Wikipedia:Reference desk/Archives/Science/2012 September 6

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September 6

Glyphosate based Herbicide

Can anyone direct me to the kinds of Glyphosate currently marketed? and the difference between a Glyphosate SL and Glyphosate WDG? Thanks! — Preceding unsigned comment added by Warrenssy (talk • contribs) 01:54, 6 September 2012 (UTC)

Google tells me that SL is a aqueous solution of the stuff, and that WDG may be a solid or powder ammonium salt formulation. Our Glyphosate article talks about various salt formulations and other mixtures/additives and their advantages. DMacks (talk) 02:04, 6 September 2012 (UTC)

Precipitation from NaBr and CaCl2

How can I analytically determine if a precipitate (of NaCl) will occur when mixing NaBr 15% by weight and CaCl2 3%-15% by weight? — Preceding unsigned comment added by Sslam (talk • contribs) 05:32, 6 September 2012 (UTC)

NaBr 90.5 g/100 mL (20 °C)

CaCl2 74.5 g/100mL (20 °C)

CaBr2 143 g/100 ml (20°C)

NaCl 359 g L−1 35.9 g/100 ml

What I can see from the given numbers is that you have to go more to 30-40% solutions to see precipitation. --Stone (talk) 07:17, 6 September 2012 (UTC)

You would need to check the oxidation states and electronegativity to discover if the reaction would occur. You would then need to check solubility tables to see at what concentration a precipitate might form. Then you'd need to hope you don't end up in super saturated territory. 83.70.170.48 (talk) 10:34, 6 September 2012 (UTC)

The oxidation states and electronegativity are of no problem with this compounds. --Stone (talk) 10:43, 6 September 2012 (UTC)

Psychosocial development

Accprding to most articles on psychosocial development, there are significant developments in adolescence and young adulthood up to about the age of 25 but are there significant developments beyond this? Clover345 (talk) 08:45, 6 September 2012 (UTC)

Erikson's stages of psychosocial development refers to another two at least. --TammyMoet (talk) 13:34, 6 September 2012 (UTC)

Piaget's theory of cognitive development has a final stage, "formal operational stage", which may not be complete in some people by their early adulthood, if ever. There's also Maslow's hierarchy of needs, which isn't strictly a theory of human development, but the top block of his pyramid (Self-actualization) is a phase of existance which most people don't develop until well into their adulthood. --Jayron32 13:44, 6 September 2012 (UTC)

Y-shaped moth

What species/genus/family includes those moths that have wings so thin and straight when folded up that they look like a Y? I googled Y moth, but it turns out that's just a moth with the letter Y as a mark on its wings. To find out, I looked at the pictures in every Lepidoptera family article on Wikipedia, and still didn't find such a moth. So what are these moths? Wiwaxia (talk) 09:25, 6 September 2012 (UTC)

Like this one? It it's a plume moth. Alansplodge (talk) 09:44, 6 September 2012 (UTC)

Yes! Like that one! Thank you! Wiwaxia (talk) 14:09, 6 September 2012 (UTC)

The picture in our article shows one with his wings extended - they're so ragged and scruffy it's not surprising that they roll them up neatly when they're not using them. I have added "Plume moth" to our incomplete List of moths. Alansplodge (talk) 11:47, 7 September 2012 (UTC)

Resolved

research paper authors and collaboration

A scientific publication of research paper has 1 to many authors from different universities/institutions. Does that always mean the research work published was done in collaboration or partnership among those authors? or Are the works done independently (without collaborating, without even knowing that someone else is doing other parts of same work) and spliced for a single paper publication? — Preceding unsigned comment added by 213.120.141.254 (talk) 09:42, 6 September 2012 (UTC)

I never heard of a forced splicing by a publisher. All the articles I know more than one author personally were written in collaboration. The amount of work from each individual might vary strongly. Even getting a very known person on the publication improving the canche of publication although that person was not really involved is also done. --Stone (talk) 10:50, 6 September 2012 (UTC)

thanks friend. — Preceding unsigned comment added by 213.120.141.254 (talk) 10:57, 6 September 2012 (UTC)

You may find the Alpher-Bethe-Gamow paper article interesting! --TammyMoet (talk) 13:32, 6 September 2012 (UTC)

In exprimental particle physics there can be vary large collaborations, with 1's to 1000's of authors. Within the small collaborations all authors may contribute directly to the paper, but for the large collaborations a smaller subgroup would work on a particlualar analysis. The other collaborators on the paper, would work on other parts of the exprement, or other analyses, but not directly this analysis. These "other" collaborators would check the work of the sub group, and suggest changes to the paper and analysis, but not all the authors would contribute to all the papers that their names are on. Dja1979 (talk) 16:52, 6 September 2012 (UTC)

I believe there have been cases where two groups submitted very similar papers to a journal at roughly the same time, and the journal editors persuaded the authors to combine forces, but I can't actually point to a specific example of that. More generally, it frequently happens that different parts of a study are carried out in different places with very little direct interaction, but the coordination is almost always done by the investigators themselves, not by external forces. Looie496 (talk) 16:57, 6 September 2012 (UTC)

I have heard of one case of that in mathematics. In case you care, it's: O. Bogopolski, A. Martino, O. Maslakova, and E. Ventura, The conjugacy problem is solvable in free-by-cyclic groups, Bull. London Math. Soc. 38 (2006). Not a famous paper, but I know one of the authors. Martino and Ventura wrote a paper together, and at more or less the same time Bogopolski and Maslakova wrote more or less the same paper. While they were being reviewed the referees noticed that the papers were basically the same, and so they had it combined all into one. Staecker (talk) 01:30, 7 September 2012 (UTC)

Taboos in other animals

I know that other animals don't have culture as sophisticated as humans, but do they also share the behavior called "having taboos?" Human examples of taboos include taboos on sex, bodily functions, nudity, etc. But do animals have any behaviors that seem to be the equivalent of our so-called taboos or is this behavior unique to humans? Narutolovehinata5 ^tccsdnew 10:44, 6 September 2012 (UTC)

Many species avoid incest, and in particular mother/son incest. Mating attempts by non-alpha males and sometimes females are often taboo. Among social predators there are sometimes specific rules about who eats a kill first, and violation of that rule can have severe consequences. Defecating in the den/lair may be a no-no, too. StuRat (talk) 10:51, 6 September 2012 (UTC)

Such restrictions may exist, Stu, but would they vary by "culture"? There are no "cultures" in non-human forms of life, I don't think, so the forms of constraint you refer to can't really be considered cultural taboos. The sorts of cultural taboos referred to by Narutolovehinata vary by culture, meaning that among humans there are cultural tendencies that have bearing on "sex, bodily functions, nudity, etc." Bus stop (talk) 13:19, 6 September 2012 (UTC)

I believe there are cultures in many social animals, in that different populations follow different codes of behavior. Common chimpanzees/bonobos are an example, with very different behaviors, although they might technically be a different species. StuRat (talk) 18:44, 7 September 2012 (UTC)

(edit conflict) There is probably a pheromone/odor component to it. Even in humans, there have been studies that show that people tend to be attracted to the smell of people who are genetically similar to themselves, but the attraction turns off when they are too similar. Wikikpedia does have an article titled Body odor and subconscious human sexual attraction which has a little bit of this; that people tend to be sexually disinterested in people that have odors that smell too much like themselves (and are thus likely close relatives). There is quite a likelyhood that a similar method for avoiding incest exists in other animals, especially in light of the fact that humans basically can't smell anything compared to other animals; many other animals with better senses of smell are quite likely to have a strong response to be disinterested, sexually, in their own parents and offspring. (post EC comment). It isn't exactly true that no other non-human animal has cultures. Chimpanzees are shown to develop distinct geographically-based tool using cultures; chimps from group A may use a certain method to extract termite from a mound, while chimps from group B use a completely different method. This difference probably represents shared group learning, which in a very primitive form of culture. this article from the popular science press covers the basics, but it is a well studied phenomenon. --Jayron32 13:25, 6 September 2012 (UTC)

I see what you're saying. This may be the rudiments of culture. This may show the spread of learning within a group (as you say). But I think you would agree that taboos that may frown on or promote gradations within behavior are specific to human culture. Covering up or exposing parts of the body occurs by degree of gradation across the "cultures" of the world. (Admittedly climate would play a role also in this.) But it seems human culture is so fine-tuned, relative to anything seen in the nonhuman world, that small differences in "dress codes" can make the difference between acceptability and unacceptability, within that culture. Bus stop (talk) 15:48, 6 September 2012 (UTC)

Jane Goodall published papers on social taboos among Chimpanzee groups, and also on the specific question posed; that is of the incest taboo within the Chimpanzee society. See this article which mentions the Chimp Incest Taboo, and this later article which heavily references it, as does this article. I can't find hewr original paper anywhere, but others reference it enough to make it clear that it was a vital work in understanding the situation. It should be noted that incest avoidance is not universal among mammals. this article discusses the variations on the theme. --Jayron32 16:58, 6 September 2012 (UTC)

The taboo word in those chimp articles is being used metaphorically--like talking about murdering horses--there is no learned rule, shame, shunning, or intervention. μηδείς (talk) 17:28, 6 September 2012 (UTC)

Taboo is a rather complex behavior. The closest analog to human culture is found primarily in learned feeding behaviors of various higher animals, such as various tool-using methods among different groups of chimps, regionally unique hunting techniques of dolphins and killer whales, and various habits unique to individual groups of crows and populations of some birds. See animal culture.

There are plenty of avoidance behaviors and negative behaviors in animals, like the neuroses caused by traumatic or unusual stimuli described in barnyard animals by Temple Grandin, and things maintained by direct aggression like pecking orders in eating or mating as mentioned above. Animals don't avoid incest, when they do, because they have a rule against it, but because as mentioned, they simply don't smell attractive to each other. When they do engage in incest they don't hide it because it is incest, even if they may hide it from a dominant male because of the sexual pecking order. Animals do not intervene to prevent incest in others or shun them for the incest if they engage in it.

Taboos in the strict sense in humans usually involve some complex arbitrary behavior, like not eating certain types of otherwise appetizing seafood, the requirement either to marry or not to marry your brother's widow, not eating meat on fridays, not shaking with the left hand. Animals do not have the conceptual capacity for those sorts of taboos in the strict sense. μηδείς (talk) 17:24, 6 September 2012 (UTC)

"Animals" is a big, varied group, to the point that it is difficult to say with any clarity or meaning that any principle such as this applies to it. Among some non-human animals, there are socially learned (and arbitrary) behaviors, and among others there are not. It isn't helpful to say definitive, sweeping statements about animal behavior, it needs to be considered on a species-by-species level to have any meaningfulness. --Jayron32 17:33, 6 September 2012 (UTC)

Can you give some examples of what you mean by an arbitrary behavior in animals? μηδείς (talk) 18:32, 6 September 2012 (UTC)

There is human behavior of "incest avoidance" and there is animal behavior of "incest avoidance" but no source (that I've seen) is suggesting that there is literally a "taboo" on incest among animals. "Taboo" implies an actuating mechanism entirely unknown to exist in the animal world. Bus stop (talk) 00:00, 7 September 2012 (UTC)

Taboos need not be arbitrary, that seems like WP:OR to me (indeed some taboos seem arbitrary to me, but that is not a defining characteristic). Our article taboo links directly to halal and kashrut as cases of systematic taboo. I posit that both of these systems have parts that were effective as a means of promoting public health. See e.g. Kashrut#Health_explanations and Halal#Explicitly_forbidden_substances. For example, refraining from eating carrion is not "arbitrary", it is in fact quite a generally good idea. SemanticMantis (talk) 03:47, 7 September 2012 (UTC)

So it turns out that some of the 613 mitzvot are mishpatim or edot, not all are chukim? Here I never suspected there might be rationales behind some taboos, unlike those against cotton/wool blends, and chicken Parmesan, yet I cleverly said "Taboos in the strict sense in humans usually involve some complex arbitrary behavior" anyway. And to think that the OED misled me by quoting sources that say taboos are often arbitrary and irrational! (I have been being sarcastic up to this point, in case you haven't noticed.) The wider definition may apply to animals metaphorically. The strict definition does not apply to animals that do not "exclud[e] something from use, approach, or mention because of its sacred and inviolable nature." (American Heritage) μηδείς (talk) 05:28, 7 September 2012 (UTC)

Sorry for coming in a bit late on this, but a very interesting "Taboo" amongst birds-of-prey is that they won't eat white food in their nest. Obviously this is to stop them eating their young, but it causes some interesting behaviour such as if they bring another bird-of-prey's chick back to the nest to feed to their own young, they can end up raising it alongside their own babies, because once it is in their nest they no longer regard it as food. People who breed owls know (or should know) that if they feed breeding owls on white mice before and during the breeding season, they can break down this "taboo", and the owls will eat their own chicks.124.191.176.212 (talk) 05:49, 10 September 2012 (UTC)

"increament in Amino Acids"

My 26 months old daugter didn't walk so far and one doctor told me that she has some increament in some Amino Acids that may effect this case and wanted to do further investigations that are not available in my country "Jorda" .. my question is what are the side effects of this Amino Acid increament for her ? Thank you all alot — Preceding unsigned comment added by 37.126.44.127 (talk) 12:20, 6 September 2012 (UTC)

I'm not sure I fully understood your question; we cannot give medical advice at the reference desk. Please consult a doctor for that. - Lindert (talk) 12:58, 6 September 2012 (UTC)

You haven't said enough for anyone to answer. I don't know if you're saying she has an abnormally high level of some amino acid, or if the doctor wants her to take an amino acid supplement. It matters a lot which amino acid it is. Start at amino acid and see if you recognize the name of it, then look up the one you want and see if you have more questions. Wnt (talk) 15:03, 6 September 2012 (UTC)

Our article on inborn errors of amino acid metabolism lists many conditions that meet the description, so it would be impossible to answer this even if we were permitted to. (I'm not keen on the title of the article, by the way.) Looie496 (talk) 16:51, 6 September 2012 (UTC)

I found some articles [1], [2], [3]. I think the title is a part of something like 'The Dielectric Increments of Amino Acids', which describes the state of the electrical property of the amino acids but not the quantity of them. -- RexRowan  Talk  17:05, 6 September 2012 (UTC)

Looie has the right idea. (And I agree on the name, and have moved that orphaned article to Congenital disorders of amino acid metabolism.) There are so many possible errors it is hard even to give suggestions on general reading. Given a young girl's life is at stake, only speaking with a medical doctor is appropriate. I would seek charity assistance if necessary to get the proper help. μηδείς (talk) 17:37, 6 September 2012 (UTC)

Overhead sun at noon in tropics

My understanding is that in the tropics, the (true-)noon sun is overhead twice per year: once when the summer solstice is approaching and the overhead sun is moving toward the Tropic of Cancer or Capricorn, and once after the solstice, when the overhead sun is moving back from the Tropic of Cancer or Capricorn toward the equator (which it will reach on the equinox). How can I find out on what dates the noon sun is overhead at a particular latitude in the tropics? Duoduoduo (talk) 14:51, 6 September 2012 (UTC)

You can calculate it from a current Ephemeris. There is also a lot of software apps that can do the calcs' for you.--Aspro (talk) 15:04, 6 September 2012 (UTC)

As seen from the Earth, the Sun appears to move along the ecliptic, which is different from the celestial equator (the position of the stars that always pass overhead at the equator), due to the obliquity of the ecliptic (i.e. the fact that the Earth's axis isn't perfectly perpendicular to the direction of the Sun). This produces what approximates simple trigonometric curve for the position of the Sun in the equatorial coordinate system - its apparent declination, I believe. This can be found on an ephemeris (though the term seems to mean very different things in some contexts). Note that there are corrections for the Earth's non-circular orbit, nutation, maybe other things? that make a professionally produced table more desirable than a back of the napkin calculation. I found such the Astronomical Almanac chart for 2013 at Google books - supposedly, according to the article and the site itself, this is available online at the Almanac's own site, but finding it there seems to be beyond my capabilities... anyway, look for the right ascension column, noting that it changes sign on the spring equinox. So far as I understand, whatever that number is will be the latitude at which the Sun appears directly overhead. Wnt (talk) 15:42, 6 September 2012 (UTC)

Since no one has linked it yet, the article Analemma is an interesting read. --Jayron32 16:50, 6 September 2012 (UTC)

Thanks, all. The Astronomical Almanac table at Google books was very helpful, as was the link to Analemma, from which I found Position of the Sun, from which I found the very helpful external link Sun position calculator . Duoduoduo (talk) 20:45, 6 September 2012 (UTC)

Changing course of the river Thames over the last 1000 years

Hi, I'm looking to find some resources that (accurately and scientifically) give the changing course / basin profile of the River Thames over the last 1000 years. Human impact has made a great difference to how and where it runs. Marshes have been drained, side channels built, land reclaimed. Any links appreciated. Cheers. Span (talk) 15:39, 6 September 2012 (UTC)

Seems to be the wrong kind of question for this page. Never mind. Span (talk) 10:57, 7 September 2012 (UTC)

No, it is exactly the right kind of question for this page. This page is staffed by volunteers, and sometimes you just get a situation where no one knows how to find the answer to your question. One option, if you are looking for scientific papers, is to use "Google Scholar" or "Google Books." You can find both of those if you select the "more" option in the black bar of Google. The "Books" option is listed on that first menu, and if you select "even more" from that menu, and page down to "Specialized search" you can find the "Scholar" option. If no one else can answer the question for you, that is one option to try. --Jayron32 12:51, 7 September 2012 (UTC)

I'll have a look at Google Scholar. Thanks Span (talk) 18:50, 7 September 2012 (UTC)

Maybe people at the Humanities reference desk? Seems a topic that could have been documented by historians. Ssscienccce (talk) 19:09, 7 September 2012 (UTC)

Science in Psychology

In science class I wondered if psychology counted as a science or a humanity. I asked my teacher and he told me that it was very much 'debatable'. I know that there are tests and such done about how people think but I'm not such of their extent - therefore how much is evidence based. I'm also aware that it doesn't seem as, um, 'science-y' as other areas of medicine.

So, my question would be: how much does science play a role in psychology and how much of it is based on logic or other methods? 86.138.171.71 (talk) 17:30, 6 September 2012 (UTC)

This has been a recent topic in science news. Various articles. Basically, psychopharmacology and neuropsychology are sciences, and psychiatry is an art. See also "That's right. Psychology isn't science. Why can we definitively say that? Because psychology often does not meet the five basic requirements for a field to be considered scientifically rigorous: (1) Clearly defined terminology, (2) Quantifiability, (3) Highly controlled experimental conditions, (4) Reproducibility, and (5) Predictability and testability."[4] μηδείς (talk) 17:45, 6 September 2012 (UTC)

It depends on how you define "science" (something that nobody has ever been able to agree upon, despite a lot of arguing about it), and what you are calling "psychology." There are branches of psychology that are highly evidenced-based and rely on completely testable assertions about how the brain works. There are branches of it that are more of a social science — still evidence-based, but more qualitative. There are branches of it which are pure therapy and don't even try to be falsifiable. And there are branches of it which are more or less philosophical in nature. It's a huge umbrella term. Even some of the notoriously non-sciencey parts of it, like psychotherapy, can be tested as therapies in a scientific fashion (e.g. try a specific type of treatment on 1,000 people versus another treatment on another 1,000, see which one makes people feel more "cured" than the other, and so on). So "it's debatable" is a fair-enough assessment, but I might break it down to, "it depends exactly what you're talking about; some parts of psychology are more debatable than others." --Mr.98 (talk) 17:59, 6 September 2012 (UTC)

Thank you for the swift answers. Very much appreciated! — Preceding unsigned comment added by 86.138.171.71 (talk) 18:22, 6 September 2012 (UTC)

I did a Psychology degree at one polytechnic, and my friend did a Psychology degree at a university. Hers was BSc: mine was BA. We never did figure out what the difference was. However, from what I studied, I can say that Medeis's comment is totally wrong in all 5 points. Sorry. Mr.98's comment is nearer the mark. --TammyMoet (talk) 19:01, 6 September 2012 (UTC)

I was quoting those five points as the central point of an article, the link to which is at the end of the quote. Did you mean that you disagree with the validity of the criteria, Tammy, or did you mean that psychology indeed does fit the 5 criteria? μηδείς (talk) 19:09, 6 September 2012 (UTC)

I think you would have a hard time arguing that someone like Daniel Kahneman (a famous psychologist) is not a scientist.. This question is essentially about the Demarcation problem. Vespine (talk) 22:36, 6 September 2012 (UTC)

I am familiar with his work, and have his recent book. I am quite unfamiliar with where, other than calling psychiatry an art, I may have stated that no psychology is science. μηδείς (talk) 23:12, 6 September 2012 (UTC)

Sorry, I've probably not indented properly, I was trying to reply to the OP, not directly to your comments Medeis.. Vespine (talk) 23:29, 6 September 2012 (UTC)

It's very much a social science. the better question is what line you've drawn/accept between "science" and the rest of the liberal arts (and i say that with a firm appreciation that the true sciences are much more rigorous and devoid of political ambitions and preconceptions than most liberal arts are). But of course people being what they are, even there we get issues. Shadowjams (talk) 10:33, 7 September 2012 (UTC)

To clarify, Peer review, reproduciable results, and all that other stuff that indicates you found something meaningful, those are what real science is. Shadowjams (talk) 10:39, 7 September 2012 (UTC)

I've seen loads of questionable psychology papers, like using psychology students to confirm hypotheses on stereotypes in society, with questions like "categorise these people as you think the average American would judge them", and the authors showing surprise at one of the results: "Although cross-culturally a gender subgroup of sexy women appeared reliably, this group did not emerge as incompetent but warm in these Massachusetts samples. Although we had brainless bimbo in mind, some of our respondents may have been thinking villainous vamp.". That's a quote from Susan Fiske...

Or when it comes to depressive realism: Test-persons get a button and a lamp, the lamp randomly on or off at each try, independent of whether or not the button was pushed. After a series of runs they are asked if they influenced the lamp or not. Depressed people judged more accurately than non-depressed ones and their results stayed the same independent of the pace at which the test was conducted. Non-depressed people judged themselves to have had more control when the time period between tries was longer. Conclusion: depressive realism effects occur because depressed people do not use all the available evidence to arrive at their judgements rather than because they are being realistic.. Conclusion justified by Within the framework of an associative model the time interval is conceptualised as the context. Integration of the time interval into the "no action, no response" situation would weaken the context’s association with the outcome, thereby allowing the response to gain more associative strength. (Msetfi, R. M., Murphy, R. A., & Simpson, J. 2007)

I distrust theories where being right means you didn't think it through... Ssscienccce (talk) 21:12, 7 September 2012 (UTC)

I've seen loads of questionable psychology papers, but also loads of questionable evolutionary biology papers, questionable sociology papers, and questionable physics papers. (There may be loads of questionable mathematics papers, too, out there in the world, but I wouldn't know). I'm not sure the fact that 90% of everything is crap necessarily tells you about the epistemological underpinnings of the discipline. --Mr.98 (talk) 01:41, 8 September 2012 (UTC)

Maybe 90% of papers are crap in all disciplines, but how many of these are notable? I wasn't talking about obscure papers or authors, rather papers that turn up in the reference list of most publications dealing with the subject. Papers that are quoted in Wikipedia articles, whose authors may have their own article in wikipedia; and in the case of Fiske even testified in court cases as expert witness regarding the subject matter. I do recognize that my examples say little about whether or not psychology is a science. Ssscienccce (talk) 12:20, 8 September 2012 (UTC)

continuous/gradient refractive index

Can anybody provide me with some equations on estimating the (radius of) curvature of a path of light passing through a medium which has a continuously-varying refractive index where the gradient is represented by dn/dx ? How would I calculate the path the light ray takes through the medium? This is a very common situation and I am puzzled why I cannot find any equations online about this situation, given that it is important for atmospheric optics, fibre optic cables, etc. 137.54.24.118 (talk) 19:15, 6 September 2012 (UTC)

Sounds like it should be in Gradient-index optics. Not my field though, so I don't know if the math there fits your need (either specifically, or as a bit of theory to derive more). DMacks (talk) 21:01, 6 September 2012 (UTC)

In general, no closed form solution exists to such problems unless n(x) happens to have a very convenient form. Often the solution is simply computed numerically. For example, the first order differential equation equivalent to Snell's Law is:

${d\theta \over dx}=-{1 \over n(x)}{dn \over dx}\,{\text{tan}}(\theta (x))$

Dragons flight (talk) 21:33, 6 September 2012 (UTC)

Yeah, per Dragons Flight, this sounds like a straightforward problem in ODE integration. If you're lucky, there's a closed form solution, otherwise use your favorite numerical approximation such as the Runge-Kutta method. We have an article Numerical methods for ordinary differential equations that discusses the basics, and there's lots of articles on more specialized methods. If you haven't studied ODE's at all, then that's your basic problem, and you should spend some time taking a class or reading a textbook (typically a second-semester calculus text). Once you have done that, the simpler approaches to numerical solutions are straightforward. You could also ask at the math desk WP:RDMA if you need further help. 67.119.15.30 (talk) 17:52, 7 September 2012 (UTC)

Can I know these very convenient forms? This is in anticipation of a problem set, which I haven't received yet. 67.233.112.218 (talk) 22:03, 7 September 2012 (UTC)

Normally one solves this kind of problem by raytracing. As noted above, there are closed-form solutions (or approximations) for certain special cases. I believe some types of gradient-index optical fiber have (approximate) closed-form solutions, but I don't recall the details.--Srleffler (talk) 17:36, 10 September 2012 (UTC)

Dawn mission

As far as I am aware, the Dawn Mission to Vesta and the planet Ceres is the first time a spacecraft will leave the orbit of one extraterrestrial body to enter the orbit of another. See this ongoing discussion. What sort of regarded sources would comment on the significance of this "first"? Thanks. μηδείς (talk) 21:18, 6 September 2012 (UTC)

Well, I just came across a rather good article in the Sep 2012 Discover. μηδείς (talk) 18:39, 7 September 2012 (UTC)