circular orbit, you are decidedly angled 90° from that. v_inf looks at other angles - like the angle to get to Hohmann, or to 2L4.

Francis says: √(v_inf² + v_esc²) - v_cir. That assumes you don't have the kick-ass thrust needed for an Oberth manoeuvre.

Want to see the GJ 876 planets?

Robert Zubrin cannot be accused of thinking small. With the hat-tip to Reynolds, now he has a telescope plan. This one would knock down the (kilo)grams needed to do space astronomy.

As for other factors, Teh Zoob seems to be competing against the Webb. This isn't a scanner; it's there to be pointed at a specific location, and to send data home. Probably not the Planet Nine solution.

Imagine, though: several Webb-like space telescopes that Rocket Lab (say) may send up into space for the same cost as the one, all working in tandem. That could be the Planet Nine scanner.

Thinking bigger (as Zubrin would) I don't know if he perused Stross but, yes, the Big Dumb Booster allows for that weight to be scaled right back up again, without risking astronauts' lives. This boils off some of the commenters' cold water on the lower-radius telescope options; raising the radius would correct the errors. So yes: I am recommending that SpaceX start here, rather than with human tourists.

A 'scope of this scale would be... impressive. Webb has only been rated for Gliese 832 b and for transits. For Zubrin's proposal, noted in the comments is Epsilon Eridani, whose planets are presently visible as... pixels. This telescope might even be able to see, say, the GJ 876 system being only 15 light years away as it is. Not to mention Alpha Centauri. Or such planets right here as we seem to be done sending probes at, namely Uranus and Neptune.

The 'scope does require a boost to pull the parabola back. That implies (to Zubrin) several sorts of mission: a 'scope spun on a tether, a propellant-limited mission, and a sail. (I'd add a statite high in Venus umbra.) For the propellant mission he'd have this thing out 3.1 AU from here: between Ceres and Hilda, more like 2530 Shipka. A mission with a sail means there is solar wind, which can interfere with the results; not, though, for results outside the Sun's electromagnetic range, as Zubrin notes for radio.

When to launch 2L4

Today we use the Hop David spreadsheet, to get Cycler 2L4's launch window after Year 2000.

Probably the 2004 or 2012 transits of Venus would have been better but on a 243 Julian year scale, as you will see, Why Two-Kays is close enough. For more precision in later synods the Manifold Thesis had a decent "brute force" writeup on how to estimate departure moments. Overall this blog shall leave the Pork Chop Plots to the unparalleled experts in bacon consumption, namely NASA.

G-d and His Spreadsheet deliver B30, δW; and B32, δAngle @J2000... Themself. Since I'm going Venus outbound B30 is -225.1878256° and B32 is -81.5153°. (Earth-to-Venus, these are positive.) Our job is to find B24.

For me that starts with B20, the travel-time in sidereal years of the destination (Earth). We just got that: 159 / 365.25636. B22 tells us that in degrees: 156.5. B24 just orients that in the 180° semicircle for 23.5° angle at launch window.

The 2000 date of departure comes from adding 2000 to that fraction of Earth sidereal.

Cycler 2L4 at Earth's L1

I spent the last 24 hours (sleep and work permitting) learning what mine own code could do. First thing I had to figure out was that left way / right way didn't always correspond with the short way / long way... in general, fewer synods mean the longer periods.

Another thing: I gave up finding what equation could get Aldrin's ass to Mars. Instead I just iterated from initial-velocity to the distance I wanted, using Newton's law of gravitational acceleration. This got me the time it took and the position and velocity vectors. Although that's the best algorithm we're ever likely to find, Microsoft's System.Numerics stuck me with 23-bit decimal places for accuracy. I could not improve on δT = a millionth of the inner planet's year. A half-minute here on Earth.

Soooo: from Venus 2L4's time to aphelion will be 159 days. I wasn't expecting a large velocity at the end given it is aphelion.

Where aphelion falls short, Longuski and McConaghy were subtracting planet speed from cycler aphelion speed. Why, I don't know - probably because of Mars' ellipse, so they quit caring. Venus has no ellipse (pretty much), and Earth's isn't a problem. For circular(ish) orbits I target SPL1 velocity which, covering a shorter circumference at the same time as planet P's year, will be slower than P. V_∞ at STL1 is about 1950 m/s.

I confess une petite surprise that the 2L4 Venus-Earth time was (slightly) more than the usual Hohmann suspects and, indeed, than 5S10[-right] which is telling me 115 days (and 600 m/s V_∞ at Earth, let alone STL1...). I note it's 53.3% of the unpatched period - and, as noted, a Left Branch where Hohmann turns Right. It looks like it dips to perihelion before running to STL1. Fry-by, one might say. Better shield it.

Local news stories

Virgo's GJ 486 / Wolf 437 - 26 light-years away - has a transiting planet. 45 light-years away is LHS 3844; this one also transits, and now has delivered enough data for some Bern Uni scholars (very proud to be at Bern) to run some simulations.

Transits are generally found where the planet rides very close to the star. The closer the better. Although, not so better for any potential colonists; as noted, neither of these planets are fit for human habitation.

I admit I find difficult to comprehend the Bernais press-release for LHS 3844 b. It doesn't seem based on observations so much on simulations based on those observations. The Wolf 437 b article is much better written although I cringe a bit at its title (hot new neighbour!!).

As for Wolf 437, here I ask why it has taken so long for a transit to be noticed from here, given that it is so close, and low-mass at that (so radial spectrometry should have noted any planets' wobble). Better late than never. Time to pre-cover its data, I think.

The Venus-to-Earth 2L4 Cycler

Now we got an approximation to a viable Venus-Earth, more exactly Venus-STL1, let's fine-tune it. Or at least mark where someone else can; I didn't get that chance today.

First, that 72 degree angle per synod is, I think, a bit less in practice. Tweaking that (but keeping the time-of-flight) the V_∞ contributing to delta-V is (usually) closer 3864 km/s. Bit less than 3876.6 km/s. Angle's down to 108° and aphelion up but still around 0.979 AU. This doesn't take into account inclination, unfortunately usually high, so as to take away all our gainz here.

To get back to Venus - making up for the lost angles - the cycler got 1168 days all within 1 AU of the Sun, so sails should do it. As compared with Hop David's 5S10 Hohmann cycler, 2L4 gets more daylight overall, but it also spends a higher fraction of its time fully laden. Maybe twice as much: he's 1/20, I'm a bit over 1/8.

As to where this km/s and 108° can be shifted: when we get to Venus, Oberth's dive into low Venus will help; and for the rest I'm looking at that tether.

TAKING THE L 3/4: Its orbit's a long-period.

Lambert, cont'd

It turned out my maths were incomplete yesterday. I blame Longuski and McConaghy for not Showing Their Work. But with Aldrin's help I got "Vinf" and the angle at the beginning. Also of course we need trajectories that get close to Earth. TL;DR - the Venus / Earth cyclers are possible but (besides Hohmann 5S10) infeasible. With one intriguing exception, the 2L4.

There are no Right cyclers below 5S10, likewise 1P3+ and 2P7+ don't exist; and my calculator wasn't good for *P5 because it kept using Venus' own orbit for that (which doesn't intersect Earth's, duh). For the others, the best I got was 2L4 "left branch". Semimajor 0.841 earth AU; unpatched period 282 days (right branch was 244 - 2S4 - but it's terrible). Eccentricity 0.163; aphelion 0.979 AU. V_∞ at Venus 3876.6 m/s. Turn angle at Venus 109 degrees. (Compare 5S10 rightbranch: 2705 m/s with no estimated turn angle.) All this assumes planar inclination and that the synods work like clocks. UPDATE 3/3: Fixed the clocks.

There should be a reverse cycler that gets from Earth to Venus about the same time. Then the thing goes around by itself until its two synods are up - bit more than three Earth years - and it is at Venus again. Also (as Hop David on the 5S10) since it is a 2P*, there will be two of these things on the move, so the other one can be boarded on the other synod.

Here's the bad news: the turn angles were frankly prohibitive for all the trajectories I looked at. For that I got none to blame but Lucifer his own dark self. The Venus / Earth Pentagram means the angles are in fifths rather than in Martian sevenths. Baseline 72 degrees, not 51.

Earth's perihelion is 0.98329 AU although, yes, the mutual ecliptic angles are a pain. In the best years of the 243 Earth/Venus cycle, I expect 2L4 will enter STL1 halo centred 0.0098 AU inward of that. There she can use the manifold for some deltaV help. But she can never use Earth's well directly and unassisted. I suppose sails are up on whatever revolutions are made after Earth.

Lambert 1, 2, 3, 4

Last Friday night (properly, Saturday morn) we looked at Lambert problems for the 13/5 Earth synod in Venus years. Since here (unlike Mars) we get a Hohmann at metonic n=5, which is awesome, I am interested in the nonideal solutions where n is 1, 2, 3, or 4. These are such Earth trajectories as might return to Venus before the metonic runs out. Maybe the Earth-Venus stretch is even under the 146 day Hohmann; maybe that's the Venus-Earth stretch, it just cannot be both.

Note that with n=2, double-boarding from Venus is possible as with the Earth-Mars S1L1. This can lower delta-V: lowering my initial launch cost and, on its cycles, how far I must dip into either planet's well. For whatever best-case scenario we might lower launch-cost further from the inner planet's L2 or maybe the outer's L1.

First: uh, what's a Lambert. Johann Heinrich Lambert found in 1776 that time-of-flight aka delta-T, for a trajectory in-system, depends only on its semimajor axis, a few constants, and some vicious mathematics. Per Matthew Peet's pdf: the equation starts with Math.Sqrt(Math.Pow(a,3.0)/μ * (α-β - (Math.Sin(α) - Math.Sin(β)))). Nobody solves Lambert directly. Peet has a graph on slide 19 (of 30), or use Gooding's code. McConaghy et al. are looking to find semi-major or period (by Kepler, the one is had from th'other) such that delta-T is a synod. Best I could do was to get the velocity vectors at r1 and r2. Unfortunately that was enough for my project.

Maybe around 7:00 this morning before work (yeah, I still do that) I tested the solver for n=5 and r=5, which is the five-synod run with five returns. When I got initial velocity near identical to final velocity, I declared victory on my code.

With that, this week, I am evaluating results for the one- and two-synod periods, five revolutions right to five revs left.

V-E DAY 3/3: Well, I'd kicked this post down the road to 1 March and its posting was premature even then. I'd only got aphelion (still progress!); and r=5 was always dumb for Venus' 72°. Real victory was achieved at, like, 6:30 AM, when I wrote a C# Forms app for Earth/Mars and checked it against Longuski-McConaghy's table. And for V/E n=5 and r=10. Let it stand as a promissary note. UPDATE 3/4: promise kept - finally. Only having weeknights and 6 AM wakeups does take a toll.