egg|nomz|egg changed the topic of #kspacademia to: https://gist.github.com/pdn4kd/164b9b85435d87afbec0c3a7e69d3e6d | Dogs are cats. Spiders are cat interferometers. | Космизм сегодня! | Document well, for tomorrow you may get mauled by a ネコバス. | <UmbralRaptor> egg|nomz|egg: generally if your eyes are dewing over, that's not the weather. | <ferram4> I shall beat my problems to death with an engineer.
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<bofh>
!meow egg|zz|egg
* Qboid
meows at egg|zz|egg
<egg|zz|egg>
!pet bofh
* Qboid
pets bofh
<bofh>
today in slightly awkward: the default t-shirt printing location for logos is suddenly a lot more awkward when one has boobs.
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<egg|zz|egg>
bofh: speaking of steric hindrance, have you looked at shirts
<bofh>
ooh, good point. I'll do that on Monday, thanks for the reminder (iirc it's on the Île Saint-Louis?)
<egg|zz|egg>
there's one shop there yes
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<egg|zz|egg>
bofh: also doubledouble
<bofh>
egg|zz|egg: yep, as I mentioned I found the rough notes earlier while looking for something else, currently making sure what I was thinking actually makes sene.
<kmath>
<Goopypanther> Voyager 1 and 2 have 64kB memory and 120bps telemetry bandwidth so with the current 19 light hour communication del… https://t.co/GaVAdTX8Jr
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* UmbralRaptor
🔪 💻
<UmbralRaptor>
(I crashed the terminal with Markov chains, apparently)
<UmbralRaptor>
"yes, it is actually called "The Disturbing Function" in celestial mechanics literature"
<egg|zzz|egg>
UmbralRaptor: yeah probably same but it's more work :-p
* egg|zzz|egg
pokes spherical harmonics in the poles
<egg|zzz|egg>
UmbralRaptor: aside from the fact that it's Lambert cylindrical rather than Mollweide, can you see something off with this geopotential map, https://i.imgur.com/VjICcnM.png
<UmbralRaptor>
egg|zzz|egg: deconvolution artifacts, and eggstremely limited high latitude coverage?
<egg|zzz|egg>
UmbralRaptor: well, it's covered alright, just garbage :-p
<egg|zzz|egg>
UmbralRaptor: as for the artifacts, it only goes to degree and order 90
<egg|zzz|egg>
but, well, it turns out that P_{90, 0} is unfriendly
<kmath>
<hikari_no_yume> @whitequark oh wow I didn't realise that site had documentation on it, I'll have to use it going forward
<egg|zz|egg>
bofh: um
<egg|zz|egg>
bofh: Pnm (sin β), |β| near π/2
<egg|zz|egg>
bofh: see <egg|zzz|egg> UmbralRaptor: aside from the fact that it's Lambert cylindrical rather than Mollweide, can you see something off with this geopotential map, https://i.imgur.com/VjICcnM.png
<bofh>
egg|zz|egg: so, basically exactly what I was asking, |\theta| near \pi/2...
<egg|zz|egg>
bofh: but what is this L you speak of
<bofh>
...actually, wait, *sin*(β) instead of cos(β)?
<egg|zzz|egg>
yes
<bofh>
egg|zz|egg: me using the wrong symbol, L clearly refers to the Laguerre polynomials,
<egg|zzz|egg>
no, you want the son-in-law, not the war
<bofh>
ugh. so Pn (cos β) ~ sqrt(β/sin(β)) * J0((n+0.5)*β) (or, more accurately but nastier to implement, ~ sqrt(β/sin(β)) * (J0((n+0.5)*β) - 0.125*β*(1-(β/tan(β)/β^2)/(n+0.5))*J1((n+0.5)*β)) ). there is an analogous expression in terms of higher-order integer Bessel functions that works for Pnm(cos(β)) that I have here TeXed up, sec.
<bofh>
But for Pn (sin β) you'd have to rederive the whole asymptotic expansion, and more to the point how the heck did you get a sin β there instead of a cos β?
<egg|zzz|egg>
bofh: no but I don't necessarily want it as a function of β anyway
<egg|zzz|egg>
bofh: because this is geodesy and not QM :-p
<bofh>
egg|zzz|egg: so for x the standard impl literally just calls acos(x) to get it
<egg|zzz|egg>
bofh: I have sin β aνδ cos β йуст as easily, from cartesian coords
<bofh>
depends, oftentimes precomputing the coefficients is *slower* if you're not repeatedly evaluating the same polynomial while it's in cache.
<egg|zzz|egg>
bofh: surely you do that at compile time like a properly insane egg,
<egg|zzz|egg>
bofh: also I found half a dozen implementations in FORTRAN
<bofh>
like, same reason most code doesn't compute explicit coefficients of a Чебышёв polynomial but instead go up via Ч_{n+1}(x) = 2*x*Ч_n(x) - Ч_{n-1}(x)
<egg|zzz|egg>
bofh: very modern fortran apparently
<bofh>
also the answer to "surely you do that at compile time" is "neither FORTRAN nor C89 have templates capable of evaluating that,"
<bofh>
(actually that may be a lie but I'm not sure I want to spend time seeing if I can compute Legendre polynomial coefficients using the C preprocessor...)
<egg|zzz|egg>
bofh: I'm sure eventually FORTRAN will have generics, it seems to have some semblance of a type systems and procedures and whatnot now
<egg|zzz|egg>
bofh: hm, but doesn't going up via Ч_{n+1}(x) = 2*x*Ч_n(x) - Ч_{n-1}(x) preclude Estrinification tricks?
<kmath>
<stephentyrone> Canon’s scheme for polynomial evaluation: "do the fastest thing that satisfies the targeted error bound."
<bofh>
well yes. if you absolutely need perf you're going to convert your coefficients out from the Чебышёв basis to the polynomial basis
<bofh>
this will always be the case. but if you can't do that conversion ahead of time or at the *latest* at compile time, doing it at runtime sucks a lot.
<egg|zz|egg>
bofh: but I think the issue I'm running into is more that Pnm is badly oscillatory near 1 of either sign
<egg|zz|egg>
"at the *latest* at compile time" << at initialization time probably works too tbh
<egg|zz|egg>
elaboration time,
<egg|zz|egg>
something something Ada terminology best terminology
<bofh>
egg|zz|egg: yeah, you'll run into that regardless. the asymptotic is expressly stable there, which is why I'm giving it,
* egg|zz|egg
elaborates the polynomial
<egg|zz|egg>
(elaboration has no other effect)
<bofh>
what's initialization time,
<bofh>
is that when you call functions from your PROGRAM that initialize a global COMMON block,
<egg|zz|egg>
bofh: yes,
<egg|zz|egg>
bofh: I mean, if your thing is long-running, doing it initially on program startup might be OK
<egg|zz|egg>
bofh: e.g. if principia wasn't so fond of doing everything in the compiler, computing this as you start KSP wouldn't be much of an issue
<egg|zz|egg>
also <3 "elaboration has no other effect"
<bofh>
egg|zz|egg: I mean my main point is that you can't do this in a library, since you can't hook main or _start and constructors aren't a thing outside of C++
<egg|zz|egg>
bofh: well, your library could have a subroutine somewhere that you call to do your precomputations
<bofh>
I mean, okay, point.
<egg|zz|egg>
CALL HAVE A CUP OF COFFEE
<bofh>
merci, just grabbed another,
<bofh>
(ahh the joys of infinite VideoLAN free coffee,)
<egg|zz|egg>
bofh: but yeah, I think Pnm's oscillations near 1 are the annoyance here
<egg|zz|egg>
maybe i should go through Pnm(sqrt(1-x^2)) near 0
<bofh>
egg|zz|egg: hm, that might actually stand a chance of working... actually wait, isn't that equivalent, since the sqrt(1-x*x) near 0 converts that to something near 1...
<egg|zzz|egg>
bofh: I mean at the end of the day you're trying to evaluate the same thing
<egg|zzz|egg>
but maybe the polynomial has nicer coefficients for evaluation there
<bofh>
Hrm, wait a second, near 1 Pn(x) -> 1 for large n, so it's not near-root behaviour that's your issue. But that shouldn't be too oscillatory to cause problems there unless n is like > 100 or something (unless I'm missing something, which is likely).
<egg|zzz|egg>
bofh: well it's n up to 90 in that imgur link
<egg|zzz|egg>
at low degree it's still OK
<egg|zzz|egg>
bofh: remember, it's not QM, it's geodesy
<bofh>
I mean okay n ~ 90 would def. be problematic, heck n ~ 50 would still be nasty.
<egg|zzz|egg>
bofh: you're making a map out of it :-p
<bofh>
Even in geodesy you're still interested in the low-order spherical harmonics tho, no?
<egg|zzz|egg>
depends how far you are
<egg|zzz|egg>
for LAGEOS, the IERS recommend degree and order 20
<egg|zzz|egg>
for Starlette, degree and order 90
<bofh>
but yes if your n is like 50 and your x is near \pm 1 or a root just use the damn asymptotic in terms of J0 (or for Jnm it'll be in terms of Jm and J_{-m-1}, moment), that's what asymptotics are *for*,
<bofh>
so order 20 is what I'd expect for, like, anything in LEO that's not, like, about to reenter. 90?!?
<bofh>
also brb about 3hrs, more AV1 talks,
<egg|zzz|egg>
bofh: LEO is a different mess because you have the atmosphere
<egg|zzz|egg>
bofh: but Starlette and LAGEOS are high-up geodesy sats
<egg|zzz|egg>
Starlette is lower, thus needs MOAR TERMS
<bofh>
like LAGEOS is at perigee ~ 5800km so 20 terms is about what I'd expect. starlette is at perigee ~ 800km so what I'd expect is actually how the hell has this thing not reentered it was launched in 1975 and it's like, so low atmospheric drag has to be severe.
<bofh>
also Starlette is the *opposite* of high-up, it's low as shit,
<egg|zzz|egg>
bofh: it's sufficiently high that you don't care about drag
<egg|zzz|egg>
bofh: "The decay in semimajor axis due to the effects of atmospheric drag is currently estimated to be -14 m/year for Starlette, and about -30 m/year for Stella (these are average values, and the decay rates may be larger near the maximum in the 11-year solar cycle, and less near the minimum of the solar cycle)."
<egg|zzz|egg>
bofh: also AAAARGH "Satellite de Taille Adaptée avec Réflecteurs Laser pour les Etudes de la Terre"
<egg|zzz|egg>
!acr -add:Starlette Satellite de Taille Adaptée avec Réflecteurs Laser pour les ÉTudes de la TErre
<Qboid>
egg|zzz|egg: I added the explanation for this acronym.
<UmbralRaptor>
That's quite the acronym
<egg|zzz|egg>
bofh: UmbralRaptor: french acronyms, esp. in aerospace, tends to be NMR-grade
<egg|zzz|egg>
"adequately-sized satellite with laser reflectors for earth studies"
<UmbralRaptor>
Hah
<bofh>
egg|zzz|egg: that seems eggstremely NMR-grade, honestly,
<egg|zzz|egg>
bofh: I think using polynomials of sin and of cos on the appropriate octants should work
<egg|zzz|egg>
bofh: hm actually no it's too garbled near π/4 for either
<UmbralRaptor>
egg|zzz|egg: now with higher latitudes?
<egg|zzz|egg>
yes but wonky in the middle
<egg|zzz|egg>
(I'm surprised it's that bad tbh, P90 should be ok at 1/sqrt(2) Ꙩ_ꙩ
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<UmbralRaptor>
Yay, no coffee maker works.
<UmbralRaptor>
…
<UmbralRaptor>
s/no/new/
<Qboid>
UmbralRaptor meant to say: Yay, new coffee maker works.
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<egg|zzz|egg>
!meow UmbralRaptop
* Qboid
meows at UmbralRaptop
<UmbralRaptop>
!pet egg|zzz|egg
* Qboid
pets egg|zzz|egg
<egg|zzz|egg>
bofh: okay so I guess at degree and order 90 I have to use the asymptotics
<egg|zzz|egg>
bofh: "there is an analogous expression in terms of higher-order integer Bessel functions that works for Pnm(cos(β)) that I have here TeXed up, sec." << meow meow meow meow
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<egg|zzz|egg>
!pet whitequark
* Qboid
pets whitequark
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<bofh_av1>
best hostname~
<UmbralRaptop>
I have questions about this remake of the Iliad.
<egg|zzz|egg>
bofh: what do you mean by degree then
<bofh>
I believe degree is equivalent to order for this case (order is a property of which spherical harmonic you are working with, starting with n=0 (s orbitals, etc). degree is a property of any polynomial, and it just happens that the polynomials here equal the degree. but in other cases you have n'th degree expressions that map to, say, 2n-1'th degree polynomials, etc).
<egg|zzz|egg>
bofh: .... okay spherical harmonics in the QM world apparently have completely different terminology as well as different normalization, great,
<egg|zzz|egg>
bofh: degree is n, order is m
<egg|zzz|egg>
bofh: the phrase "to degree and order N" is common when talking about geopotential models
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<egg|zzz|egg>
bofh: e.g., "The EGM2008 model (Pavlis et al., 2008) is complete to degree and order 2159,"
<bofh>
AAAAAAAAAAAAAAAAAAAAAAAAAAAAA
<bofh>
so first off, it's senseless to talk about m on its own since m will *always* range from -n to n and include all of those terms
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<bofh>
so of course it will be to order N, b/c it's to degree N.
<egg|zzz|egg>
bofh: no, m ranges from 0 to n
<egg|zzz|egg>
bofh: and it is frequent to truncate m below n
<egg|zzz|egg>
bofh: you need to do more geodesy
<egg|zzz|egg>
bofh: that very AAAAAAAAAAAAA sentence continues after the comma
<egg|zzz|egg>
bofh: "The EGM2008 model (Pavlis et al., 2008) is complete to degree and order 2159, and contains additional spherical harmonic coefficients up to degree 2190 and order 2159."
<kmath>
<imhirama> @ClickToZoom Sleepily interpreted the word perpendicular and watched the whole video waiting for the sheep to start… https://t.co/Fxl5ejpvml
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* egg|zz|egg
meows at bofh
* egg|zz|egg
pokes bofh
* egg|zzz|egg
stabs Mathematica
* UmbralRaptop
hands egg 3 sneks and a numpy
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* iximeow
meows at egg
* whitequark
iximeows at egg
<iximeow>
!choose garbage collectors|PIC17
<Qboid>
iximeow: Your options are: garbage collectors, PIC17. My choice: PIC17
* egg|zz|egg
ixies at meow
* egg|zz|egg
throws a gluon at whitequark
<whitequark>
PIC17
<whitequark>
PIC
<whitequark>
no
<whitequark>
just... not even once
<iximeow>
i've decided to invest thousands of dollars of hours into making celestron mounts suck less rather than buy a better mount
<iximeow>
whitequark: i have a fairly featureful pic18 emulator now though! :D
<whitequark>
begone, evil spirit
* iximeow
spooky sounds
<UmbralRaptop>
Only the evil material remains
<whitequark>
lol
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<UmbralRaptop>
!meow egg|zz|egg
* Qboid
meows at egg|zz|egg
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<egg|zzz|egg>
!wpn UmbralRaptop, whitequark, bofh, et al.
* Qboid
gives UmbralRaptop, whitequark, bofh, et al. a pre-order bell
<UmbralRaptop>
*BONG*
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<UmbralRaptop>
!u u+0007 egg|zzz|egg
<Qboid>
That's not a valid code point.
<Qboid>
UmbralRaptop: Object reference not set to an instance of an object