<GH>
[Principia] pleroy commented on issue #1244: Cardano, the first version of Principia to support KSP 1.2.2, is available [here](https://goo.gl/BCjxaF). https://git.io/vSqnb
<GH>
[Principia] pleroy commented on issue #1237: Cardano, the first version of Principia to support KSP 1.2.2, is available [here](https://goo.gl/BCjxaF). https://git.io/vSqnN
egg changed the topic of #principia to: READ THE FAQ: http://goo.gl/gMZF9H; The current version is Cardano. We currently target 1.2.2. <scott_manley> anyone that doubts the wisdom of retrograde bop needs to get the hell out | https://xkcd.com/323/
regex has quit [Ping timeout: 201 seconds]
regex has joined #principia
icefire has joined #principia
Thomas is now known as Thomas|AWAY
GregroxLaptop has joined #principia
<GregroxLaptop>
o/
<egg>
\o GregroxLaptop
<GregroxLaptop>
<3
<GregroxLaptop>
How can I change axial tilt?
<GregroxLaptop>
I assume there is MM compatibility?
<egg>
you make a gravity model cfg
<egg>
GregroxLaptop: here's an example config for Kopernicus + Principia: it has a Kopernicus file for the initial state, to patch retrobop; and it has a gravity_models cfg that principia reads, to set the tilt and oblateness (and it also has something to move KSC but you know about this stuff) https://drive.google.com/file/d/0B4y-shYXMH9Bcm9Uems0blR2NWM/view?usp=sharing
<GregroxLaptop>
what is that value which changes oblateness? Does it change the oblatness only for gravity or for scaledspace too?
<egg>
it's only a gravitational property
<egg>
principia has no Kopernicus integration, and is not in the business of changing the looks of the planets
<GregroxLaptop>
I figured.
<egg>
it just moves things
<egg>
GregroxLaptop: I can tell you that the J2 I gave Kerbin is about Mars's
<egg>
so if you give Kerbin Mars's ellipticity it should be believable I guess
<egg>
(that's not much ellipticity tbh)
<GregroxLaptop>
Is J2 the measure of oblatness then?
<egg>
ellipticity is the visual thing, aka flattening; J2 is a zonal spherical harmonic
<egg>
it describes a part of the gravitational field
<egg>
"how much it tends to be equator-heavy" in some sense
<egg>
J3 is "how much it's top-heavy", J4 is then refines the shape of the gravitational field symmetrically about the equator...
<egg>
we only do j2 right now
<egg>
eventually we want to have tesseral harmonics too
<egg>
GregroxLaptop: Zonal are in the first column; Sectoral the diagonal; the rest is tesseral
<GregroxLaptop>
but what does it mean?
<GregroxLaptop>
What do these represent?
<egg>
the shape of the gravitational field
<egg>
GregroxLaptop: you know those gravitational field maps e.g. from GRAIL or GRACE?
<egg>
you can describe the map as a sum of all of those with various coefficients
<egg>
(note that the first line doesn't matter here, it starts on the second line)
<GregroxLaptop>
So with this you could do things like having lobed asgteroids with accurate orbits?
Jesin has quit [Quit: Leaving]
Jesin has joined #principia
<egg>
GregroxLaptop: will answer in a few minutes, patching #1292 after phl's review
<Qboid>
[#1292] title: Evaluate discrete, first cut without hinting | `DiscreteTrajectory` is now a `Trajectory`. The existing use of `Hermite3` is also for interpolation of discrete trajectories (when computing apsides in `Ephemeris`), we may want to switch to `Evaluat... | https://github.com/mockingbirdnest/Principia/issues/1292
<egg>
GregroxMun: hm, lemme try to see if I can find this old notebook
<egg>
GregroxMun: do you know about Fourier series?
<GregroxMun>
Vaguely, but not enough to tell you anything other than "pretty sure there's some sine waves involved"
<egg>
GregroxMun: ok, so the idea is you have a periodic signal, and you express it as a sum of sine waves at different frequencies (that are fractions of some base frequency)
<GregroxMun>
Oh yeah I think I remember that
<egg>
GregroxMun: now you can always do that, but this is particularly useful when the signal is 1. periodic, 2. close enough to a sine wave with perturbations that are sine waves
<egg>
e.g. if you have sound, or radio
<egg>
you can cut off the high frequencies, and get pretty much the same signal
<egg>
the very idea of "cut off the high frequencies" is the Fourier transform
<egg>
if I just give you a curve, it doesn't come with high-frequency bits that can be obviously separated
<egg>
but if you express it as a sum of sines with increasing frequencies, you can drop the high-frequency stuff
<egg>
and assuming your signal isn't too annoying it's going to look the same
<egg>
GregroxMun: the idea is the same here; you have a shape (that of the isopotentials, of the gravity field) and you express it as a sum of what's called spherical harmonics
<egg>
think of them as sine waves but for spheres
<GregroxMun>
Dude.
<GregroxMun>
that's neat
<GregroxMun>
I think I understand that.
<egg>
GregroxMun: now because surfaces are more complicated than curves, instead of having one family of sine waves (harmonics of some base frequency---btw, see, the word harmonic is common to the two!), you have 2 parameters
<GregroxMun>
can you send me that link with the configs again?
<egg>
and much like sine and cosine, you in fact have coefficients C and S for each parameter pair
<egg>
GregroxMun: so J2 is (up to a constant factor) also caled C22
<egg>
it's the cosine-like harmonic 2,2
<egg>
it's bulgy at the equator/flatty at the poles
<egg>
GregroxMun: er no sorry
<egg>
C20
<egg>
the harmonic 2,0
<egg>
(there's no S 2,0 for reasons that I won't delve into)
<egg>
you also have a C and S 2,1
<egg>
those are "how much does it bulge in some direction on the equator"
<egg>
(there are two of those, because you need to specify a direction as well as the magnitude of how much it bulges)
<egg>
where and how much it bulges
<egg>
GregroxMun: so on the equator, think the moon bulging towards and away from Earth
<egg>
(or our tides bulging towards and away from the moon, but that's liquid and it changes over time and it's a mess let's not go there)
<egg>
GregroxMun: also no wait, that was 2,2, not 2,1
<egg>
GregroxMun: C 2,1 and S 2,1 are some weird intermediate thing, where you say e.g. "how much it bulges Australia-to-America"
<egg>
GregroxMun: diagonally
<egg>
GregroxMun: and then the 3,something coefficients refine that by adding more bumps, and the 4,something even more, etc.
<egg>
GregroxMun: mind you this is all about abstract surfaces
<egg>
GregroxMun: you can use them to describe the physical shape of the Moon, or the shape of the gravitational field
<egg>
but they're different things
<egg>
GregroxMun: or you can use it to describe the shape of your cat, but you're going to need *a lot* of harmonics, because your cat is very far from a sphere or an oblate spheroid or any simple spherical harmonic
<GregroxMun>
But this could do things like account for the lumpiness of Gilly, or the lobes of 67p?
<egg>
because of the special shape of the C2,k coefficients when they're extreme, maybe you can get something that vaguely looks like 67p's field with few coefficients
<egg>
but that's not really what it's for
<GregroxMun>
What is it for then?
<GregroxMun>
What is the practical purpose?
<egg>
much like you'd cut the high frequencies off of something that's kinda a sine wave, you use it for things that are kinda shaped like spherical harmonics
<egg>
oblate spheroids + small perturbations
<egg>
otherwise you need too many harmonics to be useful (which is why you shouldn't model cats with spherical harmonics)
<egg>
UmbralRaptor: I think, you're the cat astronomer here
<UmbralRaptor>
ping
<egg>
GregroxMun: you can always try hacking things together with low-order harmonics of course, but for very complex shapes it may be better to cut them up into smaller masses and sum that
<egg>
GregroxMun: many harmonics can end up getting costly
<egg>
GregroxMun: but if you can have few and have that be accurate, it's good
<egg>
so we use that for the gravitational fields of (dwarf) planets
<UmbralRaptor>
Yeah, don't use spherical harmonics for macroscale things held together by electrostatic forces.
<egg>
UmbralRaptor: eh, I think you just shove more harmonics onto the thing? I mean, once you've started supporting that, it's still close enough...
<egg>
UmbralRaptor: you certainly *get* the fields in spherical harmonics at least
<egg>
UmbralRaptor: how you use them to integrate is a different question
<UmbralRaptor>
hrm
<egg>
UmbralRaptor: but if you have the harmonics and the implementation of the harmonics anyway...
<egg>
UmbralRaptor: and it's still a sphere, not a cat
<teabot>
Steall.
<egg>
UmbralRaptor: GregroxMun: so if you had all 2nd order harmonics you could coerce them into making a peanut (important note: this is a symmetric peanut, both lobes the same shape, because 2nd order only). This feels immoral though. http://i.imgur.com/nt4Kwh6.png
<egg>
UmbralRaptor: GregroxMun: also in that image: the effect of various values of J2 in perturbing a sphere, in cross section and in 3d
<egg>
for reasonable values it flattens
<egg>
UmbralRaptor: for unreasonable values it gives you a, erm, lemniscatoid?
<UmbralRaptor>
Given the disky/boxu split for early type galaxies, it seems reasonable.
<egg>
UmbralRaptor: this paper feels like they're just hacking away at the comet and nebulously commenting about the effect of what they do: : the mass loss due
<egg>
neck region has a much bigger influence on the mass distribution
<egg>
along the z-axis (and therefore also on C20) while it
<egg>
to the thinned out part of the new shape model close to the
<egg>
has a smaller influence on the mass distribution along the
<egg>
x-axis (and therefore on C22).
<egg>
*takes a chisel and thins the neck*
<UmbralRaptor>
Snapping the neck off of a rubber duck with harmonics?
<egg>
hah
<UmbralRaptor>
So, less anything formal that throwing terms at a body until the χ²/ν is low?
<egg>
UmbralRaptor: uuuh I'm plotting those 2nd order terms and it seems like just an ellipsoid O_o
<egg>
they're not *that* high
<egg>
(or maybe I'm missing a normalization that adds an order of magnitude?)
HypergolicSkunk has quit [Quit: Connection closed for inactivity]
<egg>
UmbralRaptor: ... but then again it's nowhere near hydrostatic equilibrium right
<egg>
so the gravitational field *shouldn't* look like a duck
<egg>
GregroxMun: ^ that's an important point; on those things the field and the physical shape are very different
<egg>
(whereas e.g. on Jupiter they're the same, because fluids are nice)
<egg>
see it's not really all that duck-shaped of a field
<egg>
UmbralRaptor: I think the idea is that you first take some polyhedral super-slow model and then you try to slap harmonics onto it because polyhedra are just too slow
<egg>
UmbralRaptor: maybe in that case you could combine two masses, but it's not even obvious it would help much, and in general it's not applicable
GregroxLaptop was kicked from #principia by egg [GregroxLaptop]
<GregroxMun>
egg: I can't get anything past Eve to have a tilt with this config. Sun, Moho (for what its tiny tilt is worth), and Eve are all tilted. But nothing else is.