Date: Wed, 20 Mar 1996 14:07:10 -0600 (CST) From: MA Lloyd To: gurpsnet-l@io.com Subject: Re: Realistic Interplanetary Travel On Wed, 20 Mar 1996, Sue and Sean wrote: > A Hohmann orbit requires one short eccentricity-changing burn at the > apo/periapsis and another at the peri/apoapsis. It is not intended > for the constant low thrust of an electric drive, so I'm sure that a > different course (not "orbit," since the spacecraft would not be in > free-fall) would be used. Absolutely, but any such course uses more fuel, barring gravity assists, than impulsive burns of the same Isp. Of course you can't MAKE impulsive burns of the same Isp... On the original topic, I have appended below some clips from a recent discussion of good Orbital Mechanics books on sci.space.tech from people who usually know what they are talking about. A few others include WC Nelson Space Mechanics I have never seen this one, but it is occassionally recommended as an introduction. WT Thomson Introduction to Space Dynamics. Rather shallow, but not bad, and supposedly available in Dover reprint. Szebahely Theory of Orbits. Highly mathematical and largely theoretical. Baker and Makemson An Introduction to Astrodynamics. A personal favorite, primarily astronomy rather than spacecraft oriented, but it touches on a wide range of topics. HO Ruppe Introduction to Astronautics. Grandfather of the space engineering handbooks, two volumes. Has a nice discussion of low thrust trajectories such as those relevant to electric propulsion. Of the others mentioned below, Roy is quite good. Fundemntals of Astrodynamics is not as bad as Henry makes out, and it is cheap and easy to find as a Dover reprint. -- MA Lloyd (malloy00@io.com) ============================== From: henry%spenford@zoo.toronto.edu (Henry Spencer) Subject: books on orbital dynamics Also, a general comment: the books' material on numerical methods should be taken with a large grain of salt. That field has advanced a great deal recently, and most of these books are well behind the times. For example, most any discussion of "multistep" or "predictor-corrector" integration methods can safely be skipped -- today's Richardson methods are better than most predictor-corrector schemes, certainly better than any you'll find discussed in an introductory book (and far superior to Runge-Kutta methods for most orbital-dynamics work). For numerical stuff I recommend "Numerical Recipes", 2nd ed., Press et al, Cambridge U Press, ISBN 0-521-43064-X, $$$ but worth it. Orbital Mechanics; John E. Prussing & Bruce A. Conway; Oxford U Press 1993; ISBN 0-19-507834-9, $$. I bought this a year or two, more or less sight unseen, on speculation. When it came, I was disappointed: it was *thin*, only a couple of hundred pages, and the list of topics covered was not overly large. I put it aside for later reading. I grudgingly decided to look at it when I was reading the other books, and revised my opinion steeply upward. This book is *still* too thin. It badly needs to be twice the length so it can cover more topics. Within its limited scope, however, it does an excellent job on the basics. Even some of the things that look drab at first glance acquire more interest on closer inspection. It's up to date and well focused on spaceflight; for example, you'll find a fairly complete discussion of gravity assists. Even the notes on numerical methods are reasonably current. I recommend this as the first orbital- dynamics book for serious space cadets (those who don't plan to stop with one book). Its coverage is a bit limited for those who do want only one book, but at the moment I can't think of a better choice. Orbital Motion, 3rd ed.; A.E. Roy; Adam Hilger 1988; ISBN 0-85274-229-0 (softcover), $$. This used to be my first-book choice, and now I think I'd call it the recommended second book. This one isn't thin; although it's billed as a student text, like P&C, the author clearly has a rather more energetic type of student in mind. The coverage isn't encyclopedic but it's broad. This is the book I tend to use as a reference for everything but the really deep stuff. The one negative thing I have to say about this book is that it's a very *classical* orbital-dynamics book. The emphasis is on astronomy, not spaceflight. For example, rendezvous is barely mentioned, and although you are given the tools you need to figure out gravity assist, it's not actually discussed. On the other hand, there's a whole chapter on the evolution and stability of the solar system, and another on many-body star systems. This book is wonderful as a supplementary source but is not a good first book for a space cadet. Fundamentals of Astrodynamics; Roger R. Bate, Donald D. Mueller, Jerry E. White; Dover 1971; ISBN 0-486-60061-0 (softcover), $. This book is very widely known and it's cheap. It tends to be the first book people mention in this connection, especially in North America. I've never liked it, and finally I've figured out why. This book was written as a text for the USAF Academy a quarter of a century ago, and *that* is the root of its problems. It is completely restricted to things that the USAF Academy considered to be of immediate relevance in about 1970. You get the basics of orbits, okay, and the stuff on lunar trajectories is interesting (that was the heyday of Apollo, remember)... but other than that it falls flat. Close to *half the book* is spent on orbit determination, which to my mind is a specialist problem that deserves one short chapter in an introductory book -- if I want to know all the gory details, I'll read Escobal's book on it (see below). There's a whole chapter on ballistic-missile trajectories. And there's little on anything even slightly advanced: nothing on rendezvous, nothing on multi-body dynamics, one terse look at interplanetary trajectories, a minimal discussion of perturbations. I don't recommend this book; get P&C instead. Methods of Orbit Determination, updated edition; Pedro Ramon Escobal; Krieger 1976; ISBN 0-88275-319-3, $$$. This is *the* book on determining orbits from observations. Moreover, its early chapters are an introduction to orbital dynamics and related topics, rather terse but with unusually broad coverage (for example, it discusses how to determine when a satellite passes into the shadow of a planet, and how to determine rise and set times of a satellite orbiting a planet which is oblate rather than perfectly spherical). It's mildly useful in that regard, although I wouldn't recommend actually buying it unless you want the orbit-determination material. As I've mentioned above, in my opinion orbit determination is a specialist topic (and I would caution that it's one I'm not intimately familiar with). Nearly twenty years after this book's updating -- thirty after its first publication -- it is still considered the authority on the subject. Most good orbital-dynamics books will cover one or two methods; this book tries to cover *all* of them, and mostly succeeds. It could use another updating, as there are brief allusions to (and an added appendix on) a few topics that the original didn't cover. The comments on numerical methods could undoubtedly use updating, although the comparisons of the numerical aspects of the different methods should still be valid. But it's still the book to buy to learn about the subject. Methods of Astrodynamics; Pedro Ramon Escobal; John Wiley & Sons 1968; no ISBN; almost certainly out of print. This book is intended not as a stand-alone book, but as a followup to the orbital-dynamics material in Methods of Orbit Determination (see above). It skips the elementary material entirely, and goes straight into selected topics in optimization, interplanetary and lunar trajectories, and some related issues. A very interesting reference if you can find it, but don't buy it as an introductory book. An Introduction to the Mathematics and Methods of Astrodynamics; R.H. Battin; AIAA 1987; ISBN 0-930403-25-8. This book I've skimmed rather than read closely. (Once you read three or four of these books, you reach the point where you can just skim the table of contents looking for new topics, and rarely find any.) I would say that this book is mostly of historical interest. There's not much here that isn't in the other books, and some of it seems rather dated. The good parts are the prolog and epilog, which talk about Battin's involvement with missile guidance problems and the design of the Apollo on-board navigation system, and how crucial problems were solved. Find the book in your local technical library and read those bits. Orbital Mechanics; Chobotov (ed); AIAA 1991; ISBN 1-56347-007-1, $$$. Another book skimmed rather than read, because it's mostly redundant with the earlier ones. It goes into a little more depth on a number of topics, but only a little. More current than Battin. Might be worth considering as an alternative to Roy: less breadth, but more of a spaceflight slant. Somewhat expensive. Second edition rumored to be in the works. That's it for my reading at the moment. Comments and additions welcome. -- Space will not be opened by always | Henry Spencer leaving it to another generation. --Bill Gaubatz | henry@zoo.toronto.edu From: dakin@eng.umd.edu (Dave Akin) Subject: Re: books on orbital dynamics In article , henry%spenford@zoo.toronto.edu (Henry Spencer) wrote: > > An Introduction to the Mathematics and Methods of Astrodynamics; R.H. > Battin; AIAA 1987; ISBN 0-930403-25-8. > I'm sorry, but (IMHO) you've completely missed the boat on Battin, probably because you skimmed it rather than reading it carefully. This is by far the most mathematically rigorous of the available crop of astrodynamics books. Battin has an understanding of the theory and applications of Lambert's problem that exceeds those of us mere mortals :-), and derives everything mathematically from first principles. If someone wants to pick up enough astrodynamics to calculate an orbit or delta-V, I'll steer them somewhere else (there are several other good texts out besides those on your list), but when someone needs to truly understand the fundamentals and nuances of astrodynamics, I don't think anything can touch Battin as a reference. In fact, we've been teaching graduate level astrodynamics from Battin ever since the book was published. (I will admit to some amount of bias here - I used Battin's original book, long out of print, when I took astrodynamics in grad school - from Dick Battin...) -- David L. Akin | "The UMd Space Systems Lab: Director, Space Systems Laboratory | Where tomorrow's technology University of Maryland | is being developed sometime http://www.ssl.umd.edu/ | late tonight." From: rlorenz@lpl.arizona.edu (Ralph Lorenz) Subject: Re: books on orbital dynamics It is worth noting that the handful of 'Space Engineering' textbooks typically have a chapter or two on orbital dynamics, at least good enough for most delta-V estimations etc. The two I use are Larson and Wertz - Space Mission Analysis and Design Space Technology Library ISBN 1-881883-01-9 and Griffin and French - Space Vehicle Design AIAA Education Series ISBN 0-930403-90-8 (I would probably have bought Fortescue and Stark's Space Systems Engineering, but I have the printed set of notes from which the book was generated) In terms of orbital dynamics, the latter two are probably better. The Larson and Wertz orbital dynamics chapter is much more a 'working' chapter for looking up quick formulae for common problems (eg Stationkeeping delta-V). The book has an excellent overall 'systems' approach and covers things like constellation design and instrument viewing, which aren't addressed in the same way in the other two books. One glaring omission from Larson and Wertz is that re-entry dynamics and aerothermodynamics isn't covered at all, whereas the other two do quite nicely. Of F&S versus G&F, I'd probably prefer the former, in particular because I will never get the hang of using Btu/ft^1.5 and slug/ft^3 as units for 20th century problems - imperial units creep into G&Fs aerothermo treatments. As for orbital dynamics books per se, if I can't find it in the above books, I usually have use Roy. I have looked at Bate Muller and White, and with the single exception of its treatment of ballistic missile trajectories, I though it was horrid. Ralph Lorenz Lunar and Planetary Lab University of Arizona From: Patrick Marsden Subject: Re: "Orbital Mechanics" by Chobotov Paul Kniest wrote: >In article Max O. Lange, >mlange@vmprofs.estec.esa.nl writes: >>Hello out there, >> >>There is this fantastic book, Orbital Mechanics, by V.A. Chobotov, and I >>heard that an even better second edition was due out soon. Does any of you >>know if it's already available, or when? > >This sounds great. What are the topics covered? Is it detailed or just general? >What's the ISBN? > >Paul It's an AIAA publication. Be careful of the first edition - there are some errors, not to mention some incomplete sentences. I'm guessing the second edition will be corrected. IMO, the two best texts on the subject: Introductory- "Fundamentals of Astrodynamics," Bate, Mueller, and White, ISBN 0-486-60061-0 Advanced- "An Introduction to the Mathematics and Methods of Astrodynamics," ISBN 0-930403-25-8 -- Patrick D. Marsden | Naval Research Laboratory | Opinions are Computational Physics, Inc. | Code 7641 | mine and mine Planetary Atmospheres Section | Washington, D.C. 20375 | alone. http://ismap6.nrl.navy.mil/ | marsden@csmap1.nrl.navy.mil | (202)-404-1292 =================== From: fcrary@rintintin.Colorado.EDU (Frank Crary) Date: 16 Feb 1996 02:55:00 GMT Newsgroups: sci.space.tech Subject: Re: Interplanetary travel times question. In article , John Peck wrote: >I am having trouble tracking down a simplified, "ballpark" method for >calculating interplanetary travel times for a spacecraft under constant >acceleration. One source gives the equation >Time = (2 * sqr(A * D)) / A >where A is acceleration and D is the distance to be travelled. >This takes deceleration to stop at at destination into account. >It strikes me as inaccurate since it appears to apply only to a >static distance and the planets, of course, are moving. Yes. This equation assumes that the acceleration is very high, and the entire trip is so rapid that the planets don't have time to move significantly. In addition, the acceleration is constant, all the way. In that limit, it is correct (you need to also match velocities with the target planet, but given the high level of acceleration, that's almost a trivial detail.) Unfortunately, there is no existing rocket that could even come close to that kind of trajectory. For any realistic system, this would require absurdly great amounts of fuel. There are two, realistic and relatively simple estimates for travel times. Both make assumptions about the trajectory, but they are fairly realistic assumptions. The first is a "Hohmann" or minimum energy trajectory. This involves a short, rapid acceleration at the start and another short, rapid acceleration at the end. Between the two, the spacecraft follows an orbit with its perihelion at one planet and apohelion at the other. This trajectory, in most cases, requires the least change in velocity and therefore the least fuel consumption. In this case, the spacecraft takes half of an orbit to reach its destination. This gives a travel time of 0.25*P_1*(1 + R_2/R_1)^1.5 Where R_1 and R_2 are the distances of the two planets from the Sun, and P_1 is the period of the the first planet's orbit. This sort of trajectory is, at least approximately, that used by almost all past or existing interplanetary spacecraft and most of the proposed ones. The second possibility is a very slow, constant acceleration, of the sort you would expect from an ion drive or solar sail. If the acceleration is much lower that R/P^2, where R and P are the distance from the Sun and period of the outermost planet, then the travel time is well approximated by 2*pi*R_1/P_1*SQRT(1 - R_1/R_2)/a Where R_1 and P_1 are the distance from the Sun and the period of the inner planet, R_2 the distance between the Sun and the outer planet and a the acceleration of the spacecraft. (Also, take care to use consistent units: If a is in m/s^2, P_1 must be in seconds.) The third possibility is anything else: Long periods of acceleration at a > R/P^2; short periods of acceleration which aren't used to produce minimum energy trajectories, etc. In general, there is no simple equation for the resulting travel times. Most often, there isn't an equation at all, and the trajectory has to be solved numerically. Frank Crary CU Boulder