# User talk:NOrbeck

## Free falling body problem

Thanks for your interest in my question. Nedim Ardoğa (talk) 07:47, 25 January 2010 (UTC)

## Drastic changes

Hallo, Norbeck. I see that you're proposing and making some drastic changes. Reorganization and correction of content is a very valuable activity, and I actually do agree with what I've seen (so far) of your reasons -- but it seems that you haven't offered reasons for every substantial change you have made.

Editing is often a collective activity, and I suggest that it would go down well with the editing community, if you were to give reasons for each edit. In case of moving substantial pieces of subject-matter, I also suggest that it would be good, first, to put a note on the talk page about what you propose, and allow just a reasonable time for aware editors to add their views -- which might show some strong reasons for doing something a bit differently -- before actually doing the big edit.

With best wishes -- Terry0051 (talk) 19:30, 27 January 2010 (UTC)

I'll gladly add references explanations and justifications. Which pages are you referring to? I've proposed some drastic changes, and there are many more I like to see. The pages I've been working on haven't changed much in years, so I incorrectly assumed that no one was still interested. I should have assumed they hadn't changed because people liked them just the way they were.
I figure I've blown about 4000 hours on the classical two body problem, naturally I've found myself wasting more hours debating laymen with no commitment to the subject. At this rate fixing the errors will take months. Part of the problem is that several of the articles are nothing but unsourced confabulation, in many cases the spurious information was simply made up. Editors who have learned the subject from these pages have no way of recognizing the problem. The fact that essentially no one (besides you) has noticed the absurdity of these pages indicates that this topic has not had significant expert attention since at least 2004. Is there any way to suggest a comprehensive review and fact-check? --Norbeck (talk) 22:11, 27 January 2010 (UTC)

Thanks for your response. I find it hard to know exactly what to say, but here's a start. (I don't mean to write as if I've got lots of experience, but it might get to sound that way, so just discount it!)

Point #1 is that 'comprehensive reviews' are probably not that easy to achieve. I would liken WP more to a hive of busy bees than to an organization that does comprehensive reviews. (That's not to say that WP is disorganized, exactly. A hive of bees ends up making a pretty organized honeycomb with valuable content, but how that result is achieved can be a bit mysterious!)

Wikipedia has habits of its own. Anybody can edit, and anybody does. It's great that you are bringing the enthusiasm (and expertise, but see below) to get some sense into an area that partly lacks it. But make no mistake, your edits are going to be re-edited by other people with all levels of acquaintance with the subject -- or none. Some unsuitable edits are defended against by the anti-vandal patrollers, but others will be less easy to deal with.

One of the peculiarities is that this is a 'pseudonymous editing environment', where nobody has any credentials, and any of us who think we are experts must put aside any expectation of being acknowledged as such. (Editing WP for the better can be a pretty thankless task at times.) Edits are only as 'good' as the citations (references) or consensus (or both) that support them. (I dare to suggest that 'good in the real world' does not always equate to 'Wikipedia-good', and v.v.! The puzzle, if you like, may be to shift the WP-good-or-acceptable in the general direction of the real-world-good!) Since experts are not acknowledged as such, they can really only show their expertise by enabling verification of the content that they introduce, through citing relevant external reliable sources in support.

Reasons for edits can help acceptability. They don't have to be long and involved, there's a kind of shorthand for them, which you'll get used to. In fact the longer the reasons and arguments are, the worse it can easily be, because lengthy reasons can easily begin to look more like editor's original research (which is a no-no), and less like cross-references to reliable external sources directly on point (which are good).

I've gone on too long. I'll return with a couple of specific suggestions that hopefully you might find useful. Best wishes, Terry0051 (talk) 01:41, 28 January 2010 (UTC)

## Free fall

Hi Norbeck

I have posted a question on the talk page of Gravitational acceleration (Oct.14). You have answered that question on the Free fall page. But I want to make it clearer. Since y = 0 for free fall, arccos (y/y0) = л/2.

${\displaystyle \mathbf {t} ={\sqrt {\frac {{y_{0}}^{3}}{2\cdot \mu }}}\cdot {\frac {\pi }{2}}}$

I used your equation to calculate the free fall time from Earth orbital radius to Sun and obtained 64.56 days which is in perfect agreement with the earlier value I‘ve obtained by numarical methods. Furthermore, I obtained the following equality.

Let T be the period of orbital revolution and t be the free fall time from that orbit,

${\displaystyle \mathbf {t} ={\sqrt {\frac {1}{32}}}\cdot T}$

Since, this equality is independent of the value of μ, it is universally applicaple to all star systems. (I assumed circular orbits.)

Thanks for your very valuable contribution. (By the way, how about designing a personal page ?) Nedim Ardoğa (talk) 09:53, 28 January 2010 (UTC)

The equation for the total total free fall time is here: Free-fall time, the rest of the equations should probably be be on that page too. I didn't want to duplicate the same info but they probably belong there too.
Not to many people have discovered the relationship between orbital period and freefall time. I suggest you add it to the Free-fall time page. I used to run integrations to make these calculations too. I always wondered why the equations weren't in textbooks, later I found out that no one had discovered them yet. I guess all of the gravity experts were too busy studying GL(n,R) Wormholes and Waves in Diverse Dimensions. --Norbeck (talk) 04:53, 29 January 2010 (UTC)
The relationship above is well-known. If you want a really easy derivation with no calculus, you simply need to know that the orbital period depends ONLY on the semimajor axis of the orbit, regardless of eccentricity. A linear fall can be thought of as half of an orbit with an infinite excentricity, so the time for a fall into a large primary is just 1/2 of the period for a very "skinny" orbit of half the radius (one that goes down to just graze the primary, as happens with high eccentricity orbits). If you insert r/2 into the Kepler formula you get P proportional to r^(3/2), which in the case of r = 1/2 gives P = (1/2)^3/2 = (1/8)^1/2 of original P. Half of THIS (to give you just the "fall" P and not the return P) is 1/2* (1/8)^1/2 = (1/4)^1/2 * (1/8) = (1/32)^1/2. SBHarris 18:50, 2 February 2010 (UTC)

## Talk:Kepler's_Equation

Hello. I made some comments on the discussion page. I hesitate to edit the article itself. Bo Jacoby (talk) 05:46, 4 June 2010 (UTC).

## Please explain use of reduced mass

Please see Talk:Kepler problem in general relativity#Advantages of reduced mass in exposition? and Talk:Kepler problem in general relativity#Magnitude of reduced-mass correction. WillowW and I would like to see some explanation or justification for your introduction of reduced mass. Thank you. JRSpriggs (talk) 07:14, 10 July 2010 (UTC)

I'm not sure the change to explaining things in terms of the full two body problem instead of motion in a central force field is all that helpful. The end result is more general, but also more difficult to assimilate by laymen and beginners. The textbooks I know start with central forcefields and then explain how the two body problem can be reduced to it. Martijn Meijering (talk) 14:29, 15 August 2010 (UTC)

"Make everything as simple as possible, but not simpler" -- Einstein
"The purpose of Wikipedia is to present facts, not to teach subject matter. It is not appropriate to create or edit articles that read as textbooks" -- WP:NotTextBook

The reduced mass occurs in the analysis of 2-body systems. It has nothing to do with gravity or even forces in general; the reduced mass even occurs in kinematical equations where there are no forces at all. If confusion arises from the use of the reduced mass, the problem is not with the pages describing orbital mechanics, it lies in the pages describing elementary kinematics and dynamics. For students familar with basic kinematics and dynamics, gravitational equations neglecting the reduced mass are not "simpler", just glaringly incorrect. For example, the force between two free masses is the acceleration times the reduced mass. The fact that many readers will not be familiar with the reduced mass is an argument that its use should be stressed, not marginalized.

In practice, the gravitational 1-body problem is rarely accurate enough to be useful because most of the orbiting bodies in the universe have similar masses. One-body problems appear to violate Newton's third law, but it is possible to imagine an external force that dynamically holds the central source fixed in space. However, the "1-body gravitational problem" is strictly non-physical because unlike other 1-body problems, the central source is free by definition. The 1-body approximation is only slightly simpler than the 2-body problem, while the errors it introduces are as high as 100%.

My college professor taught the "1-body approximation" immediately before the "2-body problem". He also made it very clear each time he made a simplifying assumption or approximation. The problem with that approach here is that Wikipedia is non-sequential. There is no way to "start" with a simplified topic and then generalize it afterwards.

In a certain sense Wikipedia editors have no discretion to include or ignore the reduced mass, either it appears in the laws of nature or it does not. For example: If ${\displaystyle \scriptstyle M_{Earth}}$, and ${\displaystyle \scriptstyle M_{Moon}}$ are two stationary masses, ${\displaystyle \scriptstyle \mu }$ is the reduced mass, x is their separation, and f is the force, then: ${\displaystyle {\ddot {x}}={\frac {f}{M_{Earth}}}}$ is wrong. The correct equation is: ${\displaystyle {\ddot {x}}={\frac {f}{\mu }}}$.
We do have discretion over how equations are presented:

${\displaystyle {\ddot {x}}={\frac {f}{\mu }}={\frac {(M_{Earth}+M_{Moon})f}{M_{Earth}M_{Moon}}}}$

A better example is the total kinetic energy of two bodies:

${\displaystyle KE_{total}=M{\frac {(v_{M})^{2}}{2}}+m{\frac {(v_{m})^{2}}{2}}}$
${\displaystyle KE_{total}={\frac {Mm}{M+n}}{\frac {v_{rel}^{2}}{2}}}$
${\displaystyle KE_{total}=\mu {\frac {v_{rel}^{2}}{2}}}$

Each form has merit. The last equation looks like the familiar equation for the KE of a single body, and the second doesn't require knowing the definition of ${\displaystyle \scriptstyle \mu }$. I think that the best choice is to always include the first and last forms:

${\displaystyle KE_{total}=\mu {\frac {v_{rel}^{2}}{2}}=M{\frac {(v_{M})^{2}}{2}}+m{\frac {(v_{m})^{2}}{2}}}$

It is standard practice to assume that un-subscripted quantities are relative ${\displaystyle \scriptstyle (v_{rel}\iff v)}$. This practice is very practical and efficient, but also potentially confusing since this assumption is rarely mentioned explicitly

The word "relative" in the term specific relative angular momentum indicates that it applies to the 2-body problem. Relative quantities are shared by two bodies; there are no relative quantities in 1-body problems.
There is only one vis-viva equation: ${\displaystyle v^{2}=G(M\!+\!m)\left({{2 \over {r}}-{1 \over {a}}}\right)}$. The equation where one mass is ignored: ${\displaystyle v^{2}=GM\left({{2 \over {r}}-{1 \over {a}}}\right)}$, is not the "vis-viva equation", it is an "approximation to the vis-viva equation" -- Simplifying assumptions and approximations must always be stated explicitly. NOrbeck (talk) 14:20, 21 August 2010 (UTC)

## speed of photons

I reverted your change, since the "in perfect vacuum" qualification of speed of light is only applicable to the wave view, and the sentence you modified was about photons and other massless particles. In the particle view, vacuum is not a relevant concept. Dicklyon (talk) 05:26, 21 July 2010 (UTC)

"One consequence is that c is the speed at which all massless particles and waves, including light, must travel."
Are you telling me that the speed of a photon is not affected by the density of the medium? Do you believe that photons always travel at c, even in the earth's atmosphere? Do you believe that the concept of the index of refraction doesn't apply to photons?
To Dicklyon: I agree with NOrbeck. The speed at which light travels does not depend on whether it is considered a wave or a particle. A photon in a material medium might be deflected (bounce off of) other particles; or it might be absorbed and then replaced by another photon emitted later. In either case, the average speed of the photon is reduced below c. JRSpriggs (talk) 02:15, 22 July 2010 (UTC)
At first I had missed Dicklyon's point, then I remembered the QFT model where photons travel at c between particles. However, in this context claiming photons travel at c seems like chicanery, the reader has no way of knowing that the author is using the word 'speed' to describe the unobserved theoretical instantaneous speed of the bare photon, not the measurable speed of the clothed photon. Correct me if I'm wrong, but it seems the motivation here is to justify a literal and unintended interpretation of special relativity circa 1905, not to describe the quasiparticle of quantum field theory. There are four formulations of QFT, none more right than any other. People are free to conceptualize light propagation any way they wish, but when arbitrary non-falsifiable abstractions take priority over empirical fact, something has gone wrong.

Hello. In case you didn't know, when you add content to talk pages and Wikipedia pages that have open discussion, you should sign your posts by typing four tildes ( ~~~~ ) at the end of your comment. You may also click on the signature button located above the edit window. This will automatically insert a signature with your username or IP address and the time you posted the comment. This information is useful because other editors will be able to tell who said what, and when. Thank you. --SineBot (talk) 08:05, 24 July 2010 (UTC)

Hi, I undid this recent edit. Please provide a proper source before reverting? Could you please find a source for the acceleration section this recent edit? That would make it easier for everyone to verify. Thanks and cheers. DVdm (talk) 15:53, 24 December 2010 (UTC)

By the way, are you sure about the source (The Measurement of Time (2001) C Audoin, B Guinot. Pg 107) for the gravitational shift? You said page 107, but I don't find the equation on that page. Is this the same book? Assuming it is indeed that same book, I have replaced the ref with a proper citation and tagged it for verification fail. If the equation was derived from the source, then this would be wp:SYNTHESIS and thus wp:original research. In that case I'm afraid that we have to undo your edit. Please comment? Thanks. DVdm (talk) 16:20, 24 December 2010 (UTC)

Please do not add original research or novel syntheses of previously published material to our articles as you apparently did to Relativistic Doppler effect. Please cite a reliable source for all of your information. Thank you. -

Note. I have removed this unsourced section for the second time now. The equation of the edit does not appear in the cited source. "Mathematically identical to both the cited sources to 2nd order in c" is definitely not allowed by wp:CALC. This is wp:original research. Please do not add it again without citing a proper source. DVdm (talk) 17:12, 7 January 2011 (UTC)

For the same reason I have removed the other section that you had added for the second time now. DVdm (talk) 17:24, 7 January 2011 (UTC)

Here is the equation from the source:
File:MathpagesDopplerEq6.gif

${\displaystyle f_{o}={\frac {c-{\vec {v_{o}}}\cdot {\hat {k_{o}}}}{c-{\vec {v_{s}}}\cdot {\hat {k_{s}}}}}\cdot {\frac {\gamma _{o}}{\gamma _{s}}}\cdot f_{s}}$

These equations are absolutely mathematically identical. Lets do the math:

${\displaystyle \nu _{o}={\frac {c-{\vec {v_{o}}}\cdot {\hat {k_{o}}}}{c-{\vec {v_{s}}}\cdot {\hat {k_{s}}}}}\cdot {\frac {\gamma _{o}}{\gamma _{s}}}\cdot \nu _{s}}$
${\displaystyle {\frac {\nu _{o}}{\nu _{s}}}={\frac {c-{\vec {v_{o}}}\cdot {\hat {k_{o}}}}{c-{\vec {v_{s}}}\cdot {\hat {k_{s}}}}}\cdot {\frac {\gamma _{o}}{\gamma _{s}}}}$
${\displaystyle {\frac {\nu _{a}}{\nu _{e}}}={\frac {c-{\vec {v_{a}}}\cdot {\hat {k_{a}}}}{c-{\vec {v_{e}}}\cdot {\hat {k_{e}}}}}\cdot {\frac {\gamma _{a}}{\gamma _{e}}}}$
${\displaystyle {\frac {\nu _{a}}{\nu _{e}}}={\frac {c-{\vec {v_{a}}}\cdot {\hat {k_{a}}}}{c-{\vec {v_{e}}}\cdot {\hat {k_{e}}}}}\cdot {\frac {1}{\gamma _{e}{\sqrt {1-(v/c)^{2}}}}}}$
${\displaystyle {\frac {\nu _{a}}{\nu _{e}}}={\frac {c-{\vec {v_{a}}}\cdot {\hat {k_{a}}}}{c-{\vec {v_{e}}}\cdot {\hat {k_{e}}}}}\cdot {\frac {\sqrt {1-(u/c)^{2}}}{\sqrt {1-(v/c)^{2}}}}}$
${\displaystyle {\frac {\nu _{a}}{\nu _{e}}}={\frac {c-{\vec {v_{a}}}\cdot {\hat {k_{a}}}}{c-{\vec {v_{e}}}\cdot {\hat {k_{e}}}}}\cdot {\sqrt {\frac {1-(u/c)^{2}}{1-(v/c)^{2}}}}}$
${\displaystyle {\frac {\nu _{a}}{\nu _{e}}}={\frac {1-{\frac {\vec {v_{a}}}{c}}\cdot {\hat {k_{a}}}}{1-{\frac {\vec {v_{e}}}{c}}\cdot {\hat {k_{e}}}}}\cdot {\sqrt {\frac {1-(u/c)^{2}}{1-(v/c)^{2}}}}}$
${\displaystyle {\frac {\nu _{a}}{\nu _{e}}}={\frac {1-{\frac {\vec {v}}{c}}\cdot {\hat {k_{a}}}}{1-{\frac {\vec {u}}{c}}\cdot {\hat {k_{e}}}}}\cdot {\sqrt {\frac {1-(u/c)^{2}}{1-(v/c)^{2}}}}}$
${\displaystyle {\frac {\nu _{a}}{\nu _{e}}}={\frac {1-{\frac {|{\vec {v}}|}{c}}cos(\theta _{cv})}{1-{\frac {|{\vec {u}}|}{c}}cos(\theta _{cu})}}{\sqrt {\frac {1-(u/c)^{2}}{1-(v/c)^{2}}}}}$
${\displaystyle {\frac {\nu _{a}}{\nu _{e}}}={\frac {1-{\frac {|{\vec {v}}|}{|{\vec {c}}|}}cos(\theta _{cv})}{1-{\frac {|{\vec {u}}|}{|{\vec {c}}|}}cos(\theta _{cu})}}{\sqrt {\frac {1-(u/c)^{2}}{1-(v/c)^{2}}}}}$

If I have made a mathematical error, I apologize. If there is any particular version of the equation you prefer, please let me know.

This equation is very well known and documented, it is certainly not original research. I can provide another 4-5 references if requested. I learned this equation in high school for extra credit.— Preceding unsigned comment added by NOrbeck (talkcontribs)

They might be equivalent, but according to our basic policies (see o.a. wp:CALC) this really is wp:OR. If you want to add that particular formula, you really need a source for it in its current form. You can change some variable names, but that's about it... DVdm (talk) 21:15, 7 January 2011 (UTC)

What is not original research? WP:ATT#What is not original research?

Editors may make straightforward mathematical calculations (algebraic manipulations) or logical deductions based on fully attributed data that neither change the significance of the data nor require additional assumptions beyond what is in the source.

Wikipedia: These are not original research WP:NOT#OR

Simple calculations
Simple calculations such as population density or age differences do not constitute original research.
Any relatively simple and direct mathematical calculation that reasonably educated readers can be expected to quickly and easily reproduce. For example, if given the population and the size of a specific area, then the population density of that area may be included. More complex calculations (for instance, those involving statistics) should not be used to build an argument, because they require skills that common educated readers do not possess, or involve a large number of steps that may not be obvious, making it difficult to detect errors. "Reasonably educated" is directly relative to the topic involved.

I certainly have no concerns or preferences over the form of the equation, I leave that nonsense up to my calculator. In fact, all of the algebraic changes were performed automatically by my calculator. I was honestly unaware, and shocked to discover, that reducing equations to their simplest form is a violation of Wikipedia policy. Frustratingly, the automatic simplification feature cannot be turned off. Despite my objections, my calculator refuses to comply with WP:OR. A feature of computer algebra systems (CAS) is the ability to compare equations for equivalence. Anyone regardless of mathematical ability (or in my case laziness), can instantly verify advanced mathematical equations by pasting them into a freeware CAS application. I quite regularly have edits questioned by diligent Amish editors who have discovered discrepancies between their arduous manual calculations and the instantaneous output of my calculator, so far my calculator has always been right, and the long-suffering masochists have always been wrong. It seems no human knows as many identities, rules, and caveats as a modern CAS system, the use of advanced mathematics makes it impossible for editors to verify the machines aren't insidiously inserting original research.

Using WP: IGNORE, WP:COMMON, and WP:HERE someone other than me might argue that using the simplest, most concise, and easiest to understand form of an equation does not violate the spirit or intent of the Wikipedia guidelines. Personally, I just want readers of this article to learn how the doppler effect is actually calculated in practice for real-world applications such as GPS, pulsar timing, and avionics. Let's bust-ass and get this crutial information on-line where people can benefit from it.

Do I have your approval to use this?
${\displaystyle {\frac {\nu _{a}}{\nu _{e}}}={\frac {1-{\frac {|{\vec {v}}|}{|{\vec {c}}|}}cos(\theta _{cv})}{1-{\frac {|{\vec {u}}|}{|{\vec {c}}|}}cos(\theta _{cu})}}{\sqrt {\frac {1-(u/c)^{2}}{1-(v/c)^{2}}}}}$
Or, perhaps this? (changing only the variables to match the rest of the article)
${\displaystyle {\frac {f_{o}}{f_{s}}}={\frac {1-{\frac {|{\vec {v_{o}}}|}{|{\vec {c}}|}}cos(\theta _{co})}{1-{\frac {|{\vec {v_{s}}}|}{|{\vec {c}}|}}cos(\theta _{cs})}}{\sqrt {\frac {1-(v_{s}/c)^{2}}{1-(v_{o}/c)^{2}}}}}$ NOrbeck (talk) 05:44, 9 January 2011 (UTC)

Absolutely, yes, feel free to use the latter one. As you see, there was a serious problem with adding an equation that requires 11 (even simple) steps to be proven. If you take one of the above equations, these problemes do not arrise, since (1) you avoid making mistakes (as you did indeed), (2) you don't have to rely on notoriously unreliable CAS systems, and (3) (see wp:BURDEN) it ensures that other contributors do not have to (3.1) go check the source and (3.2) make the same calculations and perhaps the same or different mistakes, and/or (3.3) go to the talk page (as someone did indeed) and start a discussion that should not be held in the first place, which is exactly why our wp:NOR policy was set up. All this can be avoided by putting a properly sourced equation in the article.

So, please by al means, go ahead and use the bottom equation with properly explained variables and with mention of the source, if possible the book-published version of Brown's work - See http://www.mathpages.com/rr/rrtoc.htm, but don't point to lulu-dot-com because that one is blacklisted.

Same remark for the other section you had added. Just take the equation from page 107 and we're done :-)

Cheers - DVdm (talk) 11:52, 9 January 2011 (UTC)

## Problems with upload of File:MathpagesDopplerEq6.gif

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## Problems with upload of File:Doppler.gif

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