raptop 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. | We can haz pdf
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<galois> title: Bruce Macintosh on Twitter: "The TESS mission has refracting lens-based cameras rather than reflecting mirror-based instruments. It also has a very large field of view and will scan the whole sky with rapid sampling. It's completely obvious that its primary design goal is detection of space vampires.… https://t.co/uIyXSTHaJE"
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<UmbralRaptop> huh, Goldstein only mentions quaternions in an appendix
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<UmbralRaptop> … what level of tired is writing "aqq" instead of "add"
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<UmbralRaptop> How do I get a bunch of font variations on q and Q in LaTeX? Asking for a friend
<e_14159> UmbralRaptop: I've been thinking of aliasing "gut" to "git", given the frequency with which I miswrite them.
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* UmbralRaptop has typed ~/ as ~? so often that maybe…
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<egg> mofh: that won't work though, take an inclined nearly-circular GSO, the apoapsis can be very noncentral
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<UmbralRaptop> … is there a point where Green functions make enough sense that I can actually solve problems with them?
<SnoopJeDi> UmbralRaptop, hopefully, yes! Do you feel comfortable with the construction of particular solutions to a problem by convolution, once you have G(x) in hand?
<UmbralRaptop> No. Also, as best I can tell, "convolution" does not appear in Jackson
<SnoopJeDi> well, when I say that, I mean Du(x) = \int{G(x)f(x)dx}
<SnoopJeDi> err
<SnoopJeDi> \int{δ(x-x')f(x')dx'} on the RHS rather, heh.
<UmbralRaptop> Du(x) ?
<SnoopJeDi> where D is some linear differential operator
<SnoopJeDi> (on u)
<SnoopJeDi> Du = u'' + ku, for example
<SnoopJeDi> I may be butchering some of the mathy language (I never took functional analysis itself), but to me the concept makes the most sense as a way to "decompose" the forcing function. i.e. the line of reasoning in https://en.wikipedia.org/wiki/Green's_function#Motivation
<galois> [WIKIPEDIA] Green's function#Motivation | "In mathematics, a Green's function of an inhomogeneous linear differential operator defined on a domain with specified initial conditions or boundary conditions is its impulse response.This means that if L is the linear differential operator, thenthe Green's function is the solution for y of the equation..."
<UmbralRaptop> Operator, but completely unlike eg: position and momentum?
<galois> [WIKIPEDIA] Green's function#Table of Green's functions | "In mathematics, a Green's function of an inhomogeneous linear differential operator defined on a domain with specified initial conditions or boundary conditions is its impulse response.This means that if L is the linear differential operator, thenthe Green's function is the solution for y of the equation..."
<galois> title: whitequark on Twitter: "cat not kitten for long. but cat can pass for kitten.… "
<SnoopJeDi> UmbralRaptop, uhh well no, *exactly* like those if you mean the ones like d/d{p, x}
<SnoopJeDi> functions are in general vectors and differentiation/integration are maps that eat vectors and spit out vectors, so you can do all the normal linear algebra tricks; this is _most_ of what physicists learn re: PDEs when you view things from 30,000'
<SnoopJeDi> (or at least this is how I think of it)
<mofh> egg: wait, why would it be *non*central in the case of a circular orbit? in that case the apoapsis and the periapsis are *by definition* very close to one another
* UmbralRaptop stares at the problem
<UmbralRaptop> You expect me to integrate cos³(θ) by hand?
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<egg|cell|egg> Mofh wat
<egg|cell|egg> What does that have to do with the ground track mofj
<egg|cell|egg> Mfoh
<egg|cell|egg> Mofh
<egg|cell|egg> Bofh
<egg|cell|egg> Blåhaj
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<egg> rqou: the other tweet is obviously in RFC style, but do you know which one this is https://twitter.com/eggleroy/status/1162460050100772864
<galois> title: Robin Leroy on Twitter: "It is a bounded error for a sheep to graze. The possible effects are that the sheep survives, or that the sheep dies.… "
<_whitenotifier-5dfc> [Principia] pleroy reviewed pull request #2285 commit - https://git.io/fjdDl
<egg> !wpn
* galois gives egg a wolfram knife
<egg> !wpn whitequark
* galois gives whitequark a lithium safe quadrilateral
<B787_300> !wpn egg
* galois gives egg a invariant smart life
<egg> B787_300: how do you generalize the concept of central longitude of the ground track for geosynchronous satellites with ω other than 90 or 270 degrees
<B787_300> uuuum
<mofh> egg|cell|egg: oh wait you want the central GROUND TRACK longitude and not declination/right ascension?
<mofh> egg|cell|egg: absolutely no clue then
<B787_300> i dont know what that even means
<egg> for those, there is a pretty obvious central longitude
<egg> which is a nice way to characterize where the satellite is
<B787_300> hrm
<egg> (the longitude of the ascending node pass is a bit weird in the first case, because it's west)
<B787_300> that red one in link 2 is throwing me for a loop
<egg> however, if you consider the yellow tracks, it's unclear how that oought to generalizes
<egg> that red one is super eccentric
<B787_300> i want to say just take the AN and DN and average those longitudes
<B787_300> but that seems inelegant
<egg> I'd add some ixion plots to get more interesting examples and a clearer understanding but the website broke
<_whitenotifier-5dfc> [Principia] pleroy reviewed pull request #2285 commit - https://git.io/fjdDX
<iximeow> meow
<egg> B787_300: it's inelegant and it's unclear that it's the right thing to do; if the apoapsis is off on one loop to the side, ought one not care more about that loop for operational porpoises?
<egg> ixi
<egg> oh right, ixion pings you
<iximeow> meow
<egg> ιξιμεοω
<B787_300> i mean if you want really inelegant sample the orbit for longitudes and average them?
<egg> hmm, that might actually work?
<B787_300> yeah but seems so wrong
<egg> have you seen how I compute the mean elements
<B787_300> no... but i assume it is hacky
<egg> I convert the osculating elements to osculating equinoctial elements, do a linear fit on the mean longitude whose slope is the sidereal period, filter by integration over a sidereal period, convert back to classical keplerian elements
<egg> it works amazingly well
<B787_300> ...
<egg> I get results that are consistent with the usual analytic methods
<egg> B787_300: it is *very important* to perform the averaging in equinoctial elements though, instead of classical elements
<egg> that's how you can get a mean e that's less than any osculating e
<galois> title: 1967AJ.....72..994W Page 994
<_whitenotifier-5dfc> [Principia] pleroy synchronize pull request #2285: A class to represent an approximate quantity - https://git.io/fjd4j
<egg> because osculating (e cos ω, e sin ω) (really ω+Ω but it doesn't matter much) wildly spins around the origin over one revolution, and the averaging extracts the mean e
<egg> B787_300: Yes, I saw this, and many many other more modern theories; it's all useless, because it assumes you have an analytic mean element theory (or in fancier papers it derives a new one)
<egg> I need something that works even if you're in Duna orbit and being perturbed by Ike, and I'm not developing a mean element theory for that
<B787_300> ah yes
<egg> on the other hand, I don't need to do the transformation from an instantaneous set of osculating elements
<egg> it's trivial for me to predict the future, and to crunch numbers on that
<egg> the goal of mean element theories is, first to get properties that are free of short-periodic variations (and then longer-period variations)
<egg> I achieve that first part by numerical averaging (that's actually a thing that is done, it's mentioned in passing by Spiridonova et al. iirc)
<egg> but the very important part is to do the averaging on the right kind of elements
<egg> otherwise, you get garbage
<_whitenotifier-5dfc> [Principia] Pending. Build queued… - 
<_whitenotifier-5dfc> [Principia] Pending. Building… - http://casanova.westeurope.cloudapp.azure.com:8080/job/Principia/3809/
<egg> B787_300: see the effect of this procedure on TOPEX/Poséidon elements https://i.imgur.com/Rn86qMD.png
<egg> B787_300: compare the eccentricity plot with fig. 2 of https://elib.dlr.de/103814/1/Spiridonova_ISSFD_2014_upd.pdf
<B787_300> M and e seems off
<egg> nope, they're behaving exactly as expected
<egg> the osculating elements are complete crap, but the equinoctial averaging redeems them
<egg> B787_300: see the bottom plots to see why e ends up like that
<B787_300> yeah
<egg> λ is well-behaved even when osculating; this is critical to the whole scheme
<egg> because it has no singularities, it always behaves pretty decently, which means it gives us a slope, from which we get the sidereal period
<egg> the other periods you can't get from the osculating elements, you really need mean M and mean ω + M to get an anomalistic or nodal period
<_whitenotifier-5dfc> [Principia] eggrobin reviewed pull request #2285 commit - https://git.io/fjdyZ
<_whitenotifier-5dfc> [Principia] eggrobin labeled pull request #2285: A class to represent an approximate quantity - https://git.io/fjd4j
<_whitenotifier-5dfc> [Principia] Failure. Build finished. - http://casanova.westeurope.cloudapp.azure.com:8080/job/Principia/3809/
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<UmbralRaptop> !8 Convince iximeow to use Principia to figure out how to best move 433 Eros?
<galois> UmbralRaptop: no
<B787_300> !8 convince iximeow to use Prinicpa to figure out how to move enough asteroid belt objects and Diemos and Phobos to give Mars a moon with the same Mass ratio as the Moon/Earth ratio at the same distance?
<galois> B787_300: yes
<iximeow> hm
<iximeow> intriguing idea
<B787_300> i mean it could solve so many mars living problems
<B787_300> if it reheats the core from tidal pressures you could get the Martian Magnetosphere back to help keep the atmosphere
<B787_300> plus the geothermal heat could be really useful
<B787_300> and i just want to see Olympus Mons erupting again
<B787_300> and it could protect against asteriods that you inadvertently moved when you were making the moon
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