Wikipedia:Reference desk/Archives/Science/2012 May 22

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May 22

Rotating in space

If an electric motor was allowed to run while floating free in space, then presumably the armature would rotate one way and the casing the other, but at what relative speeds? I'm guessing there must be an equation relating the two rotational speeds, that somehow also involves the masses of the components. For example if the casing was very heavy compared to the armature then it it seems intuitive that it would rotate more slowly. But what exactly would that equation be? 86.177.105.243 (talk) 00:05, 22 May 2012 (UTC)

It would be "whatever is necessary to conserve angular momentum." In the general case, that means solving the constrained equations such that the torque satisfies the elecromagnetic characteristics of the motor windings; and then solving for the two angular velocities for the case and the loaded-axle (respectively). In the most general case, the angular momentum is computed using a tensor formulation; but for simple cylindrically-symmetric motors, a scalar moment is usually a good approximation. The torque produced by the motor is governed by Faraday's law; or one of its engineering approximations like the solenoid equation or an empirical motor equation.

So, we have:

torque τ = (some engineering approximation related to the input current or voltage)

total angular momentum L = ΣL_i = ΣI_iω_i (if you've got a non-serif font, you're surely finding L's and i's and 1s troublesome by now)...

$\tau ({current},{voltage})={\frac {d}{dt}}L$

$\omega _{axle}I_{axle}-\omega _{case}I_{case}=0$

...for the sign convention I've arbitrarily chosen (angular velocity always positive and direction indicated by sign). Analytical calculation for the moment of inertia I of any non-ideal shape is quite difficult; but it can be measured.

Incidentally, this is the physics behind a reaction wheel for spacecraft stabilization and orientation. Nimur (talk) 01:41, 22 May 2012 (UTC)

Thank you for your reply. This is about at the limit of my ability to understand. Can we say that if the motor is initially switched off and has no overall angular momentum, then, when the motor is subsequently switched on, regardless of the torque, it remains that $\omega _{axle}I_{axle}+\omega _{case}I_{case}=0$ (assuming no external forces applied)? Does this lead to $\omega _{axle}/\omega _{case}=I_{case}/I_{axle}$, regardless of torque? That equation appears to make some intuitive sense to me. 86.177.105.243 (talk) 01:56, 22 May 2012 (UTC)

Actually I noticed that when I converted to MathML I introduced a serious typo in my system of equations that changed the meaning of my torque equation. I have just corrected that mistake; sorry for the error. Yes, you're correct: angular momentum is conserved, regardless of the torque of the motor. And, the torque will impart an angular momentum to the load, where the moment of inertia must account for the total load. The equations need to be solved simultaneously to solve for the rotation rate for either component. Nimur (talk) 03:34, 22 May 2012 (UTC)

Wouldn't they rotate in opposite directions at the same speed? They should just have a different acceleration?

   _
  / \
 |   _
|      -----____
|               -----------
|
---------------------------
\______________
                -----------

I think that the armature should initially turn much faster than the terminal velocity; as the casing accelerates the armature should slow-down, and tend towards an asymtote. The casing also works towards an asymtote. Plasmic Physics (talk) 03:42, 22 May 2012 (UTC)

No, that is not correct. That would violate conservation of momentum, and it's neither what our mathematical formula predicts, nor what we observe to happen in experiment. Nimur (talk) 03:48, 22 May 2012 (UTC)

Oh yeah, nevermind. I didn't think it through. Plasmic Physics (talk) 03:53, 22 May 2012 (UTC)

Gravitational time dilation at the centre of a large mass

How does gravitational time dilation operate at the centre of a large mass (not a black hole though)? Does gravity affect time when it pulls in all directions? And on a related note, what time dilation effects would happen if you have a clock in between two massive objects, and is therefore pulled in two opposing directions (equally, and let's pretend the two objects will not fall into each other)? Would the opposing gravitational fields cancel out the effects of time-dilation on the clock or would the two sum together? 137.111.13.167 (talk) 02:49, 22 May 2012 (UTC)

Yes, gravitational time dilation does occur in symmetrical situations such as when a clock is midway between two identical massive objects, or when the clock is at the center of a spherically symmetrical massive object. In the weak field limit, the amount of the time dilation is proportional to the difference in gravitational potential, so the effect due to two objects is additive in a scalar sense, not additive in a vector sense. Red Act (talk) 04:24, 22 May 2012 (UTC)

Physics: Aerodynamics of Pigeon Wing.

A normal Racing pigeon has ten primary flight feathers in each wing. There is, however, an uncommon gene that duplicates the second primary flight feather. This can be seen here. Compare that to the regular, 10-flighted bird seen here.

You'll notice the first few flight feathers of the regular bird are separated at their tips, however this is not the case in the bird with the duplicated second flight feather.

What do you think will be the impact on flight efficiency and speed caused by the extra flight feather? Will the bird fly more efficiently due to the extra feather, or less efficiently due to the lack of a gap? Or another reason?

Thanks, Abbott75

A very interesting and difficult question! The second link to Wing.jpg is broken ("remote linking forbidden"). If you can fix or replace that link, you might get better answers. SemanticMantis (talk) 13:21, 22 May 2012 (UTC)

I would suspect that separated feathers create more drag, but also allow for greater control, as they can then be moved independently. For an analogue, think of separate fingers versus webbed fingers. The separate fingers are more versatile, while the webbed version makes for more efficient swimming. StuRat (talk) 18:49, 22 May 2012 (UTC)

"Whoa!" moments

I hope this is not an inappropriate question for the Science Desk, but there are so many smart people here I'd love to see the answers. Delete this question if necessary.

I was thinking this morning about "Whoa!" moments; the moments when you learn a new fact that rocks your world. Two for me I could think of right off were: 1) When I learned every bit of me used to be inside a star; and 2) When I learned the "double slit" experiment worked with only one electron.

What were your "Whoa!" moments? Tdjewell (talk) 11:29, 22 May 2012 (UTC)

Wheeler's delayed choice experiment's produced a definite "whoa," for me, especially the astronomical variant of the experiment. Some of the cognitive science experiments on consciousness (do I think, "I will extend my hand and pick up that pie," or does the hand extend and then the conscious brain rationalizes it?) are pretty mind-blowing, if true. (I hold back much judgment on the truth of brain experiments at this point — there's still a lot of fundamental unknowns out there.) --Mr.98 (talk) 12:02, 22 May 2012 (UTC)

When I heard about the experiment in Walter Jakob Gehring's lab "to introduce the mouse Small eye gene into flies ... Fly tissues were induced to form eye structures. However. it is important to emphasize that the tissues formed were fly eye structures, not mouse eye structures." When I first heard this, I was sure the person who told me it must have made a mistake. --ColinFine (talk) 14:39, 22 May 2012 (UTC)

In a more mathematical vein, I was pretty amazed to learn the Banach–Tarski paradox, and that there are exactly 17 wallpaper groups. Another fun math fact is that if you throw a dart at a [0,1] interval, the probability of hitting any number you've ever heard of is zero.SemanticMantis (talk) 15:53, 22 May 2012 (UTC)

Alain Aspect's experiment testing Bell's theorem. I second Mr.98 on those cognitive science experiments. I can't find a link to an article that discusses them; I would have thought they would be mentioned at Mental chronometry, but I don't see any mention of them there. Perhaps they didn't pan out on further research?--Srleffler (talk) 17:02, 22 May 2012 (UTC)

Relativity of simultaneity. The idea that a sequence of events happens in a specific order is a fundamental aspect of intuitive understanding in the world. If A precedes B for me, then A precedes B for you. This seems like an axiomatically true idea, and seems to be basically necessary given our intuitive understanding of how the universe works. It is also fundamentally wrong. There is no privileged frame of reference really means that: that there is no where in the universe that has a perspective which is universally true for all other locations. For any sequence of events, there is a place in the universe where that sequence can be seen to occur in a different order. If that doesn't shock your basic core, nothing will. --Jayron32 17:20, 22 May 2012 (UTC)

That quantum tunneling experiments seem to be able to transmit information faster than the speed of light, when the theory says this is impossible. StuRat (talk) 18:34, 22 May 2012 (UTC)

That inside a black hole, matter can collapse into an infinitely small gravitational singularity. StuRat (talk) 18:34, 22 May 2012 (UTC)

Superconductivity, superfluidity, and a Bose–Einstein condensate. StuRat (talk) 18:41, 22 May 2012 (UTC)

When I took the derivative of e^x... and also the first time I heard Miles Davis. Shadowjams (talk) 21:46, 22 May 2012 (UTC)

More math than science, but after not believing it for the longest time, the moment the solution to the Monty Hall problem finally made sense. -RunningOnBrains^(talk) 00:14, 23 May 2012 (UTC)

Actually that's a good one... in light of that i'll update mine... understanding how RSA works. Shadowjams (talk) 01:13, 23 May 2012 (UTC)

I had a "Whoa!" moment a couple of months ago when reading a short article in New Scientist about the unusual reproduction of some starfish (our article doesn't mention it). Starfish initially live as free-swimming larvae, which usually (per our article) settle on a substratum and become sessile. However (per the NS article), in some species, the adult form grows within the abdomen of the larva, detaches from it and settles down, while the larva continues to swim, feed, etc for weeks or months – almost as if the adult starfish had been a parasite, or two previously separate species' genomes and development had merged. I believe Darwin touched upon the latter possibility in On the Origin of Species . . . when discussing metamorphosis. {The poster formerly known as 87.81.230.195} 84.21.143.150 (talk) 12:30, 23 May 2012 (UTC)

A few more from biology: birds are dinosaurs. Several parasites can control their host's behavior, a.k.a "mind control", see zombie ants or Emerald cockroach wasp. Bdelloidea have only female individuals. They don't have sex per se, but they can uptake DNA and incorporate from the environment, from dead sisters, or even other species! SemanticMantis (talk) 13:37, 23 May 2012 (UTC)

It's easy to look for all the grander ones, but as a kid, I remember finding out that the identity of an element is determined solely by the number of protons. The elegant simplicity of it kind of shocked me. We're all used to it now, but cast your mind back....right? Throw in colour vision for me (like, how come brown and pink aren't in the rainbow?) and my recent reading of Steven Pinker's The Blank Slate. Whoa - ! so all that political correctness is just plain wrong (or thereabouts)? IBE (talk) 14:03, 23 May 2012 (UTC)

Many such moments. I learned a lot about science in primary school myself from books, and I realized that religion had to be nonsense despite many grown up people telling stories about the Bible and God as if it were fact. So, the first (and I guess most important) whoa moment was that you could actually not trust grown ups to know the facts even on points they were very sure about.

But I get whoa moments almost every week when I read about some intneresting facts. E.g. just last weeks on a t.v. documentary about the evolution of plants, it was mentioned that grass evolved in such a way as to be able to start fires that would destroy trees, making more room for them. Also, I found out rather late in my life that many vegetables didn't exist more than a few thousand years ago, being the result of selective breeding. Count Iblis (talk) 18:04, 23 May 2012 (UTC)

• There are perhaps 170,000,000,000 galaxies and 300,000,000,000,000,000,000,000 (0.3 septillion) stars in the observable universe.
• Only about 9110 stars and fewer than 10 galaxies are visible from Earth with the naked eye under ideal conditions.
• All Star Trek series and movies take place in the Milky Way (excepting for intervention by Q). Jerk182 (talk) 20:44, 25 May 2012 (UTC)

Fun examples of body parts that go on living

Here (youtube link) is an example of a turtle heart that keeps on beating half an hour after the turtle died - and a few minutes after being cut out of the body.

What are other examples of zombie body parts that just keep on going? Are there any human examples? Egg Centric 11:44, 22 May 2012 (UTC)

I presume you know about Mike the headless chicken? --TammyMoet (talk) 14:05, 22 May 2012 (UTC)

This article, published a few days ago, is an interesting read on the subject. --Jayron32 17:26, 22 May 2012 (UTC)

Ooops, I should have mentioned - that's where I got the link from! Any other good 'uns? Especially interested in human bits here.... Egg Centric 17:55, 22 May 2012 (UTC)

A snake can bite you after it has been decapitated.. Vespine (talk) 22:56, 22 May 2012 (UTC)

F-22 Raptor's deadly toxic stealth goo

http://truth-out.org/news/item/9195-pilots-as-lab-rats-the-reprehensible-risk-taking-on-the-f-22-raptor

What sort of chemicals would cause these problems? Hcobb (talk) 15:47, 22 May 2012 (UTC)

As the article notes, the US government is particularly cagey about the composition of the stealthy materials used in the construction of low-observable aircraft. They successfully resisted court efforts to uncover the materials used when building the B2, and (as Area 51#Environmental lawsuit notes) materials associated with the earlier Have Blue / F117 programme. But the lawsuit discussed in that last article does reveal, broadly, some of the chemicals detected in the tissues of plaintiffs, listing dioxin, dibenzofuran, and trichloroethylene. Materials data sheets for these list dizziness as a side effect, but in fairness dizziness, vertigo, and similar rather non-specific effects are in the materials safety sheets for a huge swathe of chemicals used in or with adhesives, paints, synthetic polymers, cleaning solvents, and other modern materials. You would think that the aircrew and groundcrew would be exposed to quite different things, as the aircrew mostly breathe a mixture of scrubbed recycled air and engine bleed air (that's what you breathe on an airliner, with people occasionally complaining that the air smells of engine degreaser); whereas it seems the groundcrew are crawling about on the outside, rubbing magic space slime into the aerosurfaces. Given USAF/DoD's success in persuading courts that even disclosing the broad chemical nature of materials to which workers have been exposed is a threat to national security, I think you can count on not getting a concrete answer to this question for many decades. As the Russians, and probably the Chinese, have big chunks of F117 (ref) surely they've got a general idea of what (last generation) stealth aircraft were made of. The Area 51 article cites 60 Minutes interview with Congressman Lee H. Hamilton who ascribes the secrecy in this regards to a USAF attempt "to protect themselves from a lawsuit." -- Finlay McWalterჷTalk 17:01, 22 May 2012 (UTC)

I don't think you have to look too hard for anything exotic. Since they reapply the stealth materials frequently, volatile compounds, present in any glue, must out-gas. This is why the safety label on just about any glue says "only use in a well ventilated area". I suspect that the hangars where they apply the stuff are not particularly well ventilated, since they don't want dust particles getting in (and people being able to view the process). These planes also bring in outside air and use that for the pilots, and that outside air must contain the toxins, especially when waiting on the ground to launch.

I suggest that both the maintenance crew and pilots use a completely contained oxygen source (oxygen bottles). I wonder if they have tried this yet. They do represent a potential fire danger, however, so a more sophisticated system could also be designed, where, instead of trying to filter out contaminants, and apparently missing at least one, they just extract the oxygen (and maybe some nitrogen) from the outside air, effectively only filtering in those gases, and nothing else. I've also wondered why they don't just take air samples and analyze them to find the problem component(s). I can see why they may not want to release this info to the public, but, for their own use, this would be quite valuable info. StuRat (talk) 18:17, 22 May 2012 (UTC)

It's hard to know what to think about this sort of thing. For all I know some foreign power has stoked the fires of these media reports simply in order to get more of the chemical data about the stealth material going through less-secure channels they can spy on. Or for all I know truthout is right. A mystery like this (e.g. "sick building syndrome") can be hard enough to crack in the best and most open of circumstances. Wnt (talk) 01:52, 23 May 2012 (UTC)

If pilots consider them so dangerous that they refuse to fly, knowing this will end their career, I believe there is a real problem. StuRat (talk) 16:13, 25 May 2012 (UTC)

Could be as simple as variations in oxygen content. Without a buffer, any fluctuation would reach the pilots. How does the system cope with temperature variations? What's the humidity? Could there be high concentrations of ionic compounds? How are transients in pressure handled by the system? In a passenger airplane you'll probably won't notice short interrupts in air supply when valves open or close, like when the system switches between low and high pressure bleed ports. There's enough air in the plane to "dilute" or dampen any transients. In the F-22, the buffer will be much smaller, and the system will have to cope with much larger and more rapid variations in temperature and pressure. Taking in air at 300°C, cooling, feeding it at high pressure to the zeolite adsorbents, pump the remaining oxygen further, switching to the other sieve while lowering the pressure so the adsorbed nitrogen is released, dump that nitrogen and start the next cycle, and controlling all this to maintain a stable output under varying conditions could be a challenge. Resolution of oxygen level monitoring may not be optimal, I doubt paramagnetic sensors can be used in planes, and electrochemical sensors have long response times. Given the hypoxia and decompression incidents, a faulty system seems more likely than toxic chemicals imo. Ssscienccce (talk) 23:15, 24 May 2012 (UTC)

That doesn't explain why maintenance crews are also affected. StuRat (talk) 05:02, 25 May 2012 (UTC)

The F-35's stealth is "baked in" rather than "splatted on", but I've yet to find a RS that points out that this means that stealth goo sickness won't be a problem with the F-35. So far all my sources say that either the F-22's stealth goo is so harmless that you could use it as a dessert topping to feed to your kids or pieces like this that paint all stealth platforms with the same toxic goo brush:

http://www.phibetaiota.net/winslow-wheeler-the-f-22-toxic-stealth-secrets-screw-sick/

Hcobb (talk) 16:07, 25 May 2012 (UTC)

Quick weather question

The National Weather Service in Tuscon has issued a Red Flag Warning for my area. I was reading the warning and had a question about some terminology used within:

.LOW PRESSURE PASSING NORTH OF ARIZONA WILL CREATE STRONG AND
GUSTY WINDS ON WEDNESDAY...WITH SUSTAINED 20-FOOT WIND SPEEDS UP
TO 30 MPH AND GUSTS TO NEAR 50 MPH. THESE WINDS...COUPLED WITH
CONTINUED HOT AND DRY CONDITIONS...WILL CREATE CRITICAL FIRE
WEATHER CONDITIONS THAT MAY RESULT IN RAPID FIRE GROWTH AND
SPREAD.

...

* WINDS...SUSTAINED 20-FOOT SOUTHWEST WINDS OF 25 TO 35 MPH ARE
 EXPECTED WITH GUSTS TO NEAR 50 MPH. THE STRONGEST WINDS ARE
 EXPECTED IN EASTERN PORTIONS OF THE WARNED AREA.

The warning is archived here.

What does "20-foot winds" mean? Thanks! -- 143.85.199.242 (talk) 17:53, 22 May 2012 (UTC)

WAG, but maybe this is the standard height off the ground that winds are measured from; that is the anemometer is located at 20 feet off the ground. It would make sense, for standardization purposes, to make the wind speed measurement at some standard height, as wind speeds will be quite different depending on where they are measured. That's just a guess tho. --Jayron32 18:02, 22 May 2012 (UTC)

Per Rachelle Willgren, writing in the "Blanco County News" in April 2011, the "Red flag warnings" for fire danger define "20 foot winds" as "the average 10-minute wind speed (mph) and direction 20-feet above the vegetation." Flames and smoke from burning brush or trees rise this high, and it is useful to know which way and how far the wind will carry them. [1] here is the National Weather Service definition. Edison (talk) 18:45, 22 May 2012 (UTC)

Your confusion is certainly justified; I had never heard this term before even working as an atmospheric scientist. It appears to be used solely for fire-weather-related purposes [2]; almost all other atmospheric science fields measure "surface" winds at 10 meters above the ground, regardless of vegetation [3]. -RunningOnBrains^(talk) 00:32, 23 May 2012 (UTC)

do most mainstream water-resistant sunscreens have dangerous ingredients?

I've read that according to the sunscreen controversy that many sunscreens contain avobenzone and octocrylene which absorb into the skin and are potent free radical generators. I would certainly like to avoid this kind of thing while protecting my skin. Where can I find waterproof sunscreens that judiciously prefer to use titanium dioxide or zinc oxide as stabilisers rather than octocrylene, as well as other dangerous ingredients? 137.54.7.13 (talk) 18:24, 22 May 2012 (UTC)

I'd expect any store which sells organic products might have such sunscreens. And don't forget about just covering up, with loose-fitting white clothes and wide-brimmed hats. Also, sit in the shade. StuRat (talk) 18:56, 22 May 2012 (UTC)

This is for looking good at the beach. There'd be no reason to have really good skin if one wasn't showing off. 76.104.28.221 (talk) 18:03, 24 May 2012 (UTC)

"Organic" isn't always a good sign that something is safe, though. Nightshade, deathcap mushrooms, and anthrax are all organic. --Carnildo (talk) 02:32, 23 May 2012 (UTC)

Gravitational Blueshift Equation

I have noticed that on the Gravitational Redshift Page there exists an equation for calculating gravitational redshift. There is no Equation on their for calculating Gravitational Blueshift, there is no Gravitational Blueshift Page, and there is a Blueshift page, but it also lacks an equation for calculating Gravitational Blueshift. The Equation:

$\lim _{r\to +\infty }z(r)={\frac {1}{\sqrt {1-\left({\frac {2GM}{R^{*}c^{2}}}\right)}}}-1$

I also failed to locate such a blueshift equation anywhere else on the internet. So I then tried to figure it out on my own. I went about this by plugging variables into the redshift equation and then attempting to discern the blueshift one through the results. I am not entirely sure I did this correctly. Please tell me if I didn't.

First off the variables:

R* = 5m

r = 10m

M = 1x10²⁷kg

G (used the compatible one) = 6.673848x10^-11 N (m/kg)²

c (not sure if this is the compatible version) = 3x10⁸m/s

λ_I = 100m

So I solved it step by step:

2GM: 2 x G x (1x10²⁷) = 1.3347696x10¹⁷

R*c²: 5 x (3x10⁸)² = 4.5x10¹⁷

2GM/R*c²: 1.3347696x10¹⁷ / 4.5x10¹⁷ = .296615467

1 - 2GM/R*c²: 1 - .296615467 = .703384533

Square Root of 1 - 2GM/R*c²: Square Root of .703384533 = .838680233

1/(Square Root of 1 - 2GM/R*c²): 1 / .838680233 = 1.192349552

1/(Square Root of 1 - 2GM/R*c²) - 1: .192349552

z(r) = 1/(Square Root of 1 - 2GM/R*c²) - 1 --> z = [1/(Square Root of 1 - 2GM/R*c²) - 1]/r:

z(10) = .192349552 --> z = .192349552 / 10 = .0192349552

Now as the page said z is a fractional change of the wavelength, I came up with this equation:

λ_F = λ_I - (λ_Iz)

When plugging this in I got: λ_F = 98.07650448

Now to figure out the Blueshift Equation I figured I had to keep the same variables (except R* and r swap values, since R* "is the radial coordinate of the point of emission (which is analogous to the classical distance from the center of the object, but is actually a Schwarzschild coordinate)." And r is "the radial coordinate of the observer").

I came up with the equation one would need after one figures out z:

λ_F = λ_I + (λ_Iz) Which in this case would be: 100 = 98.07650448 + (98.07650448z) Because for the sake of Energy Conservation the amount of potential gravitational blueshift must be equivalent to the potential gravitational redshift and so 98.07650448m would have to return to being 100m.

I then calculated what z would have to equal for such a thing to happen through these steps:

λ_F - λ_I = Required Increase: 100 - 98.07650448 = 1.92349552

Required Increase/λ_I = z: 1.92349552 / 98.07650448 = .019612195

And so, I arrived at z = .019612195

I even plugged it in to the equation to be sure:

λ_F = λ_I + (λ_I x z): 98.07650448 + (98.07650448 x .019612195) = 100

I then could not figure out a Gravitational Blueshift Equation that yielded said z value. I found many incorrect solutions. In fact, I even tried plugging into the Gravitational Redshift Equation (which I knew would not work) in desperation.

Could someone who is more experienced with this sort of calculations please help? Some of the problems I have been working on simply require a Gravitational Blueshift Equation.

Doctor Condensate (talk) 22:46, 22 May 2012 (UTC)

I'm not more experienced, but this source [4] seems to touch on it. Two things which I don't know to be true: a) a gravitational redshifted photon, reflected back from a mirror, should arrive at its source at its original frequency, implying a simple inverse relationship; b) the frequency change should match the amount of gravitational potential energy gained or lost as the mass of the photon is moved from one position to the other. (Though both would apply only in constant static gravitational fields, if even that often...) Wnt (talk) 02:41, 23 May 2012 (UTC)

These two things are true (in a static gravitational field, like the Schwarzschild solution used for the common formula Doctor Condensate has mentioned). In the Schwarzschild solution, the observed frequency f_o (observed at radius r_o) and the emitted frequency f_e (emitted at radius r_e) are related as follows:

$f_{o}=f_{e}{\sqrt {\frac {1-{\frac {2GM}{r_{e}c^{2}}}}{1-{\frac {2GM}{r_{o}c^{2}}}}}}$

If you want a "z value" as it's commonly used in astronomy for redshift, you will get a negative z for blueshift. In general:

$z={\frac {f_{e}}{f_{o}}}-1$

Substitute the ratio of f_e and f_o from the eqation above and you get your z. (I don't know any field of study where it's common to use z for blueshifts; and personally I think the ratio of frequencies is the more convenient number anyway)

Icek (talk) 03:35, 23 May 2012 (UTC)

First of all, z(r) doesn't mean z times r. It means that z is a function of r. The equation at the top only gives you the value of z in the limit where r is very large.

There's no such thing as the redshift (or blueshift) formula; it depends on the situation. The equation you gave is only valid in one specific case: the emitter is hovering at a fixed distance from a spherical object of mass M, and the receiver is hovering "at infinity" (i.e., very far away). If you want to calculate the blueshift in some situation you need to be specific about what situation that is. Note that physicists often use the word "redshift" in a way that includes blueshift, just as they use "acceleration" in a way that includes deceleration. A blueshift is just a redshift by a factor of less than one. -- BenRG (talk) 20:38, 23 May 2012 (UTC)

God, I read "Gravitational Bullshit Equation," glad I didn't see this question until now or the first reply may have been very different. RMoD (talk) 23:17, 23 May 2012 (UTC)

Thank you for the quick responses. Well, BenRG. My current work requires the following. First, an equation that calculates the redshift of light emitted from a point at a specific distance from the center of a spherical object with mass, and observed at a point directly above the point of emission (which of course is also at a specific distance from the center).

Second, I need an equation that calculates the inverse. I need to be able to calculate the blueshift of light emitted from a point at a specific distance from the center of a spherical object with mass, and observed at a point directly below it. Which, I think Icek provided for me.

For both of these, a line that passes through both the point of emission and the point of observation should also pass directly though the center of the spherical object with mass.

Doctor Condensate (talk) 00:16, 24 May 2012 (UTC)

Yes, Icek's formula is what you want. That formula works equally well whether r_e < r_o or r_e > r_o, and whether it's a redshift or a blueshift. It's even correct when the emitter and receiver aren't collinear with the center of the gravitating object. In the case of gravitational redshift (but not redshift in general), the blueshift factor of light sent from A to B is equal to the redshift factor of light sent from B to A. -- BenRG (talk) 19:09, 25 May 2012 (UTC)

Okay, thank you very much.

Doctor Condensate (talk) 02:02, 26 May 2012 (UTC)