User talk:Icek~enwiki

Welcome!

Hello,, and welcome to Wikipedia! Thank you for your contributions. I hope you like the place and decide to stay. Here are a few good links for newcomers: I hope you enjoy editing here and being a Wikipedian! Please sign your name on talk pages using four tildes (~&#126;); this will automatically produce your name and the date. If you need help, check out Questions, ask me on my talk page, or place  on your talk page and someone will show up shortly to answer your questions. Again, welcome! NTK 10:57, 9 April 2006 (UTC)
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Blue in infrared
Indeed, parts of the spectra outside the visible are often referred to using 'colours'. Blue represents simply shorter wavelengths and red longer. Such 'shifted' colours are also used on graphs. Please refer to the reference 3. quoted in the article for more information. Eurocommuter 18:52, 15 April 2006 (UTC)

Lower flux, larger diameter
(Your edit of 2003 UB313 on 2006-04-27). Hi, Icek. Indeed, my text could mislead but I’m afraid so can yours; we can do better. What I arguably failed to express is that if Bertoldi (thermal method) did assume a different position,..., he would come with a lower estimate. Regards. Eurocommuter 19:16, 27 April 2006 (UTC)
 * (follow up on your reply). Yes, it’s better but I think I got into a complicated statement by mentioning unnecessarily equator-on position. What do you think about simplifying the statement and putting an unambiguous footnote, something like this…

Assuming further the highest diameter (2500 km) and pole-on position of the object 1 the difference between the results would appear consistent…

1 If the object is in pole-on position the side facing the Sun (and the observer) gets hotter producing stronger emissions thus resulting in overestimation of the diameter using the thermal method. . Eurocommuter 19:42, 1 May 2006 (UTC)

Teleological argument
Your wrote:
 * Hi Mel Etitis, why do you consider my addition about the third premise ("The assumption of such an "undesigned designer" implies that one does not conduct scientific inquiry beyond some arbitrary point and instead accepts the "undesigned designer" as a dogma") inaccurate? Icek 21:37, 4 May 2006 (UTC)


 * Sorry, I should have explained on the Talk page (I've been trying to catch up on a backlog, and have been editing in haste recently). The problem is that it ignores the ontological argument, as well as other arguments offered by various philosophers of religion (e.g., Swinburne).  I agree that none of the arguments works, but it's incorrect to imply that it's a simple, unexplained, unargued dogma. --Mel Etitis  ( Μελ Ετητης ) 21:41, 4 May 2006 (UTC)

Pan-STARRS
I've replied on my talk page. In a nutshell, this comes from the Jewitt paper (listed in external links). -- Curps 06:09, 21 May 2006 (UTC)

Abundance of the chemical elements
Hello Icek, you commented about a table I transcripted to the article. The table is exactly as it was in the book, and, in my opinion, you're saying the same thing that is written there, it's merely an interpretation issue. I don't know how one could make it clearer though. -- Rend 04:55, 14 April 2007 (UTC)

Feynman point probability
I think you must have made an error somewhere. When I do the naive calculation
 * $$(1-(1-10^{-6})^{762})\cdot 100\%$$

I get 0.07617%, which agrees well with what the source says. Actually that way of computing it is not quite correct, because it assumes that all 762 possible ways of getting an early 999999 are independent, which they aren't (say, if there's a 999999 at position 123, the chance of finding a 999999 also at position 124 is 1/10). This makes the right answer a bit less than 0.07617%, but it cannot be what you're getting at, for even if we look for 999999's at positions that are multiples of 6 (such that the possibilities are trivially independent), I get
 * $$(1-(1-10^{-6})^{762/6})\cdot 100\% = 0.01270 \%$$

which is still larger than your value. –Henning Makholm 01:13, 24 June 2007 (UTC)

Religiosity and Intelligence
Hi IceK. FYI- I've questioned your deletion of the studies by the (Australian) National Church Life Survey, and the assumption that, being church funded, it is biased towards church friendly results. See full comment at the talk page. I can understand your comment, but believe it to be incorrect. WotherspoonSmith 11:05, 9 July 2007 (UTC)

Sweetness
Thanks for your work on the table, but what's with changing the numbers? I doubt I would have typed them all in incorrectly, so unless there's a mistake in the book I can't imagine why you would change them. Richard001 00:14, 29 August 2007 (UTC)
 * I saw the numbers and immediately thought that there's a 0 too much. If you look here, look at the respective Wikipedia articles or just use your favorite search engine, everywhere numbers about 1/10 of your values are presented. If you didn't make an error when copying the numbers from the book, I guess that the book is wrong (I don't have a tabletop sweetener at hand, if the amount of sweetener is on the label, you could compare the amount of sucrose equivalent to the sweetness...). Icek 20:10, 31 August 2007 (UTC)


 * I suppose, but it would be better if you could provide a reference here. If someone tried to check the numbers they wouldn't be supported by the current one given. A second reference explaining the error may be appropriate. Richard001 00:17, 1 September 2007 (UTC)


 * Now I have provided a reference; while the values for aspartame, cyclamate and saccharin are certainly closer to reality, the reference (which itself cites an article by DuBois et al. from 1991) unfortunately has other values for fructose (1.30) and glucose (0.59). The factors probably depend on the concentration used - DuBois et al. used a solution of water with 2% sucrose as a reference. Icek 22:25, 2 September 2007 (UTC)


 * Fructose is indeed 1.30 in solution (and doesn't change with concentration), 1.75 is when assesed as a crystal. --Sensonet (talk) 13:48, 4 January 2008 (UTC) Hello, by memory I said 1.75 it was 1.8. according to Taste chemistry book by RS Challenberger 1993 (ISBN 0751401501) the authors used Magnitude scaling method (After averaging 10-15 ratings, score were squared, and sucrose taken as unity). The source is Shallenberger & Acree 1971, which I hann't read so I don't really know the details of the testing.Sensonet (talk) 13:37, 2 September 2008 (UTC)

Hi there. You may want to keep an eye on the table. I've made a couple of minor amendments to reflect the range of values in the citations utilised, and I've added a footnote. An argumentive citation tag was subseqently added, which I have now removed. I don't have access to McMurry (1998), but I do have Guyton (1991), and 2006, as well as McLaughlin & Margolskee (1994), and I can see the tables with their figures as I write. And of course these publications should be available at any reasonably sized public library, and any half-decent university (i.e. they're not obscure publications). I did have a look for something online that matches the tabulated data, and provided a couple of citations to that effect. Looking at Schiffman et al (2000), one has to calculate the indices, which not everyone will want or be able to do (I did that sort of exercise some years ago for a number of articles, including some by Schiffman, but I'm not in a position to spend time on such an exercise again). So I relocated that reference to the "General" section. I left McMurry in place, because I have to assume that it contains the figures cited, just as others have to assume that my citations do.

The points raised by the IP editor are not without merit, just not justified for the table. They pertain to the question of how the figures are derived. However, since the figures are directly readable from available texts, the issues raised by the IP editor are not valid for the table itself. Rather, they belong in a section on these methodological issues. Regards Wotnow (talk) 13:03, 15 September 2010 (UTC)

Update: I've amended one citation in the sweetness compounds table (Srivastava & Rastogito 2003) include a url going straight to the relevant table in the text, as my own success at viewing the table from the title's url varies. While the mere fact of citations (Guyton & Hall, or McLaughlin & Margolskee, etc - but any citation on any thing) not being freely available via internet does not make them invalid, I find skepticism of those unfamiliar with a given citation understandable. Given this, I endeavour to find some sort of online citation that either suffices in itself, or corroborates an offline citation to sufficiently satisfy verification. However, no matter how much better one gets at doing this, it can still be a time-consuming effort. I do think it's worth it though. Most importantly it simply demonstrate that it's possible to do so for the sake of editors astute enough to realise this. If others pick up on such strategies, eventually the pool of people who do this increases, although it will always be a minority, as with many things in life. Wotnow (talk) 21:37, 15 September 2010 (UTC)

Creutzfeldt-Jakob disease
Hi. PNAS is a scientific journal that accepts research articles for publication through direct as well as indirect submission. If you have friends in the National Academy of Sciences, then they can "communicate" a maximum of two articles per year to PNAS via "Track 1". These articles do not go through the regular/normal procedure of peer review.

You can find that "Cells infected with scrapie and Creutzfeldt–Jakob disease agents produce intracellular 25-nm virus-like particles" PNAS | February 6, 2007 | vol. 104 | no. 6 | 1965-1970 has been "communicated" by someone called Sheldon Penman, who is indeed a member of the NAS.

If you read the said article carefully, you will find that in Figure 2D, the number of N2a+22L cells containing the so-called "virus-like particles" is less than 10%. Is it well known that N2a cells, like a lot of historical cell lines, are infected with many retroviruses that may or may not have anything to do with neurodegeneration.Edchoi 16:51, 27 September 2007 (UTC)


 * Thanks for educating me! Icek 04:53, 28 September 2007 (UTC)

April fools
I've reverted your edit to Paramecium. As far as I can tell it was just a coincidence that the journal article was published on April 1st. If you know differently then please revert me, but it does seem feasible to me. Smartse (talk) 20:06, 4 September 2010 (UTC)
 * Besides the date there are several reasons to belief that it was a joke (and somehow I hope it for the author's and the journal's sake): Read the paragraph "Cuvettes" in the section "Materials and Methods": The statements about quartz and glass are odd. He essentially states that glass and quartz are the same except for the fact that glass is amorphous - but then it would be fused silica (also called quartz glass) which is transparent to UV light at lower wavelengths than figure 1 shows.
 * Then he provides this vertical section of the experiment in figure 2 which disagrees with the proportions just described before: The wall thickness is 9 pixels, and in the text it's 1.5 mm, so 1 pixel should be 1/6 mm. But then the horizontal dimensions of the outer cuvette would be (99+1/3) mm x (99+1/3) mm, compared to 23 mm x 23 mm in the text, and for the inner cuvette 40 mm x 40 mm, compared to 15 mm x 15 mm in the text. And that means that the ratio of the thickness of the outer and inner dimensions are about 2.48 from the drawing instead of about 1.53 from the text. If he provides these drawings, why make such gross mistakes?
 * Then he adds a bit of mysticism by explaining that the experimental blocks were "randomly placed on a four by five grid".
 * A bit later he goes on and explains that the temperature in experiment 1a was kept constant for 48 hours in each of the 14 sessions, but in some it was 27 °C, in others 22 °C, and so on... and notably, neither does he provide these temperatures for experiments 1b, 2 and 3, nor does he mention the different temperatures when reporting the results and doing statistics.
 * You can probably find many more mistakes...
 * Icek (talk) 23:23, 4 September 2010 (UTC)


 * Hi Icek, in case you haven't noticed, User:Bus stop who originally added this section has replaced it and reverted me after I pointed them to this discussion. I've started a discussion on the talk page, where it would be useful if you could comment. Thanks making me see sense as well! Smartse (talk) 20:38, 27 September 2010 (UTC)


 * Sorry, I haven't been logged in for a while, so I am too late - but it seems you guys have already agreed not to include it (and the paper by Fels currently isn't listed in the reference section of biophoton either). Icek (talk) 11:27, 8 October 2010 (UTC)

Mars
I just replied it in so you shall look at it and reply it to me. BlueEarth (talk | contribs) 21:31, 7 September 2010 (UTC)

Exoplanets
Do you want to look at my formulas to calculate the celestial pole coordinates of exoplanets? Reply it to me about what you think about those formulae. BlueEarth (talk | contribs) 21:58, 14 September 2010 (UTC)

Pioneer 10
Hi, way back in 2003 a few edits where made to an article that has in the meantime been merged with Attitude dynamics and control by a non-registered user which may be you (I apologize if it wasn't you). Somewhere in these edits, the claim that Pioneer 10 used (small) solar sails for attitude control was inserted. The only confirmation for this which I could find on nasa.gov is this, and it is more a mention-in-passing and doesn't seem very reliable as it is in a general text on solar sails written by a student. Where did you (if you did indeed make this edit) get that information from? Thanks in advance for the answer. Icek (talk) 16:49, 22 March 2008 (UTC)

I want to add that the text on nasa.gov is from May 2006, so this student may well have used Wikipedia as his source. Icek (talk) 13:38, 7 April 2008 (UTC)
 * I think I referred to the wrong spacecraft. It should  Mariner 10, not Pioneer 10.  I did not make it up because I was not aware of the problem they solve before I read about it.  The fuel problem with attitude jets on long duration missions is that the vehicle slowly wobbles, first one way, then the other, with the speed of the wobble set by the minimum correction burst on the attitude thruster.  The vanes provided a control with a finer thrust that can be used to damp the wobbles, eventually halting fuel use for long periods. I do remember that it was a cheap experiment, and the mission engineers were surprised at how useful they became for reducing fuel use.  Ray Van De Walker 02:14, 30 January 2011 (UTC)

Proposed Image Deletion
A deletion discussion has just been created at Category talk:Unclassified Chemical Structures, which may involve one or more orphaned chemical structures, that has you user name in the upload history. Please feel free to add your comments.  Ron h jones (Talk) 22:54, 10 June 2011 (UTC)

All files in category Unclassified Chemical Structures listed for deletion
One or more of the files that you uploaded or altered has been listed at Files for deletion. Please see the discussion to see why this is (you may have to search for the title of the image to find its entry), if you are interested in it/them not being deleted. Thank you.

Delivered by MessageDeliveryBot on behalf of MGA73 (talk) at 17:58, 28 November 2011 (UTC).

Barlow's law
Icek, it's taken 2-1/2 years to get to it, but I and another editor are finally seriously looking into the question you raised at Talk:Barlow's law. Please come on over and take a look. —Ben Kovitz (talk) 00:27, 3 June 2012 (UTC)

Question about old relativistic rocket edit
Hi, in this 2006 edit to the relativistic rocket page you edited the "specific impulse" section to read as follows (version here):


 * The specific impulse of relativistic rockets is the same as the effective exhaust velocity, despite the fact that the nonlinear relationship of velocity and momentum as well as the conversion of matter to energy have to be taken into account; the two effects cancel each other. Of course this is only valid if the rocket does not have an external energy source (e. g. a laser beam from a space station near star; in this case the momentum carried by the laser beam has also to be taken into account). If all the energy to accelerate the fuel comes from an external source (and there is no additional momentum transfer), then the relationship between effective exhaust velocity and specific impulse is as follows:


 * $$I_{sp} = \frac {v_e}{\sqrt{1 - \frac{v_e^2}{c^2}}} = \gamma \ v_e$$


 * where $$\gamma$$ is the Lorentz factor. In the case of no external energy source, the relationship between $$I_{sp}$$ and the fraction of the fuel mass $$\eta$$ which is converted into energy might also be of interest; assuming no losses, it is


 * $$\eta = 1 - \sqrt{1 - \frac{I_{sp}^2}{c^2}} = 1 - \frac{1}{\gamma}$$


 * The inverse relation is


 * $$I_{sp} = c \cdot \sqrt{2 \eta - \eta^2}$$


 * Here are some examples of fuels, the energy conversion fractions, and the specific impulses (assuming no losses if not specified otherwise):


 * {| class="wikitable"

!Fuel||$$\eta$$||$$I_{sp} / c$$
 * electron-positron annihilation
 * 1
 * 1
 * proton-antiproton annihilation, using only charged pions
 * 0.56
 * 0.60
 * electron-positron annihilation with simple hemispherical absorption of gamma rays
 * 1
 * 0.25
 * nuclear fusion: H to He
 * 0.00712
 * 0.119
 * nuclear fission: 235U
 * 0.001
 * 0.04
 * }
 * nuclear fission: 235U
 * 0.001
 * 0.04
 * }
 * }

I was wondering, where do these equations and numbers come from? The table is confusing because in some cases the relation between $$I_{sp} / c$$ and $$\eta$$ does not seem to match the equation given earlier, $$\eta = 1 - \sqrt{1 - \frac{I_{sp}^2}{c^2}}$$, for a rocket with no external energy source; for example, "proton-antiproton annihilation, using only charged pions" is said in the table to have $$\frac{I_{sp}}{c} = 0.60$$, plugging that into the equation gives $$\eta = 1 - \sqrt{1 - 0.60^2} = 0.2$$, but the table gives $$\eta = 0.56$$. In addition, the figures for $$\frac{I_{sp}}{c}$$ for "nuclear fission" and "nuclear fusion" seem to be far higher than what I find given in other sources. The two sources here and here give specific impulse in units of time, but the specific impulse page mentions that you can convert specific impulse in units of time to specific impulse in units of velocity by multiplying by g=9.8 meters/second^2, meaning the specific impulse for fission of 500-3000 seconds given on the first page translates to 4900-29400 m/s = 1.6*10-5 c to 9.8*10-5 c, far smaller than the value 0.04 c given on your table. And the second page (a pdf file) says on p. 6 that the upper value for specific impulse in a "gas core" fission rocket would be around 7000 seconds, or 68600 m/s, or 2.3*10-4 c, still far smaller that 0.04 c. Likewise, for fusion, the first page gives an upper limit of 105 seconds or 9.8 * 105 m/s or 0.003 c, and the second page gives around 2 * 105 seconds or 0.006 c for a fusion rocket on p. 7, but then on p. 22 they note that the plans for Project Daedalus, which was supposed to use an advanced form of fusion pulse propulsion, were calculated to reach a specific impulse of 106 seconds or 0.03 c...but all of these figures for the specific impulse of fusion rockets are much smaller than the value given on your table of 0.119 c. Hypnosifl (talk) 21:38, 20 August 2012 (UTC)

Regarding the proton-antiproton annihilation: I am sorry, it seems like I messed up that one. In Robert L. Forward's proposal for such a propulsion you can find the branching ratios of the various annihilation channels on page 109. Using the most common channels (without kaons and photons), I can quickly estimate (energies are in MeV):

Here "total energy" is the sum of the rest energies of the proton and the antiproton (1876.544026 MeV); the remaining kinetic energy is the total energy minus the rest energies of the pions generated (139.57018 MeV for the charged pion and 134.9766 MeV for the neutral pion). And I assume that the kinetic energy is (on average) equally distributed among the particles (this is only approximately correct because the masses of neutral and charged pions are not exactly equal). A reliable source for the proton and pion masses is the Particle Data Group (mesons including pions and baryons including protons).

So what I intended as &eta; or fraction of mass converted to energy is 0.60072 and what I should have used as &eta; in the formula for only using charged pions is 0.39408, resulting in &Delta;v/c = 0.796.

Regarding the specific impulse for nuclear fusion and nuclear fission: That is why it says "assuming no losses", i.e. these are the absolute physical limits for any kind of rocket propulsion.

Icek (talk) 22:06, 21 August 2012 (UTC)


 * Addendum: The numbers for the masses of pions and protons differ slightly from the numbers in the linked documents; I got my numbers from an older version of the same documents, and the difference is of course very small. Icek (talk) 22:11, 21 August 2012 (UTC)


 * Thanks. I'm still not clear though, where does the equation $$\eta = 1 - \sqrt{1 - \frac{I_{sp}^2}{c^2}}$$ come from? Is it from some source like Forward's, or did you derive it from other known equations? And does the $$\eta$$ in the table not refer to "fraction of the fuel mass converted to (kinetic) energy" as with the $$\eta$$ in the equation? If they refer to the same thing, I still don't understand why the values in the table fail to obey the relationship given by the equation (and if they refer to slightly different things, this should be explained more clearly in the article; it might also be good to have the text of the article spell out the method used to calculate the values of $$\eta$$ in the table, and cite sources for the difference in the sum of rest energies of particles before and after the reaction, otherwise it isn't verifiable by other editors). Hypnosifl (talk) 22:41, 23 August 2012 (UTC)

I derived the formula: Specific impulse is always momentum of the exhaust divided by fuel mass,

$$I_{sp} = \frac{p_e}{m_{fuel}}$$

Relativistic momentum of the exhaust (which leaves with velocity $$v_e$$, and has mass $$m_e$$ different from $$m_{fuel}$$) is

$$p_e = \frac{m_e \ v_e}{\sqrt{1 - \frac{v_e^2}{c^2}}}$$

Some fraction $$\eta$$ of the fuel mass is converted to kinetic energy, so that the mass of the exhaust is

$$m_e = (1 - \eta) \ m_{fuel}$$

And the total relativistic energies of fuel (at rest relative to the spacecraft) and exhaust (moving) must be the same

$$m_{fuel} \ c^2 = \frac{m_e \ c^2}{\sqrt{1 - \frac{v_e^2}{c^2}}}$$

Substituting $$m_{fuel}$$ in terms of $$m_e$$ and $$\eta$$ and dividing by $$c^2$$ and $$m_e$$ yields

$$\frac{1}{1 - \eta} = \frac{1}{\sqrt{1 - \frac{v_e^2}{c^2}}}$$

Solving this equation for $$v_e$$:

$$v_e = c \ \sqrt{2 \eta - \eta^2}$$

Now we can substitute back into the momentum of the exhaust:

$$p_e = \frac{(1 - \eta) \ m_{fuel} \ c \ \sqrt{2 \eta - \eta^2}}{1 - \eta}$$

And therefore the specific impulse is:

$$I_{sp} = c \ \sqrt{2 \eta - \eta^2}$$

Regarding the calculation of proton-antiproton annihilation, I just noticed that I made a mistake in my reply from August 21 (and I was more correct in 2006...). The table from above lacks the masses of the charged pions, and further it lacks the actual $$\eta$$ and $$I_{sp}$$ values: Only from the $$I_{sp}$$ values we should make a probability-weighted average.

So the result is an $$I_{sp} / c$$ of 0.57 rather than 0.56 (the value I put into the article in 2006).

Let me clarify by giving you this table:

Icek (talk) 10:08, 24 August 2012 (UTC)


 * Not sure about that derivation...what frame are you using to define frame-dependent quantities like $$v_e$$ and $$p_e$$? It couldn't be a single inertial frame if you're assuming they are constant throughout the entire acceleration, but if you're using a non-inertial frame like Rindler coordinates, in that frame the velocity of exhaust particles would be constantly increasing as they moved further away from the rocket, and I'm not sure it's actually meaningful to define a "relativistic momentum" using the usual equation $$p_e = \frac{m_e \ v_e}{\sqrt{1 - \frac{v_e^2}{c^2}}}$$ in a non-inertial frame. Or are you just considering an infinitesimal time interval during which some infinitesimal amount of fuel $$dm_{fuel}$$ converts from being at rest in the fuel tank to becoming exhaust moving out the back with velocity $$v_e$$ in the ship's instantaneous inertial rest frame, and with the moving bit of exhaust having lost some mass so that its rest mass is $$dm_e$$? In that case your derivation would indeed show that if $$\eta$$ is the fraction of fuel mass converted to kinetic energy, then the specific impulse in the ship's instantaneous inertial rest frame during that infinitesimal interval would be $$I_{sp} = c \ \sqrt{2 \eta - \eta^2}$$, but I don't think that the equation would still hold if we define $$\eta$$ to be the total fraction of fuel mass converted to kinetic energy over the entire acceleration period, in the inertial frame where the rocket started out at rest (or any other specific inertial frame that's used to measure the total kinetic energy of rocket and fuel particles after the rocket uses up its fuel...most relativistic rocket equations with frame-dependent quantities are written from the perspective of the starting rest frame before acceleration, though). If you didn't intend for the equation to work for that definition of $$\eta$$ (which would seem like a fairly natural one, given the context), then the article should spell out more clearly that $$\eta$$ stands only for the fraction of fuel mass converted to kinetic energy in the rocket's instantaneous rest frame during a brief time interval, not the total fraction over the entire acceleration period.


 * As for the table, the series of columns seems to be giving an implicit account of how you arrived at the final numbers, but it would be helpful to have it spelled out for a given reaction type with a derivation where you explain each step...for example I'm not clear on what "losses" means in this context, where is the energy being lost to exactly? I would also like to know which of the values in the table were obtained from some outside source (and if so, please add cites for all the numbers that came from outside sources, or if they all came from the same source, please add a cite for the table as a whole), and which you derived using your own calculations (and for these, what equations did you use to derive them?) Another editor was asking about this too, see Talk:Relativistic_rocket...info in wikipedia needs to be verifiable in some way, although it's OK for an article to include routine calculations based on numbers/equations that are themselves verifiable, as long as there's a consensus of editors that the calculations are reasonably trivial. Hypnosifl (talk) 11:43, 24 August 2012 (UTC)


 * Actually, even if we confine our attention to an infinitesimal time interval and do all calculations in the instantaneous inertial rest frame of the ship at the start of the time interval, I'm still not sure your derivation makes sense. You say "And the total relativistic energies of fuel (at rest relative to the spacecraft) and exhaust (moving) must be the same"--but even in an infinitesimal time interval, there will be some infinitesimal change in the kinetic energy of the ship as well, and so the correct equation relating relativistic energy at the beginning of the time interval to relativistic energy at the end should include the change in kinetic energy of the the ship. If at the the beginning of the time interval there is a tiny bit of fuel $$dm_{fuel}$$ at rest relative to the rest of the ship which has mass $$m_{ship} - dm_{fuel}$$ (so the sum of the two is the total mass of the ship including all fuel), and at the end of the time interval that bit of fuel has been converted to exhaust with rest mass $$dm_e$$ and velocity $$v_e$$, with the rest of the ship having the same rest mass $$m_{ship} - dm_{fuel}$$ but now having an infinitesimal increase in velocity $$dv_{ship}$$ then if we put the total relativistic energy at the beginning of the interval on the left and the total relativistic energy at the end of the interval on the right, we'd have


 * $$m_{ship} \ c^2 = \frac{dm_e \ c^2}{\sqrt{1 - \frac{v_e^2}{c^2}}} + \frac{(m_{ship} - dm_{fuel}) \ c^2}{\sqrt{1 - \frac{(dv_{ship})^2}{c^2}}}$$


 * ...along with the condition that at the end of the time interval, the momenta must be equal in magnitude (since they are opposite in direction): $$\frac{dm_e * v_e}{\sqrt{1 - \frac{v_e^2}{c^2}}} = \frac{(m_{ship} - dm_{fuel}) * dv_{ship}}{\sqrt{1 - \frac{(dv_{ship})^2}{c^2}}}$$ Hypnosifl (talk) 12:50, 24 August 2012 (UTC)

Regarding the rocket equation, I am just considering the tangential inertial reference frame (i.e. an infinitesimal time interval). Otherwise the quantity $$\eta$$ would not be useful, as it would no only depend on the kind of fuel and the kind of rocket engine, but also on the mass ratio of fueled and empty rocket: A rocket containing just a tiny amount of fuel won't be accelerated much, and the exhaust will have almost the same velocity relative to the rest frame and relative to the rocket after burnout. With a lot of fuel, some of it will be ejected from the rocket engine when the rocket is already moving at a high speed, thus the speed of the exhaust in the rest frame will be lower on average.

And a specific impulse also only seems to make sense to me in the tangential inertial frame, even classically (if you calculate the final classical momentum from the Tsiolkovsky equation and divide it by the fuel mass, the result depends on the mass ratio).

As for your energy equation taking into account the movement of the ship, let's have a look at it:

$$m_{ship} \ c^2 = \frac{dm_e \ c^2}{\sqrt{1 - \frac{v_e^2}{c^2}}} + \frac{(m_{ship} - dm_{fuel}) \ c^2}{\sqrt{1 - \frac{(dv_{ship})^2}{c^2}}}$$

We can get rid of the infinitesimal quantity in the denominator of the right hand side of the sum on the right hand side by calculating the Taylor series (in $$dv_{ship}$$) and ignoring everything except constant and linear terms. Because only the square of $$dv_{ship}$$ occurs to begin with, there will be no linear term in the Taylor expansion, and the denominator indeed becomes 1:

$$m_{ship} \ c^2 = \frac{dm_e \ c^2}{\sqrt{1 - \frac{v_e^2}{c^2}}} + m_{ship} \ c^2 - dm_{fuel} \ c^2$$

Now the ship's rest energy cancels on both sides of the equation and we can rearrange the rest so that it's almost what I used in my derivation:

$$dm_{fuel} \ c^2 = \frac{dm_e \ c^2}{\sqrt{1 - \frac{v_e^2}{c^2}}}$$

You are right that it's more rigorous to use differential quantities; the result of the derivation is again the same formula for the relation of specific impulse and $$\eta$$. More informally I would say that we only look at a little bit of fuel at a time, and that little bit is far less massive than the ship, resulting in almost no change in velocity or momentum of the ship.

Regarding the table of etas and specific impulses.... maybe we should just delete the entries for which the formula is incorrect and write a few explanations instead?

Icek (talk) 20:24, 24 August 2012 (UTC)


 * Thanks, the comment about taking a Taylor expansion helps clarify things--I think it would be good to give a derivation mentioning the detailed assumptions of the derivation (perhaps in an explanatory note to avoid cluttering the article too much), unless we can find a published source that provides a derivation of the same final equation. I'd be fine with the solution of deleting entries for which the formula doesn't work and giving some explanations, but in each line either the value of I_{sp}/c or the value of $$\eta$$ presumably come from some published source, if they all come from the same source it could be given in the line that introduces the table, if different entries in the table come from different sources than footnotes giving the sources should be in each line. Hypnosifl (talk) 20:46, 24 August 2012 (UTC)

File:Cyclades-sat.png listed for deletion
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Re: Benzaldehyde
Hi! Sorry for the late reply, lately I'm no longer as active as I used to be on Wikipedia. Turning to your question: you're correct in that I did not enter a reference for the water solubility back then, my bad... Can't remember where I found that data, at the time I was working in a chemistry lab so it's possible I found that value on the product MSDS we had in the lab. Unfortunately I have no chance to check that MSDS any longer.

A quick google search led me here http://www.chem.unep.ch/irptc/sids/oecdsids/100527.pdf It reports a water solubility of 6.55 g/L @ 25°C for benzaldehyde, but of course this is for 25°C, not 20°C where solubility is bound to be lower.

Given all the above I think your correction sounds good to me, thanks for noticing the discrepancy! Berserker79 (talk) 10:15, 30 September 2012 (UTC)

Seems ok
This answer seems ok to me. What's wrong with it? Sławomir Biały (talk) 14:58, 5 April 2014 (UTC)
 * As far as I can see, it wasn't particularly helpful, because the issue is not testing whether a number is divisible by 3, but whether it's a power of 3. Icek (talk) 22:18, 5 April 2014 (UTC)
 * Ah, I see. Right.   Sławomir Biały  (talk) 11:31, 6 April 2014 (UTC)

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Renamed
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Ringdown
Hi, thanks for replying to my question on Reference Desk. Can you please look at Reference_desk/Archives/Science/2020_April_26 and see if I understood you correctly? 93.136.114.41 (talk) 16:36, 4 May 2020 (UTC)
 * Sorry, I log in here at irregular intervals, so I didn't see your request earlier.
 * You're right about the 2 times 11 parameters of the 2 merging black holes, the gravitational radiation will be determined only by them. In neutron stars, on the other hand, you can see hints of tidal deformation in the graviational radiation (if your observatory is better than any existing or the merger is closer than any observed so far), see the information from LIDO. Icek~enwiki (talk) 14:52, 16 May 2020 (UTC)
 * Alright, thanks for the clarification :) 93.142.75.94 (talk) 07:21, 17 May 2020 (UTC)