Readers may recall when we covered the first detection of gravitational waves from space, heralding a new era in astronomy. It was big news. Now, a second detection has been announced.
From NASA’s Astronomy Picture of the Day: (h/t to Dr. Leif Svalgaard)
A new sky is becoming visible. When you look up, you see the sky as it appears in light — electromagnetic radiation. But just over the past year, humanity has begun to see our once-familiar sky as it appears in a different type of radiation — gravitational radiation. Today, theLIGO collaboration is reporting the detection of GW151226, the second confirmed flash of gravitational radiation after GW150914, the historic first detection registered three months earlier.
As its name implies, GW151226 was recorded in late December of 2015. It was detected simultaneously by both LIGO facilities in Washington and Louisiana, USA. In the featured video, an animated plot demonstrates how the frequency of GW151226 changed with time during measurement by the Hanford, Washington detector. This GW-emitting system is best fit by two merging black holes with initial masses of about 14 and 8 solar masses at a redshift of roughly 0.09, meaning, if correct, that it took roughly 1.4 billion years for this radiation to reach us.
Note that the brightness and frequency — here mapped into sound — of the gravitational radiation peaks during the last second of the black hole merger. As LIGO continues to operate, as its sensitivity continues to increase, and as other gravitational radiation detectors come online in the next few years, humanity’s new view of the sky will surely change humanity’s understanding of the universe.
Added: I had an interesting discussion with Dr. Leif Svalgaard about gravity that I thought was worth sharing since I found the topic fascinating.
On Wed, Jun 15, 2016 at 10:52 AM, Anthony Watts wrote:
I wonder, what is the speed of Gravity waves?
Thanks,
Anthony
From: Leif Svalgaard
Sent: Wednesday, June 15, 2016 12:04 PM
To: Anthony Watts
Subject: Re: GW151226: A Second Confirmed Source of Gravitational Radiation
The same theory that predicts them [GR] also predicts that they propagate with the speed of light.
Gravitational waves are ‘ripples’ in the fabric of space-time caused by some of the most powerful processes in the universe – colliding black holes, exploding stars, and even the birth of the universe itself. Albert Einstein predicted the existence of gravitational waves in 1916, derived from his general theory of relativity. Einstein’s mathematics showed that massive accelerating objects (such as neutron stars or black holes orbiting each other) would disrupt space-time in such a way that waves of distorted space would radiate from the source. These ripples travel at the speed of light through the universe, carrying information about their origins, as well as clues to the nature of gravity itself.On Wed, Jun 15, 2016 at 12:08 PM, Anthony Watts wrote:
Yes, but how does the universe have gravitational cohesion at that speed? Maybe the waves are speed of light, but the effect of gravity across distance must be instantaneous, otherwise how would galaxies manage to form or stay together?
A
On Wed, Jun 15, 2016 at 12:24 PM, Leif Svalgaard wrote:
The effect of gravity is not instantaneous. We know this because the finite speed is needed be make the predicted positions of planets [and spacecraft] come out right.
Galaxies form because the gravity of Dark Matter helps to draw the intergalactic matter together.
See also http://scienceblogs.com/startswithabang/2010/08/25/what-is-the-speed-of-gravity/
Note: several updates were made to this story about an hour after publication, to correct the title, to replace “gravity waves” with “gravitational waves” so that they weren’t confused with the meteorological term “gravity waves” which I’ve always thought was wrongly named, and to add some new discussion I had with Dr. Svalgaard about the speed of gravity. Also added was an illustration. I’m sorry for the issues, I had partially written the story and set it to auto-publish hours ahead, and then I got distracted by a phone call and didn’t complete the story before it published.
Smokey, the em force is incredibly stronger than gravity over all distances, the equation itself doesn’t change if you put a big number in it. Your statement is misleading. What we do find is that the coulomb force is seen by us to operate over small distance, relatively speaking, because imbalance of charge we see, lightning, etc., or create, capacitors, batteries, etc., is quickly rectified by nature, e.g. sparking, discharges, currents – and this because the force is so incredibly strong. It is this way all over the universe, so between great masses in same, there is can never be a huge imbalance of charge, so no significant coulomb forces over those distances. A 5g teaspoon of electrons on earth would attract a 2kg mass bag of protons on the sun with a force of 10 000Kg, i.e. that 5g teaspoon on earth would only stay on earth if weighed down with a 10 ton truck, say. Obviously 5g electrons in one space is impossible, the atomic bomb shows what happens when you mess with imbalance of charge. This, to clarify, is why we don’t see coulomb forces over huge distances, because there does not exist an imbalance of charge over such distances that would give rise to those forces. It is possible that plasma ejections from quasars, etc., electrons in one jet and protons in the other could be interesting, but I don’t think that has been detected, yet.
There is a huge amount of stuff out there we just cannot see, it does not emit or reflect enough light for us to see it. However good our instruments, there’s a lot we just cannot see, nor see the local effect of, hell we can’t even spot large asteroids in our own solar system until conditions are just right. This matter, very real and detectable under the right conditions comes under the term dark matter just as much as the more exotic, imaginary or otherwise stuff.
To correct my earlier 10^34 factor error, the comparison of the coulomb force to(over) force of gravity between an electron and a proton is 2 x 10^39.
@Neillusion:
Your figures are ONLY accurate at atomic distances; the fall-off of the EM force over distance at BEST is two orders of magnitudes greater than that of gravity. In other words, changing the distance absolutely does affect the EM force more than it does for G, it’s something you can test empirically in your own garage.
Make sure you’re using the right equations, and (less importantly) like/matching units; those two things can be a big trap for the unwary.
Neillusion is absolutely correct. We actually have students do this calculation in the Introductory Physics class after we first introduce Coulomb’s Law (that describes the electrical force between two point charges).
@ur momisugly Joel Shore: You guys aren’t doing the math wrong; you’re doing the wrong math.
I see what you’re trying to say about charge/mass ratios, but that’s really only part of the problem. The base problem is the use of those motionless 2-point charge equations to describe something that can in no way be describe as a 2-point motionless charge, and then on top of that comparing them to gravitational equations that assume one is working in 1 Earth gravity a la Newton.
I have no argument w/Coulomb’s Law, or with the math you’re having people do, I’m simply saying that those aren’t the right equations to use to describe, e.g., why the force of a magnet on a given object decreases so much more rapidly with distance than gravity does.
Also just to complete the picture, the coulomb force to (over) gravity force between two protons is 1 x 10^36 and between two electrons 4 x 10^42
OK, if we can observe black holes merging should we not visually observe also stars merging (or close to be merging?)?
I would guess there are much more stars out there then black holes?
Have any binary stars been observed which come close to the definition of a potential ‘soon’ merger? With soon I mean in astronomic times…
@Larry Plume P.: The answer is, unhelpfully, “yes & no.” The Bottom Line Up Front is that stellar mergers are likely much more common than black hole mergers, but are still not exactly “common,” and most are too dim to see from Earth, even those located within our own galaxy. Meanwhile, LIGO and other follow-on instruments (holding my breath figuratively for the LISA mission) should eventually be able to detect black-hole mergers like the ones we’ve seen so far (we think!) from most of the observable universe, more than making up for their comparative rarity. This will very possibly render black hole mergers more apparent to us than stellar mergers for quite a long time… which in a way makes sense, since they are very much more powerful events and so should be “visible” from a much, much wider portion of the universe.
I’ll post the discussion below in case anyone’s interested in yet another typically long Smokey post. +_+;;;
It is assumed based upon observations that there are many more stars than there are black holes (stellar mass or otherwise) in the universe. Observation of stars in our own galactic neighborhood indicates the majority of stars we can individually resolve are found to occur in bound orbital systems of two or more stellar objects at a time (binaries, trinaries, and so on). This being the case, we do see many binary stars (~40%-50% of those observed, by some estimates), some of which are expected to merge in the not-too distant (cosmologically-speaking) future. Nevertheless, space is big, and most stars are nowhere merging, even in closely orbiting binaries (<1AU).
(See here, for one example of a pair that might be merging sooner rather than later: http://metro.co.uk/2015/10/21/kiss-of-death-telescope-spots-two-stars-so-close-they-are-merging-5454095/)
Being the big plasma/gas bags that they are, an observed stellar merger is thought likely to be a bit showy in the local neighborhood, but even a merger of large stars would be hard to visually catch & verify at distances greater than say, from here to one of the Magellanic Clouds. Such a merger would also not be nearly as energetic as the merger of neutron stars, let alone of black holes. The latter especially are comparatively rigid objects which merge in a matter of seconds to milliseconds, whereas stellar objects are much more fluid — two very large stars becoming a single homogenous mass could take weeks+ in a process which would almost certainly trigger super-nova explosions and the formation of a black hole even before fully completed.
As a mental image for comparison, imagine two pair of small objects orbiting at close proximity in otherwise empty space. Now imagine that the first pair is, say, two 20 kg clumps of Jello pudding, and the second is, say, two 20 kg bricks: assuming sufficient attraction (maybe they have opposite magnetic charges to help out? Sure, why not!), the first pair will slosh and splash and eventually wobble into a single unit, while the other will more or less instantly bump together to form a single unit out of two. The former is something like stellar mergers, the latter something more like black hole mergers.
Another understanding from observations of binary pairs is that it is quite common for a large (say, red giant) star to have a much smaller companion (say, a white dwarf) as a partner. When these two objects get close enough, the dwarf star sucks material from the outer atmosphere of the larger companion producing novae which are used as "stellar candles" due to their predictable brightness. But what's REALLY weird is that it should be theoretically possible to have the smaller (much hotter & more rigid) companion orbit the larger star while brushing up against the outer layers of the larger one's stellar atmosphere — or weirder still, totally inside the surface of the larger star! Sadly, we haven’t directly visualized this yet either that we know of… and in one sense, how would we if a given “binary” has one star orbiting permanently INSIDE of the other? Also, what would be the exterior evidence that a formerly intact-yet-interior companion had become homogenized (or hadn’t yet, for that matter)? Is there some way to measure the outer surface to pin-point the “moment” the two stars actually merged, instead of being a binary pair? In this circumstance, all we can do for now is guess.
So this was the needlessly long answer to Lars P.’s shorter questions, which I will now (again) sum up: Yes stellar mergers happen, and though they are probably much more common than black hole mergers, they are (as of now!) much less visible to our instruments, and likely to remain that way for a long time.
Smokey
Youa re obviously comfortble with stellar evolution and reactions.
Let me borrow your background and intelligence for a few moments. (I promise I will return it undamaged, interest-free and unused! Even though that doesn’t sound quite right.)
The most common 3 elements in our solar system are dominated by the sun, Jupiter & Saturn’s hydrogen and Helium. On earth (and probably the other rocky planets, moons and asteroids), the list is very different: Helium is second, making up almost all of the remaining 25%. Oxygen is a distant third. On earth, oxygen is the most common element, making up about 47% of the earth’s mass. Silicon is second, making up 28%, followed by aluminum (8%), iron (5%), magnesium (2%), calcium (4%), sodium (3%), and potassium (3%).
These are built up from 1H1, 1H2, and 2He4 nuclei into the heavier elements by fusion in star cores, then (theoretically) blow back into space if a supernova blows out the fused results.
So, for the most common elements (including iron at AW = 56), what is the optimum fusion sequence needed to make the result? 12Carbon6 (for example) requires how many sequential supernovas? What is the optimum cycle to make Neon, Oxygen, Magnesium, Silicon, Sulfer and the far heavier iron?
Obviously, if a smaller star runs through enough cycles to create modest weight elements, those are not discharged into the interstellar dust clouds
Or just one – one that burns long enough to continue past the first hydrogen->Helium chain reactions? But, if that long-burning supernova burns carbon into heavier elements, which supernova created the Oxygen, Nitrogen, Silicon, Neon, Mg, Sulfer chains?
Those early-formed elements are not all burned out in the series of sequential supernova explosions that made the iron, nickle, lead, and uranium (etc) that we know exist in the solar system, but somehow you have to have enough sequential supernova’s that did exist to make everything. And every supernova explosion needs millions of years of dust particle coasting through interstellar space at sub-light speed just to get to the next yet-to-be-formed supernova location.
At a 13.5 billion year old universe, with our star 4 light years from the nearest star (and not getting much closer nor farther away!), and with no supernova remnants anywhere near this arm of the Milky Way galaxy (and in a galaxy arm that has been stable for the 4.5 billion years that the earth has NOT been hit by supernova debris!) there does not seem to be enough time to make the 10^57 element nuclei we know exist here.
Thanks for the short and long answers Smokey!
Fascinating kiss of death picture of VFTS 352, unfortunately our life span is too short to observe it to the end….
Stupid question, to the possibility of one smaller companion orbiting inside a larger star, wondering if it may be derived that also a smaller planet could be orbiting inside a star, like for instance a Mars or Earth size planet orbiting inside the sun?
Would it be still keeping its consistence or would it be vaporized and blown apart? Is there a critical mass over which such entity would survive as a distinct entity inside a star?
Oh, and whilst we are at stupid questions and you were so kind to answer mine – here is another one, maybe you can help clear it?
Whilst we see the Sun in the position where it was 8 minutes ago, the gravitation pull is coming from its actual position which is different.
Whilst light and gravitation travel with the same speed, why do we not see the Sun in the same position as where the gravitational pull is coming from?
@Larry Plume P.:
Question #1) A planet isn’t likely to survive being heated past the vaporization point of its constituent elements, at least not for very long. White dwarves and neutron stars are made of much sturdier stuff, but even these are expected to spiral fairly quickly down to the core of whatever star they merge with… assuming the larger star survives the process!
Question #2) Actually the gravitational pull of the Sun is just as time-lagged as the light that we see. Thus if one were to (as the scenario goes) “magically vanish the Sun from its point in space,” we would continue on blissfully unaware for ~8.5 minutes… in other words, our path through space wouldn’t change until the Sun’s light went out, as the changes in the curvature of space space-time which keep us on our orbital path wouldn’t be felt until then.
Smokey (Can’t do a thing about wildfires)
June 20, 2016 at 2:16 am :
Question #2) Actually the gravitational pull of the Sun is just as time-lagged as the light that we see.
To my knowledge that does not work like this. If one computes the gravitational pull time-lagged, as the light, the orbits would not be stable. Astronomers do compute the gravitational pull as if being instantaneous, not time-lagged.
” Astronomers do compute the gravitational pull as if being instantaneous, not time-lagged.”
I believe they have thought their way past this and now believe it travels at C and not instantaneous. What you mentioned was what many thought not long ago though.
Lars P., I think someone else(s) also had a question about the speed of gravity up-thread, but micro6500 is correct.
1. While Newtonian mechanics ARE generally used for spacecraft orbital calculations, it is because they’re much easier to work with… NOT because they produce the most accurate results! For one, most spacecraft orbit in circumstances which do not require relativistic accuracy in order to accurately predict their motion (see 2). For another, any measurable difference between Einstein & Newton is quickly erased by a much bigger fly in the calculation ointment: atmospheric drag, which acts upon satellites even out to the GPS constellation, and for which neither set of equations can accurately account due to the chaotic & variable nature of the Earth’s thermosphere.
2. Einstein’s field equations are needed to accurately calculate Mercury’s orbit (specifically, the precession of that orbit over time) because unlike spacecraft moving around the Earth or about the solar system, Mercury is close enough to a massive-enough body that Newtonian calculations of its orbit diverge measurably from observed reality over time. Calculations using Einstein’s equations (to my knowledge) have yet to diverge from the margin of observational error.
3. The “speed of gravity” doesn’t factor much into the previous two points because neither the spacecraft nor the Earth, nor Mercury nor the Sun (and thus the displacement in space-time caused by these bodies) are moving very fast. Only in instances such as the hypothetical the “Missing Sun” problem does it come into play, in which cases the field equations predict the information regarding such a sudden absence will propagate at the speed of light. So far observational evidence supports that conclusion:
In 2003 a team announced at the AAS meeting in Seattle that they had used radio signals from a distant quasar passing near Jupiter to get a rough idea of the actual value for the speed of gravity. The team announced that “the propagation speed was equal to the speed of light within an accuracy of 20 percent,” and that even allowing for observational error, “”we can confidently exclude any speed for gravity that is over twice that of light.”” From the linked article: “If the speed of gravitational propagation were infinite, the apparent position of the quasar should have moved in a perfect circle due to the bending of the radio waves, Kopeikin said. Instead, it inscribed an offset ellipse, shaped roughly as would be expected if the speed of gravity and the speed of light were equal.” (http://www.nbcnews.com/id/3077353/ns/technology_and_science-science/t/first-test-gravitys-speed-upholds-einstein/)
In 2012 a Chinese team published a paper in which they claimed to have empirically measured the speed of gravity as being within 5% of c (95% – 105%, iirc) by looking at the difference between the calculations of an infinite speed of propagation versus the actual observations of the pull of the solar tides on the Earth’s crust (link to the full paper is WAY too long to share, but it’s in the references for the Wikipedia article on gravity).
In both cases detailed observations showed empirically that the speed of gravity is finite and likely to match c as predicted. I haven’t heard of other more recent experiments which overthrow or modify these results, but that doesn’t mean they don’t exist.
Thanks for the answers Smokey. It seems the speed of gravity may be equal with the speed of light, but it does not seem to be proven in that experiment:
http://www2.lbl.gov/Science-Articles/Archive/Phys-speed-of-gravity.html
“Einstein may be correct about the speed of gravity but the experiment in question neither confirms nor refutes this,” says Samuel. “In effect, the experiment was measuring effects associated with the propagation of light, not the speed of gravity.”
Another very interesting thought experiment about GPS I found in a post about Van Flanders (name at the end of your link)
http://www.ldolphin.org/vanFlandern/
” Dingle’s Question:
University of London Professor Herbert Dingle showed why special relativity will always conflict with logic, no matter when we first learn it. According to the theory, if two observers are equipped with clocks, and one moves in relation to the other, the moving clock runs slower than the non-moving clock. But the relativity principle itself (an integral part of the theory) makes the claim that if one thing is moving in a straight line in relation to another, either one is entitled to be regarded as moving. It follows that if there are two clocks, A and B, and one of them is moved, clock A runs slower than B, and clock B runs slower than A. Which is absurd.”
Dingle’s Question was this: Which clock runs slow? Physicists could not agree on an answer. As the debate raged on, a Canadian physicist wrote to Nature in July 1973: “Maybe the time has come for all of those who want to answer to get together and to come up with one official answer. Otherwise the plain man, when he hears of this matter, may exercise his right to remark that when the experts disagree they cannot all be right, but they can all be wrong.”
So to say, if the clocks of the GPS satellites are set to run slower to be in agreement with the clocks on the Earth, how comes that agreeing to relativity from the point of view of the satellite the Earth clocks should be running slower?
Smokey, I am not convinced by your claim, actually believe you are wrong, w.a.d.r.. Could you direct me to or you yourself provide a compelling explanation? Comparing Fc=kQ1Q2/d^2 and Fg=GM1M2/d^2, nowhere can I find any source that says this Fc falls off at greater distance more than Fg.
The reason why we don’t see Fc at any distance cosmic or solar, only earthly (lightning), is because charges even themselves out so earth here and a distant earthlike planet, the other side of the universe would have neutral, none differing charge, so no Fc.
you mention a garage expt. perhaps you could be more detailed about that, thanx
As with my reply to Joel above, It’s not that you’ve done the math wrong, you’ve just done the wrong math.
The experiment has to do with using a magnet, a floor- or table-mounted bar of metal or magnet, and a force gauge. When one plots the force needed to disengage the magnets from one another, one finds that the force does NOT vary as inverse square, but rather as 1/r^4, assuming nothing is placed between those items to attenuate the field. It is this, among other attributes of the combined EM force, that shows definitively that point charges are not what should generally be calculated when trying to determine the effect of EM over distance.
From point to point on a wire, sure. From place to place on a lightning strike, even: grand, at least for rule-of-thumb calculations. But trying to calculate the effect of the EM force between moving objects (not particles) on a solar system scale, no sir. For that you absolutely need to incorporate the various field equations. IOW, the math in your earlier example is correct, but it only applies if the equivalent point charges exist AS POINTS, there are no other magnetic fields, EM flows or interactive materials between the two, and they are stationary w/respect to one another at the start of your calculation.
Even then, I’d look at it askance, because those types of masses/collections of charged particles that you use for an example are routinely thrown around in thunderstorms here on Earth (at least in terms of the excess charges). Since the difference in charge should be enough to not only counter gravity but the tensile strength of the metal, how come struck lightning rods aren’t ever torn from their mounts and thrown tens of kilometers into the air? In fact, if Coulomb’s law were the primary rule governing lightning formation/generation, we should see many examples of the cloud charge potential being neutralized not with sparks of lightning, but by the actual dragging of oppositely charged material up from the ground and into contact with that part of the cloud! We don’t see that, so something else must be happening that goes beyond the 2-pt. charge equation.
(As per your comment posted while I was typing this, one can separate “magnetic” from “electric,” but the EM force governs them both; trying to use “electric” equations to calculate EM effects for large-scale events without taking that into account is what I am terming “the mistake.”)
@Smokey ( I hope the wild fires are looked after)
“assuming nothing is placed between those items to attenuate the field”
. That “assuming” to me is the problem. There is always something “in between”. That to me is where the ” theories” fall apart
Also, Smokey, the magnetic force is different again and I believe falls off proportional to 1/d^3, I’d have to check that.
In the Fc vs Fg stakes, the language/semantics used suggest a direct comparison between those two, as I have tried to explain a couple of times.
Charge accumulations, + vs -, do not exist at planetary or solar scales, so we don’t see them or observe such effects as would be produced – it is not because the force has fallen off in a different way to gravity.
If am using the wrong math then am at a loss to understand and need help with what you are trying to say.
What may be the most important take-away is that we agree that EM doesn’t operate (usually) over stellar distances. ^_^
It’s only the method of calculation I take issue with, because it is that indiscriminate use of Coulomb’s Law that gives the Electric Universe theory it’s power, especially when combined with a semi-scientific discussion of how “gravity doesn’t work like we think it does, Einstein was wrong, and the Sun is made mostly of Iron!”
The force between two magnets decays like 1/d^4. (See, e.g., here: http://www.physicspages.com/2013/06/25/force-between-two-magnetic-dipoles/ ) The faster decay is because there are no magnetic monopoles (i.e., no isolated north poles without a south pole). So, a “magnet” is really a magnetic dipole.
If you have an electric dipole (a + charge and – charge of equal magnitude separated by some distance) then the force of interaction between two such electric dipoles would also go as 1/d^4 (as long as the distance d is much larger than the size of the dipole, i.e., distance between the + and – charge).
So, there is no inherent difference between the behavior of the electric and magnetic force except for the fact that, as I said, magnets necessarily come in pairs of north and south poles so there is no magnetic analogy to having an isolated electric charge.
Just to complete the discussion and bring in gravity: For gravity, there is no such thing as negative mass, which means there is a gravitational monopole but no such thing as an isolated gravitational dipole (i.e., if you do a multipole expansion https://en.wikipedia.org/wiki/Multipole_expansion of any mass distribution, there will necessarily be a monopole term). So, this is sort of the converse of what is true for magnetic force.
So, perhaps this is the sense in which what Smokey says and what Neillusion and I have been saying can be thought of as sort of expressing the same idea in different ways: The electromagnetic force does tend to drop off more quickly at large length scales because there are no magnetic monopoles and, although there are electric monopoles, you tend to have near-neutral net charge over large enough lengths scales (so that the monopole term essentially disappears). For the gravitational force, on the other hand, you always still have the monopole term, so it drops off more slowly with distance.
I haven’t really thought about it in this way before, but I at least tentatively think this could be a reasonable way of expressing how things work.
Thanks, Joel. This explains it in a different way, and maybe does a better job than what I was saying.
Racookpe1978,
Acoustics from the big bang lead most astrophysicists to believe the universe is infinite. Infinite space and time. Of course, then, the big bang was only some local event 13.7 bya and not the beginning of the universe as we think of it, but infinity gives one plenty of time to cook up all your elements.
Smokey, mmmm. not happy
This all started in respect of ‘hearing’ black holes merge due to change of gravity/spacetime. The forces in my opinion are way way to small to detect.
If you take away from that conversation that coulomb forces do not operate on cosmic scales, I think you’d be making a mistake, rather large one too.
quasars are said to be ejecting jets of electrons into space, hundred of thousands of light year jets. This charge will have enormous forces associated with it and other charges in the universe, i.e. another quasar somewhere else ejecting protons/+ve plasma. Your own argument on the complexity of forces E/M, actually magnetic, garage expt, supports the electric universe’s point of view as I understand it. But, to stay on point, such charge would have a phenomenal effect, much more than gravity, tens of orders of magnitude exactly as explained. To be dismissed by you so easily is disappointing. These should be investigated and reported on by astrophysicists, for the effect must be hugely significant in formative stages of the cosmos and elsewhere.
Back to the point, a cosmic discharge of accumulation of charge, like sparks crackling faster and faster as you bring the excess charge closer to the opposite charged body…
With respect to the smallness of the measurements, Neillusion, it’s true that trying to measure something that’s moving on the scale of 1/10000 of a proton using a ruler is going to be pretty difficult. Fortunately, LIGO (and eventually, LISA) doesn’t even try, instead using basic scientific principles which are well-understood to magnify the effect of an otherwise imperceptible change in the universe.
The magnification methods used (as well as those used to dampen the effects of interfering phenomena) are actually both intuitive and common-sensical, so go check them out & then we can discuss how those methods might or might not work as well as we’d like them to. In fact, my biggest issue with the project to date is not it’s results (finally!), but with the cost/time which have been spent in achieving them. As someone else I heard put it, “The two published detection papers by LIGO to date are possibly the most expensive in the entire history of science!”
As for our debate as to the appropriate use of a particular 2-pt charge equation, perhaps I’ve done a poor job of explaining myself; perhaps Joel’s posts will clarify things a bit better. The bottom line from my perspective is that Coulomb’s Law is not used in astrophysics because in most astrophysics, it isn’t the right equation to use.
I’m not saying the equation isn’t “valid” or “truthful.” I’m saying using it to do something like predict the interaction of particles in the Earth’s outer atmosphere with the solar wind is analogous to calculating the CAPE on a spring morning in Norman, OK with a sling hygrometer: you need more information than that particular tool gives you.
Your question regarding lightning suggests you do not appreciate the numbers or scales involved.
Lightning transfers, on average, 15Coulombs of charge.
1 Coulomb is equal to 6.23 x 10^18 point charges.
There are 6.?? x 10^23 atoms in a mole, so 12g carbon for example…
If we are dealing with electrons, that weigh 1/2000th the proton, then it works out that, within one order of magnitude!,
15Coulombs electrons charge weighs 15 x 1/(2000 x 12) x 10^-5
=~ 6 x 10^-8 grams, if protons, x by 2000.
The force over say 1000m is (10^10 x 200)/(1000 x 1000) = 2 x 10^6N.
So the lightning cloud is spread over 1000m sq and weighs a few 10’s of millions of kgs and is tugged downward (the ground up) by approx 200 000kg coulomb force – this spread over a kilometer sq. area as is the charge, so any one small piece of say roof tile of say 30cm by 30cm, say 1000sq cms will have 1000/100000×100000 th the charge and individually a negligible force pulling it upward ~ 20grams – this is why it is not ripped off the roof.
There are so many thing wrong with this…
Fist they have to verify the first detection that happened during an engineering run, and they discounted the sanity check..