egg changed the topic of #principia to: Logs: https://esper.irclog.whitequark.org/principia | <scott_manley> anyone that doubts the wisdom of retrograde bop needs to get the hell out | https://xkcd.com/323/ | <egg> calculating the influence of lamont on Pluto is a bit silly…
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[Principia] pleroy closed pull request #2996: Additive operators for converting vector-valued and affine valued polynomials - https://git.io/JGvDJ
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[Principia] pleroy pushed 8 commits to master [+0/-0/±14] https://git.io/JGJcH
<discord->
Ashnoom. — man, launching to the correct LAN relative to earth makes interplanetary flight plans _so_ much easier
<discord->
Ashnoom. — I am only doing prograde burns essentially 😮
<discord->
Ashnoom. — with a minor mid-course correction in the range of 5m/s
<discord->
Butcher. — Correct.
<discord->
Butcher. — You shouldn't need to do mega normal burns.
<discord->
Butcher. — @egg why are the directions normal and binormal rather than normal and bitangent?
<discord->
Al2Me6. — Isn't that just what the Frenet vectors are called? At least that's what I learned in multivar calc.
<discord->
Butcher. — Ah yes. It seems so.
<discord->
egg. — yeah, as @Al2Me6 said, this is what the terminology is; a bitangent seems to be something else entirely
<discord->
Butcher. — Even though for a given plane they're is only one normal. Grumble.
<discord->
Butcher. — Even though for a given plane there is only one normal. Grumble. (edited)
<discord->
egg. — yes, but there is no plane
<discord->
Butcher. — Is the orbit not the plane? I guess not outside of kepler approximations.
<discord->
egg. — yeah the terminology is chosen to work for arbitrary curves
<discord->
Butcher. — I suppose in a curve you have two normals. 🤔
<discord->
Butcher. — I suppose on a curve you have two normals. 🤔 (edited)
<discord->
egg. — yup, the normal to the curve (within the plane of the osculating circle), and the normal the plane containing the tangent and the normal, *i.e.*, the binormal
<discord->
egg. — (annoyingly the KSP term « radial » isn’t synonymous with the usual term « radial », which is towards the primary (down) rather than towards the centre of the osculating circle)
<discord->
Butcher. — All the pieces fit now.
<discord->
Butcher. — Yes, I use radial to mean down a lot.
<discord->
Butcher. — Because that's what all the papers use.
<discord->
egg. — A common system of axes is defined by radial (down) and along-track (projection of tangent on the horizontal)
<discord->
Butcher. — That's what I use for my orbital guidance.
<discord->
Caravans of Rockets (He/He). — I have to create a trigonometry problem for my algebra 2 math class, anything interesting that I can create that is related to spaceflight/physics?
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<raptop>
Silliness like the best time/direction to launch to minimize flight time for interstellar travel
<discord->
Ashnoom. — Basically mechjeb
<discord->
Zeusbeer. — a cool, I use that too
<discord->
Ashnoom. — I launch a planner rocket
<discord->
Zeusbeer. — oh
<discord->
Ashnoom. — Turn on hack gravity one in orbit
<discord->
Ashnoom. — Once
<discord->
Ashnoom. — Create a maneuver more with MJ node planner
<discord->
Ashnoom. — Remove the prograde burn
<discord->
Ashnoom. — And observe the LAN
<discord->
Ashnoom. — Of the expected maneuver
<discord->
Ashnoom. — I mean outcome
<discord->
Ashnoom. — That's one way. The other is with hyper edit
<discord->
Ashnoom. — Just place a probe, and keep changing its LAN until the MJ transfer planet thing gives you the lowest deltaV, and observe LAN
<discord->
Butcher. — You can script it in kos (or calc in krpc) or hand calc it.
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<discord->
egg. — the name « algebra 2 » makes me think of Galois extensions more than trigonometry…
<discord->
egg. — Also yes, raptop has good suggestions (and Kepler’s equation is fun and a good exposure to the fact that transcendental equations exist)
<discord->
Al2Me6. — Algebra 2 comes before precalc in the American curriculum
<discord->
Caravans of Rockets (He/He). — yeah, if it's not too complicated I'll use it. Thanks!
<discord->
Al2Me6. — Oh, we're talking about high school math, not university
<discord->
Butcher. — We have maths here (pure, applied and statistics if you want to break it up).
<discord->
egg. — (and that Algebra II does have Galois theory, as it should :D)
<discord->
egg. — why would we ever talk about that, or call it math(s) :-p
<discord->
Zeusbeer. — coming back to the question, you could maybe use the 60 degree l4 angle using something pleasant using the 30/60/90 degree ratio triangles, and maybe with a second spacecraft somewhere else
<discord->
Al2Me6. — Umm... basically more algebra? My precalc class had (if I remember right) trig, matrices, conics, basic summation stuff, and a brief introduction to limits.
<discord->
Zeusbeer. — coming back to the question, you could maybe use the 60 degree l4 angle using something pleasant with the 30/60/90 degree ratio triangles, and maybe with a second spacecraft somewhere else (edited)
<discord->
Zeusbeer. — sounds like mathD for us
<discord->
Zeusbeer. — sounds like math-D for us (edited)
<discord->
egg. — (the word « algebra », having lost any meaning, weeps in a corner)
<discord->
Zeusbeer. — abstract algebra != algebra I suppose (edited)
<discord->
Zeusbeer. — geometry != algebra
<discord->
egg. — (I guess the matrices are a bit of linear algebra, the rest sounds calculusish)
<discord->
Al2Me6. — Umm... basically more algebra (as in, continuing/expanding on the content of Algebra 1 and 2)? My precalc class had (if I remember right) trig, matrices, conics, basic summation stuff, and a brief introduction to limits. (edited)
<discord->
Zeusbeer. — geometry != algebra, or maybe it is (edited)
<discord->
Zeusbeer. — (casually deleting all my false hypothesises )
<discord->
Zeusbeer. — ( casually deleting all my false hypothesises ) (edited)
<raptop>
Butcher: precalc is messing around with a bunch of silly algebra and trig instead of doing something useful like calculus or statistics
<discord->
Zeusbeer. — ( casually deleting all my false hypothesises, as my brain wakes up ) (edited)
<raptop>
Except anyone in precalc has already done a bunch of algebra and trig
<_whitenotifier>
[Principia] pleroy closed pull request #2998: Support for affine-valued polynomials in Newhall - https://git.io/JGTmg
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[Principia] pleroy pushed 9 commits to master [+0/-0/±17] https://git.io/JGTH6
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[Principia] pleroy 6ee78ce - Bring in Newhall changes and fix the test.
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[Principia] pleroy 3f72034 - Value, not Argument.
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[Principia] pleroy dc582cb - Newhall for affine-valued polynomials.
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[Principia] ... and 6 more commits.
<discord->
Zeusbeer. — also if precalc is anything like math-D here, they'd get a lot of statistics and infinite integrals
<discord->
Zeusbeer. — also complex numbers ❤️
<discord->
Zeusbeer. — also complex numbers and differential equations ❤️ (edited)
<discord->
Al2Me6. — Oh, no, zero stats or integration involved. Stats as a whole is _very underrepresented_ in the "standard" American math curriculum
<discord->
Al2Me6. — The class is much less interesting than what you're imagining
<discord->
Zeusbeer. — Math-D is nonobligatory choic, but a very useful one for preparing for uni
<discord->
Zeusbeer. — Math-D is nonobligatory choice, but a very useful one for preparing for uni (edited)
<discord->
Al2Me6. — Nah, it's not proper linear algebra. Basically throwing matrices (row reduction, determinants, that sort of thing) in your face without any underlying formalism and seeing what sticks (or rather, what doesn't).
<discord->
Al2Me6. — Umm... basically more algebra (as in, continuing/expanding on the content of Algebra 1 and 2)? My precalc class had (if I remember right) trig, vectors, matrices, conics, basic summation stuff, and a brief introduction to limits. (edited)
<discord->
Paculino (ŝi/ri/she/they). — Trigonometry and a little bit of basic statistics
<discord->
Paculino (ŝi/ri/she/they). — It has a few sections on triangles
<discord->
egg. — @Caravans of Rockets (He/He) Note that solving for β is a transcendental equation (so you probably do not want to ask for that, unless you want to go off a tangent into the wonders of root finding, or perhaps series of Bessel functions), but you have a nice classical geometry problem right there of writing the equation, which is obtained by expressing the circle area DAQ as a function of e and β
<discord->
egg. — (M=β+e sin β, which is Kepler’s equation, where β is more often written E; not sure why that author went with β, it’s not like Kepler uses letters anyway, it’s all loooong sentences in Latin)
<discord->
egg. — (and then you can also relate the true anomaly, the angle PAD, to the eccentric one)
<discord->
egg. — @Caravans of Rockets (He/He) to put things in context if you are not familiar with Kepler orbits: the area M=DAQ, where we take the radius BD to be 1, is the mean anomaly, which is proportional to time since periapsis (recall Kepler’s laws involve sweeping areas); the geometric construction in that figure shows how it is related to the true anomaly ν=PAD (the Planet-Sun-Perihelion angle, which is a
<discord->
egg. — By playing with the triangles ARQ & BRQ you quickly get
<discord->
egg. — and (using the fact that the sector QBD has the area E, and adding to that the area of the triangle ABQ, which ought to be a high school classic),
<discord->
egg. — M=E+e sin E.
<discord->
egg. — With that you can compute M from ν (when will the planet be at the given position on its orbit).
<discord->
egg. — Going from M to ν (where will the planet be at the given time) involves solving M=E+e sin E, which is interesting (but probably out of scope for you).
<discord->
Zeusbeer. — Egg would make a great math-B final exam question designer
<raptop>
The wrath of egg is sometimes just a mathematics lecture
<discord->
egg. — …except the figure is incorrect, because it has anomalies from the aphelion, and thus we see that the area DAQ is β+½e sin β, who reviewed this paper
<discord->
egg. — @Caravans of Rockets (He/He) to put things in context if you are not familiar with Kepler orbits: the area M/2=DAQ, where we take the radius BD to be 1, is (half) the mean anomaly, which is proportional to time since periapsis (recall Kepler’s laws involve sweeping areas); the geometric construction in that figure shows how it is related to the true anomaly ν=PAD (the Planet-Sun-Perihelion angle, w
<discord->
egg. — By playing with the triangles ARQ & BRQ you quickly get
<discord->
egg. — and (using the fact that the sector QBD has the area E/2, and adding to that the area of the triangle ABQ, which ought to be a high school classic),
<discord->
egg. — M=E+e sin E.
<discord->
egg. — With that you can compute M from ν (when will the planet be at the given position on its orbit).
<discord->
egg. — Going from M to ν (where will the planet be at the given time) involves solving M=E+e sin E, which is interesting (but probably out of scope for you). (edited)