8 ms·

Basics of Space Flight: Orbital Mechanics

236 points by dodders 11y ago

Gladdyu 11y ago
Great! A manual to Kerbal Space Program.
- Vespasian 11y ago
  The master of KSP Scott Manley did a small series of orbital mechanics videos a while back https://www.youtube.com/playlist?list=PLYu7z3I8tdEm-oVAzO8EHRAqAFG5RmNPl https://www.youtube.com/playlist?list=PLYu7z3I8tdEm-oVAzO8EH...
  - Malic 11y ago
    ...fly safe!
- baobabaobab 11y ago
  I actually used this page as a guide to write a orbital rendezvous computer plugin, back before that was a built in feature in the game. It's the best (in depth) resource on orbital mechanics I ever found.
runholm 11y ago
I can either read this for an hour, or play Kerbal Space Program for 50 hours and learn most of it. Pft, easy choice. (I will then read the article and realize what I was doing wrong the whole time.)
- blkhawk 11y ago
  Well I am pretty sure playing KSP will give one a much deeper "feel" for orbital mechanics. The linked page contains all the math if you actually want to calculate the orbits optimally. I think i will stick with mechjeb. :)
  - arrrg 11y ago
    Yeah, KSP is great for getting an intuitive feeling for what one would have to do to navigate space successfully – at least to the point where one would be able to identify grossly inefficient behavior immediately and be able to do something that’s somewhat effective at getting where you want to go (though probably not most effective). I think that’s pretty awesome, mostly because orbital mechanics is not something we think of being able to have an intuitive understanding of, at least if you don’t have the requisite math background (and maybe even then not). With KSP, at least if you play it long enough, you really do gain a rough intuitive understanding, even if you do not ever calculate anything. But one should probably also mention that it is time-inefficient and, well, not exactly rigorous. (Both of those things don’t matter that much since it’s just a game.) Obviously you can also break out the calculator and approach it that way (but I don’t think that’s necessary, except maybe when it comes to interplanetary stuff and getting the right angles). The game is luckily easy enough to brute force things and when you are stuck around KSP’s Mars equivalent with little fuel you can still always fiddle around with maneuver nodes forever to see if there is some way out – and then be forced to learn to be efficient that way.
  - hugh4 11y ago
    Solving things analytically is overrated and only possible in rare circumstances. Everything I need to solve orbital mechanics is F = Gm1m2/r^2
- martincmartin 11y ago
  Relevant xkcd: https://xkcd.com/1356/ https://xkcd.com/1356/
dvh 11y ago
Couple months ago I started working on space shooter/simulator, just for fun. Newtonian physics, html canvas. It had 2D top view (F2 key) and 3D view (F3 key), but because canvas is quite slow on fullscreen I usualy switched rendering off (F1 key) and then I spent most of the debuging time there. I only needed few data to be displayed so I only rendered speed, distance fuel etc. as numbers. Then I added yaw pitch roll indicator and even though it was on canvas, because only small part was changing it was kinda fast, so I started adding more and more avionics and eventually the instrument flight [1] aspect of it become much more interesting that realistic planet renderings and I completely neglected 3D view [2]. The most fun so far was programing docking autopilot. So if you haven't make your own space simulator, you should, it's fun. (unfortunately it's not finished and not even in publishable state) [1] https://drive.google.com/file/d/0B5SCh06PKpVtZHowN1l0TEw3cGs/view https://drive.google.com/file/d/0B5SCh06PKpVtZHowN1l0TEw3cGs... [2] https://drive.google.com/file/d/0B5SCh06PKpVtUzMxSGNhRy1vVlE/view https://drive.google.com/file/d/0B5SCh06PKpVtUzMxSGNhRy1vVlE...
- exDM69 11y ago
  Do you have more links or source code to your project available? I also dabble with space-related programming projects and I'd be interested in seeing your stuff.
  - dvh 11y ago
    i polish it a little bit and release it as chrome app in few months
- drjesusphd 11y ago
  I am also interested. I've been curious what strategic elements a real space combat situation (on the scale of a solar system) demands, and if an interesting game can be made out of it.
  - mLuby 11y ago
    Check out Atomic Rockets—great resource on realistic space combat ideas. (no stealth, lasers or missiles?, etc) http://www.projectrho.com/public_html/rocket/index.php http://www.projectrho.com/public_html/rocket/index.php
blkhawk 11y ago
its amazing for how many of the diagrams i think - "heh i did that and sorta know how to wing that by hand in KSP".
- Vespasian 11y ago
  I got the same feeling. You can learn a lot through trial and error. Probably the need to know everything comes in once you have to pay for that extra dV or if you plan to put your colleagues on thousands of tons of explosive rocket fuel ;)
VLM 11y ago
I flew Orbiter to Mars from earth, docked with the ISS, also made a game of trying to visit each of Jupiter's satellites about 10-15 years ago http://orbit.medphys.ucl.ac.uk/ http://orbit.medphys.ucl.ac.uk/ Its interesting to look at the MFD design for mission planning as an applied version of the linked page. I have not played much KSP, is there anything as realistic as orbiter? From what little I've seen it tended toward comical set of pants, like comparing ChopperLifter to MS flight sim. Orbital docking dynamics are weird. If you undock from the ISS and thrust up a little bit, in half an orbit you'll come right back. Increasing or reducing your speed along the orbit (moving front or back) will eventually affect your altitude. Docking isn't as simple as "if you wanna go forward, thrust forward". All the control mix; like hovering a helicopter but slower. Flying "in formation" can be very expensive in terms of fuel depending on the formation, or it can be free if in a favorable geometry. There is a classic very hard sci fi story along the lines of extorting someone who doesn't know orbital mechanics by literally throwing them off a space station, and the victim panics not knowing he'll be back in half an orbit seeing as escape velocity is a little faster than a human shove! One amusing anecdote is for an inclination change greater than 60 degrees or so, its cheaper to land and take off again or go on a very high orbit into deep space and change your inclination there. The ISS is at a very high inclination and at least energetically, to put the thing into a GTO around inclination 0 or so, it would be cheaper to land and re-launch the thing.
- baobabaobab 11y ago
  >I have not played much KSP, is there anything as realistic as orbiter? No, it's the most realistic game about spaceflight, but it's not a simulator.
  - dragonwriter 11y ago
    It's definitely a simulator, just not primarily an in-cockpit simulator.
    - outworlder 11y ago
      Given enough mods, the in-cockpit experience becomes rather satisfactory. I've flow missions to the moon and back completely in-cockpit
brennankreiman 11y ago
Mike Bostock's D3 can do some interesting visualizations based on satellite.js http://bl.ocks.org/syntagmatic/6c149c08fc9cde682635 http://bl.ocks.org/syntagmatic/6c149c08fc9cde682635
exDM69 11y ago
This page is mostly a digest of the book "Fundamentals of Astrodynamics" by Bate, Mueller and White (known as the "BMW" after the authors). This page is useful as a reference but not really good for learning material. I find the Wikipedia pages on this subject a bit shallow too (one of these days I'll contribute improvements to the Wikipedia pages), so if you intend to learn this stuff, obtaining a book is the only viable option (if you know of other good online resources, please share with us. I don't). The 1st edition BMW book from 1971 is available for dirt cheap (15-20 USD), the 2nd edition came out just a month ago but it's poorly available (I'm still waiting for my copy from Amazon). There's a few more pages (incl. interplanetary mission planning) if you go up one level: http://www.braeunig.us/space/ http://www.braeunig.us/space/ Finally, here's a project of mine that implements a bunch of algorithms for two body orbital mechanics: https://github.com/rikusalminen/twobody https://github.com/rikusalminen/twobody These algorithms are mostly based on the BMW book as well as a bunch of research papers from the 1960s to 1990s. Look around in different branches for some of the more advanced algorithms (including a search for closest approaches and sphere of influence transitions like Kerbal Space Program and a boundary value problem solver for interplanetary travel), they're still work in progress. One day I'll turn this into a mission planner software for space simulator games (or some kind of game, not sure yet). If you happen to need some orbital mechanics algorithms, take a look of the above and I'm happy to answer any questions or help with this.
- fancyketchup 11y ago
  Spacecraft Attitude Determination and Control, edited by Wertz, is another classic. Used copies are available for around 35 USD, but new copies usually over 200 USD.
  - exDM69 11y ago
    Spaceflight Dynamics by William E. Wiesel is also a good book with a broader overview into much more topics, including attitude dynamics and rocket dynamics. As opposed to the BMW which only covers orbital motion, but in more depth. Orbital Mechanics by Prussing and Conway (of Laguerre-Conway fame) is also a very nice book, going into more details of advanced orbital motion, including some more modern methods. But damn, aerospace engineering books are really expensive. I've spent a small fortune on these books.
Cheyana 11y ago
While getting ready for work this morning I was thinking about this very thing while I was brushing my teeth. I was thinking it would be nice to learn what the actual orbits of all 8 planets are, relative to the sun, and here I get into work and this is posted. Now granted, I just wanted to know just the orbits as this stuff is way over my head, but I guess it would be good to learn it.
yoha 11y ago
In case it might be of some use to anyone, I started a guide for beginners on the subject: https://airsick.guide/ https://airsick.guide/ . For Python fans (or anyone with a computer, really), there is also a (very simple) library designed with KSP in mind: https://github.com/qsantos/spyce https://github.com/qsantos/spyce.
- exDM69 11y ago
  Interesting... This function from your project: https://github.com/qsantos/spyce/blob/master/cext/orbit.c#L86 https://github.com/qsantos/spyce/blob/master/cext/orbit.c#L8... Looks somewhat similar to what I did a few years ago in a now-abandoned project of mine: https://github.com/rikusalminen/libkepler/blob/master/src/kepler.c#L329 https://github.com/rikusalminen/libkepler/blob/master/src/ke... Did you by any chance, happen to look at my code for reference? Or are they somewhat similar just out of coincidence and similar naming conventions? If you did, in fact, look at my project for reference, I'm glad to have helped! Just for comparison, here's the orbit determination from initial conditions code from a newer project of mine. It doesn't compute the classical orbital directly, because that tends to add numerical error (ie. first you compute inclination using acos() and a moment later you compute the orientation matrix using cos(inclination)). https://github.com/rikusalminen/twobody/blob/master/include/twobody/orbit.h#L73 https://github.com/rikusalminen/twobody/blob/master/include/... You can, of course, get the classical elements from the orbit, they are useful for presenting human-readable numbers.
  - yoha 11y ago
    I don't remember looking at this project. I think I did read other implementations of this algorithm, and they all end up very similar, so it's probably due to algorithm itself. It might be interesting to link to all codebases that might be relevant. Maybe I will add a list to https://airsick.guide/tools.html https://airsick.guide/tools.html. --- I only searched briefly for more stable methods. Thanks for the reference, I'll have a look!
    - exDM69 11y ago
      Yeah, there aren't too many ways of detemining orbital elements from initial conditions so it is very likely that the code implementing that ends up looking the same. The similarity in variable names and naming_conventions made the two functions look rather similar. What comes to stability: given just a single pair of (position, velocity) vectors, it's hard to make something that is really stable. If you have several pairs, you can use the method of least squares to try to fit an orbit into observations. Not using too many arcus trig functions (acos, asin), will give a bit better results near zero. Additionally, not having to solve the Kepler's equation would be an improvement for near-parabolic trajectories. In other words: it might be preferable to store (true anomaly at epoch, timestamp of epoch) rather than time of periapsis passage or mean anomaly at epoch to avoid this. The issue is that E - e*sin(E) loses numerical precision when e is near 1 (parabolic) and E is near zero. Same applies for the hyperbolic equivalent of Kepler's equation. Anyway, nice to find people with similar interests! Good luck with your projects.
antognini 11y ago
We are actually very fortunate that the Earth is not very spherical, because without that satellites on the high inclination orbits like the polar orbits and the Molinya orbits would crash into the Earth. Due to perturbations of the Moon, high inclination orbits have a tendency to be pushed from low eccentricity to very high eccentricity. (This is known as the Kozai-Lidov mechanism.) However, the fact that the Earth's gravitational potential is not exactly spherical (it has a quadrupole moment) makes these orbits precess, and this precession happens to be fast enough to suppress the eccentricity oscillations. There is a very good and very readable article by Scott Tremaine on this subject here: http://arxiv.org/abs/1309.5244 http://arxiv.org/abs/1309.5244
- Retric 11y ago
  It would be very unusual for a planet to be spherical as it would have to not be rotating.
  - nsxwolf 11y ago
    What about Venus? It rotates really slowly compared to Earth.
    - antognini 11y ago
      The quadrupole moment of Venus is much, much less than that of the Earth. For comparison, the relative difference between the radius at the equator and the radius at the pole of Earth is about 0.3%. For Venus it's less than one part in 100,000. However, Venus doesn't have a moon, so there's no third body to cause Kozai-Lidov oscillations [1]. [1]: Actually, this is not strictly true, since the Sun acts as a third body. However, it's so much further away that the Kozai-Lidov effect from the Sun is weak. That's why the Venus Express was able to maintain a polar orbit around Venus.
ececconi 11y ago
The book Fundamentals of Astrodynamics" by Bate, Mueller and White, where it seems like these notes come from was my Orbital Mechanics textbook in college. Our final project was to program a crude missile defense system. Great book. It's an old one, but I highly recommend it. It's one of the few textbooks I saved from college.
unchocked 11y ago
There's another interesting approach to orbital mechanics using geometric algebra. Paper below is from 1983, has anyone come across a later application? http://adsabs.harvard.edu/full/1983CeMec..30..151H http://adsabs.harvard.edu/full/1983CeMec..30..151H
ghaff 11y ago
Another classic book in the field is An Introduction to the Mathematics and Methods of Astrodynamics by Richard Battin of Draper Labs who passed away fairly recently. He developed and led the design of the guidance, navigation, and control systems for the Apollo flights at Draper. https://www.bostonglobe.com/metro/2014/02/23/richard-battin-developed-and-led-design-guidance-navigation-and-control-systems-for-apollo-flights/vxP9iIEfKuKpR7eCfes4fO/story.html https://www.bostonglobe.com/metro/2014/02/23/richard-battin-...
jcadam 11y ago
I remember getting a basic primer on this stuff when I attended a USAF Space Operations course back when I was in the Army Reserve. Our textbook (and an excellent book for the layperson interested in this sort of thing) was Understanding Space [1]. It's still sitting on my bookshelf at work and I occasionally have a reason to crack it open. As a software engineer in the aerospace industry, I was once working on a project to create a simulator for a new satellite program. I got stuck with writing a simulation model for the Attitude Determination and Control system (rather than something non-physics-y like the communications system). A lot of my job involved taking matlab scripts from the scientists and translating them into Ada code. An understanding of the basics of orbital mechanics came in very handy, as otherwise I would really not have had any way of knowing if my model was generating nonsensical output. Not to mention the onus was always on me to prove to a scientist that there was a bug in his algorithm. [1] http://www.amazon.com/Understanding-Space-Introduction-Astronautics-Technology/dp/0073407755/ref=sr_1_1?ie=UTF8&qid=1444234742&sr=8-1&keywords=Understanding+Space http://www.amazon.com/Understanding-Space-Introduction-Astro...
swagopopotamus 11y ago
Nice reference. Maybe now more of the stuff I hear on the orbital mechanics podcast (http://www.theorbitalmechanics.com/ http://www.theorbitalmechanics.com/) will make sense.

236 points by dodders 11y ago

Gladdyu 11y ago

Great! A manual to Kerbal Space Program.

Vespasian 11y ago
The master of KSP Scott Manley did a small series of orbital mechanics videos a while back https://www.youtube.com/playlist?list=PLYu7z3I8tdEm-oVAzO8EHRAqAFG5RmNPl https://www.youtube.com/playlist?list=PLYu7z3I8tdEm-oVAzO8EH...
- Malic 11y ago
  ...fly safe!
baobabaobab 11y ago
I actually used this page as a guide to write a orbital rendezvous computer plugin, back before that was a built in feature in the game. It's the best (in depth) resource on orbital mechanics I ever found.

runholm 11y ago

I can either read this for an hour, or play Kerbal Space Program for 50 hours and learn most of it. Pft, easy choice. (I will then read the article and realize what I was doing wrong the whole time.)

blkhawk 11y ago
Well I am pretty sure playing KSP will give one a much deeper "feel" for orbital mechanics. The linked page contains all the math if you actually want to calculate the orbits optimally. I think i will stick with mechjeb. :)
- arrrg 11y ago
  Yeah, KSP is great for getting an intuitive feeling for what one would have to do to navigate space successfully – at least to the point where one would be able to identify grossly inefficient behavior immediately and be able to do something that’s somewhat effective at getting where you want to go (though probably not most effective). I think that’s pretty awesome, mostly because orbital mechanics is not something we think of being able to have an intuitive understanding of, at least if you don’t have the requisite math background (and maybe even then not). With KSP, at least if you play it long enough, you really do gain a rough intuitive understanding, even if you do not ever calculate anything. But one should probably also mention that it is time-inefficient and, well, not exactly rigorous. (Both of those things don’t matter that much since it’s just a game.) Obviously you can also break out the calculator and approach it that way (but I don’t think that’s necessary, except maybe when it comes to interplanetary stuff and getting the right angles). The game is luckily easy enough to brute force things and when you are stuck around KSP’s Mars equivalent with little fuel you can still always fiddle around with maneuver nodes forever to see if there is some way out – and then be forced to learn to be efficient that way.
- hugh4 11y ago
  Solving things analytically is overrated and only possible in rare circumstances. Everything I need to solve orbital mechanics is F = Gm1m2/r^2
martincmartin 11y ago
Relevant xkcd: https://xkcd.com/1356/ https://xkcd.com/1356/

dvh 11y ago

Couple months ago I started working on space shooter/simulator, just for fun. Newtonian physics, html canvas. It had 2D top view (F2 key) and 3D view (F3 key), but because canvas is quite slow on fullscreen I usualy switched rendering off (F1 key) and then I spent most of the debuging time there. I only needed few data to be displayed so I only rendered speed, distance fuel etc. as numbers. Then I added yaw pitch roll indicator and even though it was on canvas, because only small part was changing it was kinda fast, so I started adding more and more avionics and eventually the instrument flight [1] aspect of it become much more interesting that realistic planet renderings and I completely neglected 3D view [2]. The most fun so far was programing docking autopilot. So if you haven't make your own space simulator, you should, it's fun. (unfortunately it's not finished and not even in publishable state) [1] https://drive.google.com/file/d/0B5SCh06PKpVtZHowN1l0TEw3cGs/view https://drive.google.com/file/d/0B5SCh06PKpVtZHowN1l0TEw3cGs... [2] https://drive.google.com/file/d/0B5SCh06PKpVtUzMxSGNhRy1vVlE/view https://drive.google.com/file/d/0B5SCh06PKpVtUzMxSGNhRy1vVlE...

exDM69 11y ago
Do you have more links or source code to your project available? I also dabble with space-related programming projects and I'd be interested in seeing your stuff.
- dvh 11y ago
  i polish it a little bit and release it as chrome app in few months
drjesusphd 11y ago
I am also interested. I've been curious what strategic elements a real space combat situation (on the scale of a solar system) demands, and if an interesting game can be made out of it.
- mLuby 11y ago
  Check out Atomic Rockets—great resource on realistic space combat ideas. (no stealth, lasers or missiles?, etc) http://www.projectrho.com/public_html/rocket/index.php http://www.projectrho.com/public_html/rocket/index.php

blkhawk 11y ago

its amazing for how many of the diagrams i think - "heh i did that and sorta know how to wing that by hand in KSP".

Vespasian 11y ago
I got the same feeling. You can learn a lot through trial and error. Probably the need to know everything comes in once you have to pay for that extra dV or if you plan to put your colleagues on thousands of tons of explosive rocket fuel ;)

VLM 11y ago

I flew Orbiter to Mars from earth, docked with the ISS, also made a game of trying to visit each of Jupiter's satellites about 10-15 years ago http://orbit.medphys.ucl.ac.uk/ http://orbit.medphys.ucl.ac.uk/ Its interesting to look at the MFD design for mission planning as an applied version of the linked page. I have not played much KSP, is there anything as realistic as orbiter? From what little I've seen it tended toward comical set of pants, like comparing ChopperLifter to MS flight sim. Orbital docking dynamics are weird. If you undock from the ISS and thrust up a little bit, in half an orbit you'll come right back. Increasing or reducing your speed along the orbit (moving front or back) will eventually affect your altitude. Docking isn't as simple as "if you wanna go forward, thrust forward". All the control mix; like hovering a helicopter but slower. Flying "in formation" can be very expensive in terms of fuel depending on the formation, or it can be free if in a favorable geometry. There is a classic very hard sci fi story along the lines of extorting someone who doesn't know orbital mechanics by literally throwing them off a space station, and the victim panics not knowing he'll be back in half an orbit seeing as escape velocity is a little faster than a human shove! One amusing anecdote is for an inclination change greater than 60 degrees or so, its cheaper to land and take off again or go on a very high orbit into deep space and change your inclination there. The ISS is at a very high inclination and at least energetically, to put the thing into a GTO around inclination 0 or so, it would be cheaper to land and re-launch the thing.

baobabaobab 11y ago
>I have not played much KSP, is there anything as realistic as orbiter? No, it's the most realistic game about spaceflight, but it's not a simulator.
- dragonwriter 11y ago
  It's definitely a simulator, just not primarily an in-cockpit simulator.
  - outworlder 11y ago
    Given enough mods, the in-cockpit experience becomes rather satisfactory. I've flow missions to the moon and back completely in-cockpit

brennankreiman 11y ago

Mike Bostock's D3 can do some interesting visualizations based on satellite.js http://bl.ocks.org/syntagmatic/6c149c08fc9cde682635 http://bl.ocks.org/syntagmatic/6c149c08fc9cde682635

exDM69 11y ago

This page is mostly a digest of the book "Fundamentals of Astrodynamics" by Bate, Mueller and White (known as the "BMW" after the authors). This page is useful as a reference but not really good for learning material. I find the Wikipedia pages on this subject a bit shallow too (one of these days I'll contribute improvements to the Wikipedia pages), so if you intend to learn this stuff, obtaining a book is the only viable option (if you know of other good online resources, please share with us. I don't). The 1st edition BMW book from 1971 is available for dirt cheap (15-20 USD), the 2nd edition came out just a month ago but it's poorly available (I'm still waiting for my copy from Amazon). There's a few more pages (incl. interplanetary mission planning) if you go up one level: http://www.braeunig.us/space/ http://www.braeunig.us/space/ Finally, here's a project of mine that implements a bunch of algorithms for two body orbital mechanics: https://github.com/rikusalminen/twobody https://github.com/rikusalminen/twobody These algorithms are mostly based on the BMW book as well as a bunch of research papers from the 1960s to 1990s. Look around in different branches for some of the more advanced algorithms (including a search for closest approaches and sphere of influence transitions like Kerbal Space Program and a boundary value problem solver for interplanetary travel), they're still work in progress. One day I'll turn this into a mission planner software for space simulator games (or some kind of game, not sure yet). If you happen to need some orbital mechanics algorithms, take a look of the above and I'm happy to answer any questions or help with this.

fancyketchup 11y ago
Spacecraft Attitude Determination and Control, edited by Wertz, is another classic. Used copies are available for around 35 USD, but new copies usually over 200 USD.
- exDM69 11y ago
  Spaceflight Dynamics by William E. Wiesel is also a good book with a broader overview into much more topics, including attitude dynamics and rocket dynamics. As opposed to the BMW which only covers orbital motion, but in more depth. Orbital Mechanics by Prussing and Conway (of Laguerre-Conway fame) is also a very nice book, going into more details of advanced orbital motion, including some more modern methods. But damn, aerospace engineering books are really expensive. I've spent a small fortune on these books.

Cheyana 11y ago

While getting ready for work this morning I was thinking about this very thing while I was brushing my teeth. I was thinking it would be nice to learn what the actual orbits of all 8 planets are, relative to the sun, and here I get into work and this is posted. Now granted, I just wanted to know just the orbits as this stuff is way over my head, but I guess it would be good to learn it.

yoha 11y ago

In case it might be of some use to anyone, I started a guide for beginners on the subject: https://airsick.guide/ https://airsick.guide/ . For Python fans (or anyone with a computer, really), there is also a (very simple) library designed with KSP in mind: https://github.com/qsantos/spyce https://github.com/qsantos/spyce.

exDM69 11y ago
Interesting... This function from your project: https://github.com/qsantos/spyce/blob/master/cext/orbit.c#L86 https://github.com/qsantos/spyce/blob/master/cext/orbit.c#L8... Looks somewhat similar to what I did a few years ago in a now-abandoned project of mine: https://github.com/rikusalminen/libkepler/blob/master/src/kepler.c#L329 https://github.com/rikusalminen/libkepler/blob/master/src/ke... Did you by any chance, happen to look at my code for reference? Or are they somewhat similar just out of coincidence and similar naming conventions? If you did, in fact, look at my project for reference, I'm glad to have helped! Just for comparison, here's the orbit determination from initial conditions code from a newer project of mine. It doesn't compute the classical orbital directly, because that tends to add numerical error (ie. first you compute inclination using acos() and a moment later you compute the orientation matrix using cos(inclination)). https://github.com/rikusalminen/twobody/blob/master/include/twobody/orbit.h#L73 https://github.com/rikusalminen/twobody/blob/master/include/... You can, of course, get the classical elements from the orbit, they are useful for presenting human-readable numbers.
- yoha 11y ago
  I don't remember looking at this project. I think I did read other implementations of this algorithm, and they all end up very similar, so it's probably due to algorithm itself. It might be interesting to link to all codebases that might be relevant. Maybe I will add a list to https://airsick.guide/tools.html https://airsick.guide/tools.html. --- I only searched briefly for more stable methods. Thanks for the reference, I'll have a look!
  - exDM69 11y ago
    Yeah, there aren't too many ways of detemining orbital elements from initial conditions so it is very likely that the code implementing that ends up looking the same. The similarity in variable names and naming_conventions made the two functions look rather similar. What comes to stability: given just a single pair of (position, velocity) vectors, it's hard to make something that is really stable. If you have several pairs, you can use the method of least squares to try to fit an orbit into observations. Not using too many arcus trig functions (acos, asin), will give a bit better results near zero. Additionally, not having to solve the Kepler's equation would be an improvement for near-parabolic trajectories. In other words: it might be preferable to store (true anomaly at epoch, timestamp of epoch) rather than time of periapsis passage or mean anomaly at epoch to avoid this. The issue is that E - e*sin(E) loses numerical precision when e is near 1 (parabolic) and E is near zero. Same applies for the hyperbolic equivalent of Kepler's equation. Anyway, nice to find people with similar interests! Good luck with your projects.

antognini 11y ago

We are actually very fortunate that the Earth is not very spherical, because without that satellites on the high inclination orbits like the polar orbits and the Molinya orbits would crash into the Earth. Due to perturbations of the Moon, high inclination orbits have a tendency to be pushed from low eccentricity to very high eccentricity. (This is known as the Kozai-Lidov mechanism.) However, the fact that the Earth's gravitational potential is not exactly spherical (it has a quadrupole moment) makes these orbits precess, and this precession happens to be fast enough to suppress the eccentricity oscillations. There is a very good and very readable article by Scott Tremaine on this subject here: http://arxiv.org/abs/1309.5244 http://arxiv.org/abs/1309.5244

Retric 11y ago
It would be very unusual for a planet to be spherical as it would have to not be rotating.
- nsxwolf 11y ago
  What about Venus? It rotates really slowly compared to Earth.
  - antognini 11y ago
    The quadrupole moment of Venus is much, much less than that of the Earth. For comparison, the relative difference between the radius at the equator and the radius at the pole of Earth is about 0.3%. For Venus it's less than one part in 100,000. However, Venus doesn't have a moon, so there's no third body to cause Kozai-Lidov oscillations [1]. [1]: Actually, this is not strictly true, since the Sun acts as a third body. However, it's so much further away that the Kozai-Lidov effect from the Sun is weak. That's why the Venus Express was able to maintain a polar orbit around Venus.

ececconi 11y ago

The book Fundamentals of Astrodynamics" by Bate, Mueller and White, where it seems like these notes come from was my Orbital Mechanics textbook in college. Our final project was to program a crude missile defense system. Great book. It's an old one, but I highly recommend it. It's one of the few textbooks I saved from college.

unchocked 11y ago

There's another interesting approach to orbital mechanics using geometric algebra. Paper below is from 1983, has anyone come across a later application? http://adsabs.harvard.edu/full/1983CeMec..30..151H http://adsabs.harvard.edu/full/1983CeMec..30..151H

ghaff 11y ago

Another classic book in the field is An Introduction to the Mathematics and Methods of Astrodynamics by Richard Battin of Draper Labs who passed away fairly recently. He developed and led the design of the guidance, navigation, and control systems for the Apollo flights at Draper. https://www.bostonglobe.com/metro/2014/02/23/richard-battin-developed-and-led-design-guidance-navigation-and-control-systems-for-apollo-flights/vxP9iIEfKuKpR7eCfes4fO/story.html https://www.bostonglobe.com/metro/2014/02/23/richard-battin-...

jcadam 11y ago

I remember getting a basic primer on this stuff when I attended a USAF Space Operations course back when I was in the Army Reserve. Our textbook (and an excellent book for the layperson interested in this sort of thing) was Understanding Space [1]. It's still sitting on my bookshelf at work and I occasionally have a reason to crack it open. As a software engineer in the aerospace industry, I was once working on a project to create a simulator for a new satellite program. I got stuck with writing a simulation model for the Attitude Determination and Control system (rather than something non-physics-y like the communications system). A lot of my job involved taking matlab scripts from the scientists and translating them into Ada code. An understanding of the basics of orbital mechanics came in very handy, as otherwise I would really not have had any way of knowing if my model was generating nonsensical output. Not to mention the onus was always on me to prove to a scientist that there was a bug in his algorithm. [1] http://www.amazon.com/Understanding-Space-Introduction-Astronautics-Technology/dp/0073407755/ref=sr_1_1?ie=UTF8&qid=1444234742&sr=8-1&keywords=Understanding+Space http://www.amazon.com/Understanding-Space-Introduction-Astro...

swagopopotamus 11y ago

Nice reference. Maybe now more of the stuff I hear on the orbital mechanics podcast (http://www.theorbitalmechanics.com/ http://www.theorbitalmechanics.com/) will make sense.