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
<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.… "
* 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?
<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
<_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
<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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