[HN Gopher] Orbital Mechanics
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Orbital Mechanics
Author : belter
Score : 152 points
Date : 2023-04-30 13:45 UTC (9 hours ago)
(HTM) web link (www.braeunig.us)
(TXT) w3m dump (www.braeunig.us)
| aj7 wrote:
| https://spsweb.fltops.jpl.nasa.gov/portaldataops/mpg/MPG_Doc...
| detrites wrote:
| > Satellite orbits can be any of the four conic sections.
|
| This seemed to leave out something important. All "orbits" are in
| reality, spirals. Away, or toward things they're orbiting.
|
| Seems like it should be made clear at the outset that the _ideal_
| of an orbit as these ellipses or cones is only an idealised
| version of reality that is actually impossible, without
| additional, specific input generated to reach it.
| pdonis wrote:
| _> All "orbits" are in reality, spirals. Away, or toward
| things they're orbiting._
|
| What are you basing this on? In Newtonian gravity, which is the
| model used by the article in question, it's false.
| detrites wrote:
| > in reality
| biorach wrote:
| ... well this is embarrassing
| rhn_mk1 wrote:
| As long as we don't have a Perfect, True, Unified theory of
| gravity, I don't think you get to say that "in reality" is
| self-explanatory. It can reasonably mean Newtonian dynamics
| or relativity, or I don't know what else.
|
| Would you clarify?
| detrites wrote:
| Sure.
|
| Let's meet again on this site in about 7 or 8 billion
| years, maybe 9.
|
| I'm sure it'll become crystal clear.
| NotYourLawyer wrote:
| If you want to learn orbital mechanics, just play KSP.
| lucgommans wrote:
| Sort of. KSP teaches you rocket building and how precious fuel
| is. You need to invest a lot of time to get to the stage where
| you transfer between planets. You also can't just pick up the
| resident star, give it a whack, and see what happens to the
| solar system (because it's all two-body mechanics).
|
| That's what I wanted to learn about: orbital mechanics, but as
| a game. I could not find anything online so I built it myself.
| The UX is bad, I've been meaning to improve it but you know how
| it goes. Apologies in advance if the interface is beyond
| comprehension: it's not you, it's me.
|
| Default 3-body demo: https://lucgommans.nl/p/badgravity/
|
| Earth orbit:
| https://lucgommans.nl/p/badgravity/#b64params=eyJ0aW1lcGVyc3...
|
| Use arrow keys to control the space craft that looks oddly
| similar to the letter "A". You're orbiting Earth (denoted with
| E) and there is also the international space station roaming
| around, as well as the moon if you scroll to zoom out.
|
| Try getting near the ISS or even the moon! It's tricky if
| you're doing this for the first time.
|
| For me, this really helped to get a feel for orbital mechanics.
| I never played KSP more than a few minutes on a friend's PC,
| but based on Juno:NewOrigins (simplerockets2) being rather
| similar, I don't really enjoy the engine building aspect or the
| aspect of constantly being out of fuel. It's more realistic
| obviously, but spacecraft design wasn't my goal. I wanted to
| understand how things in orbits affect each other and this lets
| you do that.
|
| You can also take control of the earth in the "bodies" menu.
| Set engine thrust to some giganewtons or whatever and fly the
| earth to a new place :). Or try some of the scenarios in the
| menu. Also note the simulation speed on the top left, otherwise
| getting to e.g. the moon takes a while.
| misnome wrote:
| This _specific_ page was instrumental when learning orbital
| mechanics via playing KSP.
| teraflop wrote:
| The mathematical explanations on this page will teach you lots
| of stuff that will be useful when playing KSP, but the reverse
| is much less true.
|
| Yes, KSP will help you build an _intuition_ for orbital
| mechanics, but you can play it for years and never learn how to
| _calculate_ something as simple as the length of an orbital
| period at a given altitude.
| hgsgm wrote:
| I don't work for NASA, so my calculations would be useless.
| sdenton4 wrote:
| I find the intuition extremely helpful - without the
| intuition, it's hard to build a gut feeling for the
| interrelation and relative importance of the bits in the
| jargon soup for any given question - apijove vs ascending
| node, and so on.
|
| What works best is therefore a combination of the two: I have
| often found myself digging into the math when I want to get
| something /really working/ in KSP. You start the game by
| trying to keep the burning end pointing down (and eventually
| sideways), but the Rocket Equation forces us learn about
| Hohmann Transfers if we want to get anywhere interesting.
| (And maybe even get back again.)
|
| Notably, it's the /constraints/ that create the need to
| optimize, which push us from playing back to the math. The
| sibling commenter who doesn't like dealing with fuel misses
| the point: Caring about fuel pushes us to find the
| mathematical tools to solve our problems.
|
| Compare to Outer Wilds, which has a really fun physics
| simulation - you can whip around planets like a madman - but
| there's no real constraints on fuel, and the solar system is
| small enough that speed isn't really a problem, either. No
| constraints means no one ever has to figure out a Hohmann
| transfer.
| baq wrote:
| If delta V isn't a concern, you can optimize for
| brachistochrone trajectories instead.
| moffkalast wrote:
| Then you install Principia and realize that everything you know
| is a lie and it's all about N times more complicated.
| HelloNurse wrote:
| If you want to play KSP, learn orbital mechanics.
|
| Seriously, understanding dynamics and other basic physics in
| depth never hurt anyone, while real use of orbital calculations
| is much rarer than playing games, writing SF and so on.
| z3t4 wrote:
| I think I used this site or a similar one when learning KSP -
| learning is easy when you make it fun.
| teddyh wrote:
| https://xkcd.com/1356/
| loloquwowndueo wrote:
| Better to not say "just" - from HN front page
| https://justsimply.dev/
| wongarsu wrote:
| Then how about: One common way to learn orbital mechanics is
| playing ksp. For this you need to [buy a computer] [purchase
| and install the game] and [do the tutorial]. For maximum
| enjoyment it is recommended to watch [Scott Manley's
| playthroughs on YouTube] between sessions to deepen your
| understanding.
| NotYourLawyer wrote:
| No this really is a "just."
| lucgommans wrote:
| Not for me at least (though I think loloquwowndueo was
| mostly joking)
| JKCalhoun wrote:
| When I saw the reference to conic sections right from the start I
| felt a familiar cloud settling over my mind. Without telling me
| how orbiting bodies (or the Solar System as an example) are like
| a cone, I find even the mention of conic sections to be
| tangential at best (perhaps distracting at worst?).
|
| I got off the rails a bit staring at the diagram. A circle is of
| course a very specific case of an ellipse -- seems off-topic to
| even include that specificity except for the fact that everyone
| does include it in a conic section diagram.
|
| A parabola looks like another very-much edge case where the slice
| has to be exactly parallel to a line running the length of the
| cone. Not as steep and it is instead a very long ellipse. Steeper
| and it stays within the cone all the way down to infinity -- a
| hyperbola, I guess. Or is it only a hyperbola when the slice is
| exactly vertical? (The diagram has no response.)
|
| It looks like if I read the text some of these are explained.
| Maybe I'm a picture-book kind of guy.
|
| But then there are all the edge cases one can imagine if the
| slice goes through the very vertex of the cone. Leaving those
| possibilities on the table without explanation also leaves my
| mind wandering, probably derailed from the original intent of the
| discussion....
|
| Maybe I'm overthinking it, ha ha.
| lamontcg wrote:
| > I got off the rails a bit staring at the diagram. A circle is
| of course a very specific case of an ellipse -- seems off-topic
| to even include that specificity except for the fact that
| everyone does include it in a conic section diagram.
|
| Circles are mathematically special and horrible and can cause
| real singularities in the mathematics. Normally you measure
| Keplerian elements relative to the Periapsis which is the
| closest approach of the orbit. A perfectly circular orbit has
| no closest approach, it is all closest.
|
| Circular, equatorial, polar and parabolic orbits often need to
| be treated specially. For any algorithm those are often corner
| cases, they definitely need testing.
|
| I've found division by zero errors in a professionally written
| implementation of Shepperd's method of orbit propagation in a
| circular retrograde orbit.
|
| That same method of orbit propagation has fairly horrible
| problems with near-parabolic orbits, intrinsically.
| adastra22 wrote:
| You are overthinking it. Conic sections are critical to the
| math here, and the difference between elliptical and hyperbolic
| orbits is the difference between capture and slingshot.
| PaulHoule wrote:
| Personally I've seen a privileging of geometry over algebra
| that leads people in the wrong direction. Who cares what you
| can do with a straightedge and compasss? Based on what we
| know now the 'conic sections' would better be called the
| 'gravitational curves' or something like that.
| adastra22 wrote:
| People learn in different ways. Abstract equations make no
| sense to me, but if I see a little picture of conic
| sections, it makes perfect sense to me. Because I'm a
| visual thinker with a strong geometric intuition.
|
| The pieces are there for the people who need it.
| OhNoNotAgain_99 wrote:
| [dead]
| belter wrote:
| 8 years ago - https://news.ycombinator.com/item?id=10345734
| dang wrote:
| Thanks! Macroexpanded:
|
| _Basics of Space Flight: Orbital Mechanics_ -
| https://news.ycombinator.com/item?id=10345734 - Oct 2015 (57
| comments)
|
| _Orbital Mechanics_ -
| https://news.ycombinator.com/item?id=6228016 - Aug 2013 (1
| comment)
| agys wrote:
| Love the clarity and crispness of the pixelated
| illustrations/graphs.
| phcreery wrote:
| I wonder how they are created
| antegamisou wrote:
| This type of learning material, lacking any desperate 'ELI5'
| oversimplifications and laying out the proper amount definitions
| and equations without having to resort to fancy animations to
| keep the -quite often indolent- reader engaged, is unfortunately
| scarce in today's web, as is evident from the website's layout.
|
| Here are two favorite readings for anyone willing to delve more
| into the subject: Orbital Mechanics for
| Engineering Students by Howard D. Curtis
|
| https://www.amazon.com/Orbital-Mechanics-Engineering-Student...
| Fundamentals of Astrodynamics (aka BMW) by Roger R. Bate, Donald
| D. Mueller, Jerry E. White, William W. Saylor
|
| https://www.amazon.com/Fundamentals-Astrodynamics-Second-Dov...
|
| Another great textbook as suggested by _musgravepeter_ in the
| comments is Fundamentals of Astrodynamics and
| Applications by David A. Vallado, Wayne D. McClain
|
| https://www.amazon.com/Fundamentals-Astrodynamics-Applicatio...
| sritchie wrote:
| Better yet, keep proper definitions and equations and then
| drive interesting animations from "real deal" code!
|
| I've been working for a couple of years on a computer algebra
| system written in Clojure (named "Emmy") designed for writing
| this like. It's a port of Gerald Sussman's scmutils library,
| plugged in to a bunch of modern graphics libraries.
|
| Here are a few examples, shamefully lacking exposition since
| much of this is JUST working and I was powering through demos
| for a talk:
|
| - particle in a quartic potential well:
| https://sritchie.github.io/clojure-conj-2023/notebooks/conj/...
|
| - Phase Portrait of the Pendulum:
| https://sritchie.github.io/clojure-conj-2023/notebooks/conj/...
|
| - Colin's torus geodesics: https://sritchie.github.io/clojure-
| conj-2023/notebooks/conj/...
|
| - Taylor Series https://sritchie.github.io/clojure-
| conj-2023/notebooks/conj/...
|
| - (p, q) torus knot: https://sritchie.github.io/clojure-
| conj-2023/notebooks/conj/...
|
| - Dual Number Visualization:
| https://sritchie.github.io/clojure-conj-2023/notebooks/conj/...
|
| I'd love a textbook like the one you link above with figures
| that feel almost like Kerbal games, powered by the real code in
| the book that is ALSO generating the math you see.
|
| See https://github.com/mentat-collective/emmy for more
| information if this is interesting.
| antegamisou wrote:
| That's really cool work you've done there !!
|
| Indeed the key to efficient learning is to provide the user
| the ability to have some sort of _parameters play around_
| interaction to better understand the underlying complicated
| equations involved in the examples you posted.
|
| Projects like Manim are cool, don't get me wrong, but I've
| observed that since 3B1B's skyrocketing popularity, similar
| channels are in a way misusing it to only create fancier
| videos without necessarily containing the respective high-
| quality material imperative to convey concepts.
|
| Hopefully _Emmy_ gains the traction it deserves which should
| be high even going by the preliminary demos you 've shared.
| hgsgm wrote:
| I don't see how poor mobile-hostile web design helps education.
| musgravepeter wrote:
| Both these books are on my book shelf and are very good. Bate
| et. al. especially since it is a Dover book and very
| affordable.
|
| The book that is always on my DESK is "Fundamentals of
| Astrodynamics and Applications" by Vallado. There is also a
| website with code from the book for Hohmann and Lambert
| transfers among other things. <self-promotion>This has been
| indispensable in creating my Unity Asset "Gravity
| Engine".</self-promotion>
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