# Software for celestial mechanics

1. Jan 17, 2007

### lalbatros

Hello,

I would like a in-depth approach to some questions, like the Mercury's perihelion question. Precise definitions, precise result, access to full information.

I think that computer programs and related input data are probably the most precise answer to my need. What is calculated is dictated by theory and the results are dictated by the calculations.

Could some of you indicate me where I could find public software for Celestial Mechanics together with the needed input data (properties of the planets and the sun). I am equally well interested by pure Newtonian mechanics as by the PPN formulation.

Michel

2. Jan 17, 2007

### pervect

Staff Emeritus
3. Jan 17, 2007

### lalbatros

Thanks a lot pervect.

Do you know if this software contains the calculations based on Newtonian Mechanics of is it a based on interpolating pre-calculated tables?

Michel

4. Jan 18, 2007

### lalbatros

Hello,

I found a open source software called ORSA.
Would you know of similar source code related to celestial mechanics?
I am interrested by all sorts of numerical methods, and curious for symbolic maths on this topic.

thanks,

Michel

5. Jan 18, 2007

### Chris Hillman

What question is that?

Hi, lalbatros (Michel?),

Are you asking about precession of perihelia of Mercury as treated in gtr? If so, can you clarify why you feel that the treatment of Einstein's formula found in standard textbooks is inadequate?

An obviously relevant book is N.T. Roseveare, Mercury's perihelion, from Le Verrier to Einstein, Oxford University Press, 1982. And if you want the original sources, I guess you can start with Urbain J. Le Verrier (1811-1877), Théorie du mouvement de Mercure, Paris: Bachelier, 1845.

6. Jan 19, 2007

### lalbatros

Chris,

My idea is to have an hands-on approach on a few questions in GR. (as a hobby)
The applications I consider are:

• the perihelion question, myself with the numbers, not in a book
• the pionner 10/11 question, same approach

The second point may be more difficult because it involves orbits and a complicated analysis of the Doppler data. I could also be interrested by a simplified approach, just to look at the different effects. I would also like to compare the approximated ppn force formula with an exact solution.

And I don't know how these topics will compete with my regular job!

Thanks,

Michel

7. Jan 19, 2007

### Chris Hillman

Hi, Michel,

I appreciate that you are trying to describe what you have in mind, but I still can only guess what you want to do even in broad outline. It certainly isn't making things any easier that (as I guess), English is not your first language, but I am trying to take this into account!

I have the impression that you might be trying to say that you wish to review in great detail, regarding the observed motion of the inner planets and the observed motion of certain spacecraft, the entire process of
1. formulating a theory of gravitation,
2. forming a model in said theory of N-body motion in a planetary system,
(3a. designing methods of tracking planetary motion from Earth),
(3b. designing a spacecraft mission to study the alleged Pioneer effect),
4. taking observations,
5. analyzing the data.
Please don't take this the wrong way, but it worries me that I keep noticiing indications in your posts (and this is independent of the possible language barrier) that you have little idea of how the above process works, and that you are vastly underestimating the complexity of this process or the kinds of things which can go wrong.

Let me try again: people go to school to become astronomers, and this requires not only long years of classroom study, but more to the point, intense individual tuition with hands-on experience in the lab. And while many hear the call, few are eventually chosen, in part because this is such a demanding field. In my view the demands placed upon observational astronomers is particularly enormous, in terms of the sheer amount of stuff they need to master. In contrast, on the theoretical end, I consider mastering gtr (and related ideas like PPN) to be by far the least challenging task faced by an untrained amateur hoping to understand in detail the scientific issues involved here. BTW, few observational astronomers are masters of gtr; they mostly rely on their theoretical colleagues to handle the theoretical side. There is good reason for this: they are responsible for the really hard stuff, so it makes sense to delegate responsibility, as it were, wherever possible.

In short, you need to be a master of ordinary science (which requires not only training but extensive experience as a working scientist) before you can hope to follow the twists and turns of extraordinary science!

Let me try yet again: anyone truly wishing to understand all the issues would need to be among other things like a mechanic with enough knowledge to take apart a four-engine jetliner and put it back together again. Ditto, for an airport radar system. Ditto, for a million line FORTRAN program. That is just in terms of having practical experience with some of the "ordinary physics" which might explain the alleged effect, as well as with the data analysis issue.

Some specific points:

Well, I know that it is quite possible to learn gtr from books, as a hobby, since I did just that. But I had the benefit of extensive formal training in math, which was invaluable--- I doubt I could have picked up much gtr if I had been attempting to simultaneously pick up all the mathematical background, entirely on my own. One reason for this is that all the textbooks assume students share some common background, and while it would be difficult (and incredibly tedious) to try to explain this in detail, I am confident that most who have that background and who think about how they and their colleagues learn new material will be very much aware of how neccessary it is that one be prepared to understand what one reads in textbooks, by having formal training up to the starting point of the textbook in question.

By the same token, I happen to have a bit of laboratory experience in astronomy, so I have at least some appreciation of how many skills are needed to design experiments, take measurements, and analyze the data. There is a good deal of flying by instinct which takes judgement and experience; these are things which simply cannot be taught in any book. You have to learn them on-the-job in a lab, I think.

You failed to respond to my challenge to describe this alleged "question". This might be a mere problem of French(?) to English; maybe you meant "precession of perihelia phenomena"? But in any case, I have the sense you think there is room to doubt that Einstein's formula gives good results (or that more accurate formulas, typically derived in the context of gtr or the wider context of PPN formalism, give even better results); there is not!

This seems to suggest you expect to see the experimenter's notebooks, as it were, but I put it to you that without extensive laboratory experience, one has no chance whatever of understanding such a notebook. Similar comments for computer programs used in tracking spacecraft, for analyzing the data, and so on.

Here at least we all agree that there is an open problem: is the alleged Pioneer effect real, and if so, how does it manifest itself and what is its simplest explanation? (Roughly speaking.)

OK, about those orbits: did you notice that I have alluded on several recent occasions to the fact that the mathematical models used in the literature for tracking spacecraft are quite awkward hybrids of Newtonian and relativistic physics? There is actually a good reason for that, and it reinforces my point: this stuff is so complicated and has been built up in such tiny increments of trial and error that it would not be easy for NASA to adopt fully relativistic methods. Yet, the hybrid is being strained, perhaps to the breaking point, and there has been increasing interest in recent years (motivated by wider issues that resolving the alleged Pioneer effect, to be sure) in exploring fully relativistic navigation systems, among other things for purposes of spacecraft tracking and navigation in Solar system missions. But these proposals are sufficiently revolutionary that everyone agrees that NASA/ESA would need to put in huge effort and eventually test the waters with some kind of spacecraft mission intended primarily to test a rudimentary Coll navigation system (or some variant). I suggested that with sufficient cleverness (and astronomers are very clever indeed at getting maximal bang from the taxypayers buck), perhaps such a mission could double as a mission studying the alleged Pioneer effect in a "cleaner" manner.

What is this "PPN force formula"?

What exact solution would that be? To what equations? In what theory?

Do you mean: some kind of "exact solution" describing test particle motion in some spacetime model? Or some kind of "exact solution" describing the geometry of a spacetime model, allowing for some kind of hypothetical new physics?

Well, this is the thing. Why do you think you have the knowledge and expertise to study these issues? I am guessing that you think that only because you lack my level of astrometry-related knowledge and experience, which is certainly not enough to enable me to study many of the issues involved myself, but is enough for me to have some idea of why I lack enough knowledge and experience to be able to study very many of them! IOW, I know (or have some idea of) how much I do not know. And I have some appreciation of this: for which issues I might be able to acquire sufficient background to understand sufficiently well to follow the developing saga in some depth, and which issues I will have to leave to others who have the above-mentioned practical experience as working astronomers.

Which brings me to another point which I should stress in case it is not already obvious from what I said above: figuring out what is going on in the alleged "Pioneer effect" (if it indeed exists) will be a communal effort, because no one scientist has anything even approaching mastery of all the stuff which is involved in excluding possible sources of error, critiquing suggested theoretical models, and so on.

Again, please don't take this the wrong way! The bottom line is that science is really, really hard. Cutting edge science is the hardest of all. Scientists aren't trying to exclude anyone from sitting at the table, it is just that these issues are so extensive, manifold, subtle, and challenging that it takes not only long years of "book learning" but extensive on-the-job experience to appreciate most of them.

Last edited: Jan 19, 2007
8. Jan 19, 2007

### lalbatros

Chris,

Thanks a lot for your detailled reaction.
Just a quick answer right now concerning the question of -say- my background.

I have studied nuclear engineering in the late 70's. (to simplify how things work in my country).
I worked in plasma physics for 7 years and got a PhD in physics.
During that time I also started to learn theoretical physics for the fun, in addition to the plasma physics (wave propagation, turbulence, stability, fluctuations, ...). I read at least 50% of Landau, 90% of MTW (in 1983), and a lot of others things like Arnold, Sedov, Messiah, and also a lot about thermodynamics.
Clearly I am hobbyist in everything I do, and felt more confortable to switch to a totally different job: something in the heavy industry, where I am still working full time. I do a lot of different thing there including programming, process modeling, optimisation, ... and related hobbies like "calculation of phase diagrams", object oriented programming, ...

The "exercices" that I have choosen may look very naïve, but actually I am not obliged in any way to go in all details. I think that the data interpretation in itself is not very interresting and needs a lot of background. My first aim is to learn something by myself, this is sometimes easier than trying to understand some books. I have some precise point in mind, as explained previously. In addition, celestial mechanics should not be so complicated, considering that this was done without computers long ago.

Finally, note that the typical lifetime of such activities is 3 month, usually I switch to something else then. Often I oscillate between my job-hobbies and physics.

Thanks,

Michel

9. Jan 19, 2007

### lalbatros

Chris,

I read your answer a second time and I understand it completely, and I can only agree.
I was myself integrated in a large-scale research team for several years, and I know very well what team-science means. I wrote only three papers as first author, but was co-author of maybe 50 papers each with maybe 20 to 100 co-authors.

I should only make clear again, that as a hobbyist, I simply want to go a little bit further than simple readings in a book. I would like to (re-)discover things in a more realistic way, and enjoy such an approach. In addition, I also want to have a sharper understanding of some questions.

For example, for the drift of the perihelion, I would like to build a simple approximate formula including contributions from each planet, I would like also to evaluate roughly the order of magnitude of some correction to a simple model (oblateness, center of mass, GR, ...). I am sure I can find that somewhere, even on the net. But that is no fun!

What I call the PPN force formula is formula (3) in the Study of the anomalous acceleration of Pioneer 10 and 11, by Anderson & al.. I would start by considering some simple particular cases: radial motion and circular motion. In these particular case, I think it is possible to get exact solutions or very precise numerical solutions. I would like to try a comparison with the approximation from formula (3). At the same time, I would have the opportunity to understand the meaning of each term in the equation (3) and it would make it easier for me to understand the derivation of these kind of formula. In MTW, § 39.11 in not an easy piece, I guess I did not read it in 1983 (no pencil marks!).

Finally, I can't resist to tell you how I learned english.
I started at page 1 in MTW !
I attended some courses when I was at page 300 in MTW.
My pencil annotations in MTW indicate clearly how I assimilated the vocabulary.
This story goes a little further, but this becomes then a very personal story.
If I was obliged, I would only keep one book: MTW.

Michel

10. Jan 19, 2007

### Chris Hillman

On understanding precession and Pioneer anomaly

Hi, Michel,

That's quite impressive! Thank you for not over-reacting to my "proactive" warning.

I know it is difficult to provide such information without appearing to be tooting your own horn, but it is enormously valuable in knowing how to respond, and if you say something like "It might be helpful to know that my background includes ...", I think everyone would immediately understand why you have described your background.

Well, as you probably know one crucial issue involves meshing contributions from the motion of the other planets (particularly Jupiter) which in Einstein's day were treated by Newtonian means. What Einstein did in 1915 was to assume that as per the linear field equation of weak-field approximation to gtr, he could simply imagine subtracting off all the contributions which had been explained by Le Verrier and others in purely Newtonian terms. In fact, at that time, what people were talking about was what an "anomalous" extra precession which they couldn't seem to explain in Newtonian terms, and as Einstein famously stated, the moment when he found that his approximate calculation exactly matched the reported value of this anomalous term was one of the most intense moments of his life. Anyway, there are some subtle technical issues involved which you can infer from Weinberg's textbook.

Mastering enough Newtonian dynamics to follow the Newtonian computations in detail might well be a greater challenge that mastering gtr, depending on your background. As you probably know there are many textbooks which can provide the background you would need; I'd probably recommend Hagihara, Celestial mechanics (three volumes), MIT Press, 1970+, since that should contain everything you could possibly need. There are of course much shorter and more recent textbooks, but not all of these would really address your needs, I think.

As for solar oblateness, I have run some computations on that myself and came up with the result mentioned in Lightman et al., Problem book in relativity and gravitation, Princeton University Press, 1979, so I can probably provide some pointers there.

This is enormously helpful. I think I now have a much idea of what you have in mind, and now it sounds much more reasonable! A few judicious citations to an arXiv paper can be very helpful both in terms of explaining what you have in mind and also in terms of providing evidence that you are willing to follow up on any citations somelike me might provide (and also, it is nice to see that the paper you cited is in fact relevant to your question!).

OK, their Equation (3) is actually the acceleration; in the context of gtr, "gravitational force" would require some explanation. And even if they hadn't mentioned PPN, terms containing factors like $\frac{3+4\, \gamma}{2 \, c^2}$ would scream "PPN" to experienced readers (this $\gamma$ is a PPN parameter having nothing to do with elementary STR).

Even Einstein's crude 1915 approximate formula for the "extra-Newtonian precession" is in fact derived from an approximate solution to the equation of motion for a test particle in the Schwarzschild vacuum solution. (I am oversimplifying a bit--- Einstein was actually using the weak-field approximation to the exact Schwarzschild solution, which was found a few months later, and it turns out that this apparent simplification actually involves a subtle difficulty which is discussed by Weinberg.)

Good choice! Reading MTW certainly turned out to be a life-altering experience for me also.