# Astronomers discover star racing around black hole at Milky Way center

UCLA astronomers report the discovery of a remarkable star that orbits the enormous black hole at the center of our Milky Way galaxy in a blistering 11-and-a-half years—the shortest known orbit of any star near this black hole.

The star, known as S0-102, may help astronomers discover whether Albert Einstein was right in his fundamental prediction of how black holes warp space and time, said research co-author Andrea Ghez, leader of the discovery team and a UCLA professor of physics and astronomy who holds the Lauren B. Leichtman and Arthur E. Levine Chair in Astrophysics.

The research is published Oct. 5 in the journal *Science*.

Before this discovery, astronomers knew of only one star with a very short orbit near the black hole: S0-2, which Ghez used to call her "favorite star" and whose orbit is 16 years. (The "S" is for Sagittarius, the constellation containing the galactic center and the black hole).

"I'm extremely pleased to find two stars that orbit our galaxy's supermassive black hole in much less than a human lifetime," said Ghez, who studies 3,000 stars that orbit the black hole, and has been studying S0-2 since 1995. Most of the stars have orbits of 60 years or longer, she said.

"It is the tango of S0-102 and S0-2 that will reveal the true geometry of space and time near a black hole for the first time," Ghez said. "This measurement cannot be done with one star alone."

Black holes, which form out of the collapse of matter, have such high density that nothing can escape their gravitational pull, not even light. They cannot be seen directly, but their influence on nearby stars is visible and provides a signature, said Ghez, a 2008 MacArthur Fellow.

Einstein's theory of general relativity predicts that mass distorts space and time and therefore not only slows down the flow of time but also stretches or shrinks distances.

"Today, Einstein is in every iPhone, because the GPS system would not work without his theory," said Leo Meyer, a researcher in Ghez's team and lead author of the study. "What we want to find out is, would your phone also work so close to a black hole? The newly discovered star puts us in a position to answer that question in the future."

"The fact that we can find stars that are so close to the black hole is phenomenal," said Ghez, who also directs the UCLA Galactic Center Group. "Now it's a whole new ballgame, in terms of the kinds of experiments we can do to understand how black holes grow over time, the role supermassive black holes play in the center of galaxies, and whether Einstein's theory of general relativity is valid near a black hole, where this theory has never been tested before. It's exciting to now have a means to open up this window.

"This should not be a neighborhood where stars feel particularly welcome," she added. "But surprisingly, it seems that black holes are not as hostile to stars as was previously speculated."

Over the past 17 years, Ghez and colleagues have used the W.M. Keck Observatory, which sits atop Hawaii's dormant Mauna Kea volcano, to image the galactic center at the highest angular resolution possible. They use a powerful technology, which Ghez helped to pioneer, called adaptive optics to correct the distorting effects of the Earth's atmosphere in real time. With adaptive optics at the Keck Observatory, Ghez and her colleagues have revealed many surprises about the environments surrounding supermassive black holes, discovering, for example, young stars where none were expected and seeing a lack of old stars where many were anticipated.

"The Keck Observatory has been the leader in adaptive optics for more than a decade and has enabled us to achieve tremendous progress in correcting the distorting effects of the Earth's atmosphere with high–angular resolution imaging," Ghez said. "It's really exciting to have access to the world's largest and best telescope. It is why I came to UCLA and why I stay at UCLA."

In the same way that planets orbit around the sun, S0-102 and S0-2 are each in an elliptical orbit around the galaxy's central black hole. The planetary motion in our solar system was the ultimate test for Newton's gravitational theory 300 years ago; the motion of S0-102 and S0-2, Ghez said, will be the ultimate test for Einstein's theory of general relativity, which describes gravity as a consequence of the curvature of space and time.

"The exciting thing about seeing stars go through their complete orbit is not only that you can prove that a black hole exists but you have the first opportunity to test fundamental physics using the motions of these stars," Ghez said. "Showing that it goes around in an ellipse provides the mass of the supermassive black hole, but if we can improve the precision of the measurements, we can see deviations from a perfect ellipse—which is the signature of general relativity."

As the stars come to their closest approach, their motion will be affected by the curvature of spacetime, and the light traveling from the stars to us will be distorted, Ghez said.

S0-2, which is 15 times brighter than S0-102, will go through its closest approach to the black hole in 2018.

The deviation from a perfect ellipse is very small and requires extremely precise measurements. Over the last 15 years, Ghez and her colleagues have dramatically improved their ability to make these measurements.

Co-authors on the research include Mark Morris, a professor of physics and astronomy at UCLA, and Eric Becklin, UCLA professor emeritus of physics and astronomy.

**Ghez's research**

In 1998, Ghez answered one of astronomy's most important questions, showing that a monstrous black hole resides at the center of our Milky Way galaxy, some 26,000 light-years away from Earth, with a mass approximately 4 million times that of the sun. The question had been a subject of raging debate among astronomers for more than a quarter of a century.

In 2000, she and colleagues reported that for the first time, astronomers had seen stars accelerate around the supermassive black hole. Their research demonstrated that three stars had accelerated by more than 250,000 mph a year as they orbited the black hole. The speed of S0-102 and S0-2 should also accelerate by more than 250,000 mph at their closest approach, Ghez said.

In 2003, Ghez reported that the case for the Milky Way's black hole had been strengthened substantially and that all of the proposed alternatives could be excluded. In 2005, she and her colleagues took the first clear picture of the center of the Milky Way, including the area surrounding the black hole, using laser guide star adaptive optics technology at the Keck Observatory.

"The pivotal research by Ghez's UCLA group using the Keck Observatory has evolved from proving that a supermassive black hole exists in the center of our galaxy to testing the very fundamentals of physics," said Taft Armandroff, director of the W.M. Keck Observatory. "This is truly an exciting time in astronomy."

Ghez's research program currently receives its primary funding from the National Science Foundation, the Keck Foundation, the MacArthur Foundation, and the Lauren B. Leichtman and Arthur E. Levine Family Foundation, with additional funding from the Preston Family Endowed Graduate Fellowship in Astrophysics (supported by Howard and Astrid Preston), the Janet Marott Student Travel Awards, and the Gordon Binder Post-doctoral Fellowship. Significant funding was also provided by the Packard Foundation for early stages of this work.

Ghez is the first woman to receive the prestigious Crafoord Prize from the Royal Swedish Academy of Sciences, which she was awarded this May.

Explore further

**More information:**"The Shortest-Known–Period Star Orbiting Our Galaxy's Supermassive Black Hole," by L. Meyer et al.,

*Science*, 2012.

**Citation**: Astronomers discover star racing around black hole at Milky Way center (2012, October 4) retrieved 22 August 2019 from https://phys.org/news/2012-10-astronomers-star-black-hole-milky.html

## User comments

RealityCheckValeriaTParsecVendicarDWhat makes your reference frame a spacial case?

"but it's clock-tick 'count' ONLY, and NOT TIME OR DISTANCE that has slowed or shrunk!" - NonRealityCheque

RealityCheckRealityCheckCave_ManRealityCheckHi, pleased to meet you.

Hehehe. By all means don't let the facts get in the way of your 'opinions'. I have no idea who VendicarD is, nor do I really care. I only discuss the facts in evidence in this case, and not the man. Try it sometime, mate. :)

Silverhilldtyarbroughyyz"The Shortest-Known–Period Star Orbiting Our Galaxy's Supermassive Black Hole" is available on the arXiv preprint server: http://arxiv.org/abs/1210.1294

RealityCheckSilverhillSupport your claims with actual mathematics (or links thereto).

Peter HentVendicarD"What makes the observer who INTERPRETS observations as 'time slowing' and 'distance shrinking"?" - RealityCheck

RichardmcsquaredLurker2358Well, if a particle is moving fast enough, then if Relativity both increase that particle's mass and decreases it's length, then when it is moving fast enough it would become a disk-shaped black hole in one reference frame, while appearing unchanged in another reference frame.

This paradox is unacceptable.

For example, if a particle is moving 0.999c it will have 22.366 times the mass, and 0.0447 of the length, therefore 0.0447 of the volume, therefore the density of such an particle becomes roughly 500 times the original density in one reference frame, while being unchanged in a co-moving reference frame.

As you can see, tack on a few extra "9's" for accelerator speeds, and the particle should become a microscopic black hole.

Lurker2358Proton mass = 1.672621777(74)e−27 kg. (wiki)

Now that's ten orders of magnitude.

Every 2 "9's" in the decimal as a fraction of the speed of light causes Lorentz formula to increase the mass by an additional order of magnitude, AND reduce the length by roughly 1.5 orders of magnitude.

So the density of the proton would go up by a factor of roughly 500 for every two "9's" in the decimal place.

So at 0.99999c:

Length: 0.00447 * original length.

i.e. One nanometer becomes 4.47 picometers, one picometer becomes 4.47 femtometers, and one femtometer becomes 4.47 attometers.

Mass: 223.6 * original mass

Density: 50,000 * original density

Since it's an exact metric, you can predict the next pair of "9's" by factors of 10 and 100 respectively.

0.9999999c gives.

Mass: 2236 ...

Length 0.000447 ...

Density: 5,000,000 * original density.

see below.

Lurker23580.9999999999999999999999951c

When I plug this value into the Lorentz equation, I getthe following mass and length scaling factors for the "other," co-moving reference frame.

Mass: 319,438,282,499.9699...

Length: 3.130495168499e-12

(abbreviated).

Density: 102,040,816,326,530,612,168,034.4123

"proper Radius" of proton: 0.8768 fm or 8.768e-16 m.

"Proper mass" of proton: 1.672621777(74)e−27kg

When I plug in that value to the escape velocity formula, I get a schwarzchild radius of:

7.930473764570068e-43 m.

The actual "radius" in the length-compressed dimension for THAT actual particle detected would be:

2.7448181637399232e-27 m

This is still 17 orders of magnitude too large, HOWEVER, because the length goes down by a factor of 10 for every two 9's and the mass increases likewise, the schwarzchild radius increases with V.

Lurker2358So then a Proton should become a microscopic black hole when it's velocity equals or exceeds 0.999,999,999,999,999,999,999,999,999,999,995,1c

I used comas to help count, even though I'm not sure if that's proper. That's 32 i's and a 51.

This looks like a lot, but if they detected a proton with 9 fewer 9's for it's velocity, then I see no reason why "somewhere" and "somehow" in the universe there wouldn't be a proton with this much velocity. It would seem like there would have to be such particles somewhere.

1, So then how would we detect them?

2, are they large enough to consume other sub-atomic particles, or are they too small to interact?

nevermind

Lurker2358v = 0.999,999,999,999,999,999,999,999,999,999,995,1c

It turns out this is, within margin of error of the numbers cited by wiki, the exact speed at which a proton should become a black hole, and it's also the exact speed at which the proton's length becomes exactly twice the Planck length, or it's radius in the direction of motion is compressed to Planck length.

Surely this would be a microscopic black hole, but I don't think our accelerators have gotten that fast.

You can't do the math for this in a calculator, because the calculator doesn't have large enough variables to save the values to enough significant digits to do it with enough precision to be useful.

FleetfootNo, this is what happens when popular press authors dumb science down to the point where it has more in common with discredited nineteenth century concepts than current theories. "Caveat Emptor!" indeed.

FleetfootYou have the problem the wrong way round, Einstein's actual theory is purely geometrical. The idea of "time slowing down" or "distance shrinking" is the metaphor.

FleetfootMost of the posts in this thread are based on misconceptions.

Relativity says that mass is invariant, it does not change with speed. It also says that, in their own rest frame, moving objects do not shrink and clocks tick normally. All the effects observed are geometric in origin and result from projection of values in one coordinate frame onto a different set of axes.

Lorentz Aether theory says objects shrink when moving relative to the aether, moving clocks tick slower and mass increases.

Both theories result in the same maths in flat space (the Lorentz Transforms) hence cannot be distinguised experimentally or by thought experiments, you are wasting your time trying.

FleetfootThe reason why relativity is overwhelming accepted is that it was extended to GR which models gravity. In GR, the geometrical basis of special relativity is modified to include 4D curvature driven by the stress-energy tensor (for example in the form of mass). There has never been an aether-based equivalent and the limit of GR as the mass tends to zero is the geometry of the Minkowski Metric, i.e. special relativity. GR is of course extraordinarily well supported by experiment and observation.

Lurker2358Who's relativity are you using?

Einstein's relativity most definitely says that mass is variant from one reference frame to another, and it varies by a scale of 1/(sqrt(1-(v^2/c^2))).

Therefore if a proton is moving at the velocity I gave above, with the 32 "9's," as measured in some reference frame "A," then in the co-moving reference frame, that is the frame where the proton appears stationary, the proton will be a black hole, at least based on the VARIABLE mass and length predicted by Einstein's and Lorentz equations combined with the escape velocity equation (to find the schwartzchild radius.

Lurker2358Truth be told, we couldn't accelerate a ship anywhere near the speed of light, even if only Newton's mechanics were true, nevermind Einstein's relativity, because the variance of mass really doesn't become logistically significant until 0.3c anyway. If you can accelerate to 0.3c in Newton's mechanics, then the extra ~5% mass predicted by Relativity equations is not that big of a deal after all, and only requires a relatively small increase in fuel to fix.

When you get to like 0.6c, you're an extra 80% of mass. As I recall, the fuel requirement of an ideal rocket goes up by power of 1.5, so needs ~2.42 times fuel of Newton's mechanics.

Lurker2358This means that contrary to popular understanding, further increases of our rocket ships velocity is not significantly impacted by the Theory of Relativity AT ALL until at least about 0.3c to 0.4c, which we are nowhere near achieving.

The limits of Newtonian mechanics alone is far more than we have ever come close to overcoming.

New Horizons spacecraft velocity: 21km/s = 21,000m/s

This is 14,278 times less than the speed of light, or ~1,428 times less than 0.1c.

0.1c is the slowest that you could theoretically travel in a colony ship to make it between two nearby stars in one "generation," as used for the unit corresponding to about 40 years.

Since mass is only affected by one half of one percent at this velocity, then Relativity is not the main prohibition to interstellar travel, because we can't even move fast enough for it to be a factor.

colheita sombriaFleetfootAs I said, the two approaches result in identical equations so in every situation, they both make identical predictions. SR can never be distinguished from LET directly (but GR reduces to SR, not LET).

FleetfootAll the effects exist and are measurable but they are geometric in GR. Time doesn't "slow down", it simply maps to different coordinate durations due to geometric projection.

No, it is a single set of self-consistent equations but different authors explain it in different ways. Words are a poor substitute for maths.

Of course, just project between the coordinate axes.

FleetfootI am discussing standard undergraduate relativity as it is taught as a precursor to GR. See Taylor & Wheeler "Spacetime Physics" for example.

Exactly, it would be paradoxical for it to be a proton in one frame but a black hole in another. The real science is unambiguous, a proton is a proton regardless of the frame of the observer.

FleetfootThe energy required rises non-linearly to infinity when v=c. You can treat that using the Newtonian equation for kinetic energy and infer that mass increases but the geometric understanding of relativity merely uses a more complex equation with invariant mass.

There's nothing wrong with using relativistic mass as long as you are careful to account for all effects but you need to understand the invariant approach too if you want to go on to understand GR.

ValeriaTFleetfootDon't be silly, you know perfectly well there is no such thing as "AWT".

FleetfootSimilarly, Newton wrote in the Scholium of the Principia that space was absolute and there was such a thing as absolute motion relative to that space, but in the mechanics he derived from that notion, any hint of absolute motion disappears and is replaced by Galilean Relativity. Einstein's experiments on the photoelectric effect were the basis for QM (Planck's original understanding was that EM radiation was bursts of waves rather than particles) yet Einstein never accepted QM. It is not unusual for scientists to be responsible for breakthroughs with which they are subsequently uncomfortable.

However, that is all irrelevant, it is a matter of fact that the equations of GR are purely geometric and Newtonian mechanics is Galilean invariant regardless of the preferences of their authors.

Q-StarBefore YOU can have a theory, you must first have some piece,,, some infinitesimal part, some fragment,,,, no matter how small,,,, of the reality we find ourselves in to base your theory on.

Your reality is in some universe completely outside of the universe you are finding yourself stranded in. I can see why you are a failed science FICTION writer.

Oh yeah, I almost forgot,,,, please never, ever, help your kids with their homework,,, otherwise they will find themselves the objects of ridicule and derision.

Q-StarP.S. Good move taking down your "theories". I don't blame you for not wanting to endure the reviews of your "theories".

VendicarDAnother one bites the dust.

Such Humiliation.

Q-StarThanks, that is more fun than a person deserves in this life. The "Yarbrough Paradoxes" are a hoot. They sound like the writings of a person with a sever delusional disorder fueled by some sort of illegal substance. If he had spent the time required to write all that drivel actually reading and studying, he would be a post-doc by now.

I bookmarked for when we need a good laugh at work.

TheGhostofOtto1923"Later studies indicate that the top cruise velocity that can theoretically be achieved by a thermonuclear Orion starship, assuming no fuel is saved for slowing back down, is about 8% to 10% of the speed of light (0.08-0.1c). An atomic (fission) Orion can achieve perhaps 3%-5% of the speed of light. A nuclear pulse drive starship powered by matter-antimatter pulse units would be theoretically capable of obtaining a velocity between 50% to 80% of the speed of light. In each case saving fuel for slowing down halves the max. speed."

-Like I say google is your friend. Your only friend.

RealityCheckFleetfootThat is just the LET interpretation of the effects. To explain the MMX, you also need length contraction and to explain the reduced acceleration of high speed electrons in electric fields measured by Thomson you need relativistic mass but taken together these ad hoc phenomena produce identical results to SR.

As I said in a previous post, it is only when you move on to GR that the interpretations can be distinguished.

RealityCheckLIke I said, the accelerator imparts additional energy to accelerated particle. The internal energy state increases its internal inertia and slows its internal processes which are interacting with accelerating fields, such that a feedback loop of more-inertia-slower-interaction-processes-with-external-fields is established....which results in lesser and lesser effectiveness of any constant external field acceleration force, so increase in external field strength is less and less effective as particle internal energy/inertia increases and slows interaction and increases 'latency of acceleration effect' in a non-linear way. :)

FleetfootOr "relativistic mass" as it is usually known. You also need length contraction and since these are observer independent effects, the cause needs to be velocity relative to some reference, the substance commonly called the "luminiferous aether".

As I said, you are simply restating Lorentz's aether theory.

RealityCheckcoastwalkerFleetfootThe difference between clocks in relative motion is observed, internal changes is one interpretation but it also matches SR's geometric explanation.

Because the amount of clock slowing observed on planes is the square root of the total effect in the MMX. You need length contraction by an equal amount to explain the null result of the MMX. Put those together and you get LET.

RealityCheckFleetfootI'm not sure why you say "no", I wasn't disagreeing with the fact that it is observed, just noting that it doesn't distinguish between the interpretations.

I think you need to look up the experiment, to explain the null result, aether theory needs to assume that the material of the arms of the interferometer is length-contracted, not the photons. Materials such as invar alloy or fused quartz have been used for example.

RealityCheckValeriaTFleetfootAh, ok, thanks for clearing that up. When we say a clock on a plane is slowed due to speed, that means it produces fewer ticks over some arbitrary duration than a clock which is not moving, i.e. it is relative to a "stationary" clock.

It may not be a necessary part of your ideas, but it is necessary experimentally. If length contraction doesn't come out of your maths as well as clock slowing, it will fail to predict the null result for the MMX.

FleetfootRubbish, the wave motion is the vector sum of the motion of each point on the wave relative to the source plus the flow of the water. Try adding a flow of the medium to your animation and see what happens.

RealityCheckAnd the MMX interpretation as "also requiring contraction" is an unnecessary 'artifact' of the abstract/theory mathematical/geometrical equations/analysis construct which are invalidly overlain on the actual observation/data. It is the assumptions/interpretations therefrom that are misleading. Garbage in garbage out. If observations are left to speak for themselves (as I pointed out), no such 'overlays' necessary. :)

FleetfootThen you have no way of determining the duration over which the counts occur. You need two

No, it is nothing more complex than Pythagoras theorem. Try working it out yourself, there are plenty of explanations all over the web.

SilverhillFleetfootNo, each beam creates its own reference by exciting sodium atoms in the ionosphere, they are in fact essentially parallel. The apparent convergence is just an example of perspective:

http://www.qedcat...9151.png

ValeriaTRealityCheckOh, I see what you're getting at. :) All that the plane needs is the usual speed indicator system (Pitot Tube or whatever) already calibrated for speed readout during two runs over same route distance. Two different 'Pitot Tube indicator' speeds over same route will do. The 'standard run' is set with the first run, and the second run will tell what's what when compared. The test clock's 'absolute counts' just have to be sufficiently different for each run to show the speed-related 'tick process slowing' for the faster speed run.

Re MMX: Pythagorean theorem doesn't involve "distance contraction', nor does MMX assumptions beforehand. No theoretical post-run analysis 'assumptive/interpretative overlays' change that. Cheers. :)

Fleetfoot"calibrated for speed", that sounds as though you need a clock ;-)

If that's all you have, you can equally well say that the clock was at rest on both runs and the Earth moved faster hence the distance was length-contracted ;-)

Unless you compare two clocks, you don't have an unambiguous result.

Correct, it it just tells you the length of the hypotenuse given the other two sides, but the point is that that is all the "complex maths" you need to show that there would be a fringe shift in the MMX if clocks slow but the arms don't contract. As I said, look up the analysis and try it for yourself, you'll find you cannot get a null prediction without length contraction.

FleetfootNope, the motion is simply the vector sum of the two motion components (wave and medium) for gravity waves and capillary. Liquids don't support transverse modes (i.e. HORIZONTAL displacement of the surface perpendicular to the direction of propagation).

RealityCheckYeah, that's what I meant when I said "Oh, I see what you're getting at." :)

But it can be done by establishing standard run 'count' at one very slow speed and then make same run at higher speed. Neither speed need be 'measured' as such, just observed to BE one much slower than the other. It is sufficient to know that the fuel consumption and drag effects etc on plane have increased during second (hence faster) run over same distance/route. No other 'timing' involved. Same test clock; differing counts for demonstrably slow/faster runs. ;-)

Re MMX: But there is no 'clock' and hence no 'contraction' element in MMX setup or analysis assumptions. Hence no need to include any 'time' or 'contraction' in analysis of results. Just behaviour of the photons.

Cheers! :)

FleetfootBut not necessarily the same distance, that's why I emphasised "unambiguous".

The cycles of the light act as a clock. As I said, try doing the calculation, you will find you cannot make it work without length contraction. This was known in the 19th century, it is a really trivial piece of maths and written up in many web sites.

RealityCheckThe route distance is between markers for different runs over same route. No need to invoke subtle assumptions about such gross start-end points for same clock count start-end over same route for slow/fast runs.

Re MMX: No need for 'cycles' to be clocks. The leading and trailing edge of beams/waveforms is what it is. Direct overlay between split beam components will tell absolute beam/waveform differences (if any) by that overlay (interference indicates difference, no interference indicates no difference in waveform (leading-edge to trailing edge for each 'leg' beams). No need to introduce 'timing' of events or any 'contraction' to explain something that is not inherently required for the 'events' to take place and compared absolutely between split beam fronts/rears at overlay stage for extracting 'interference (or not) information in absolute pattern terms. No maths/clock/other abstract assumptions/analysis required.

Gotta leave for town. See ya. :)

SilverhillFleetfootNot the point, you need to prove it doesn't change, you can't just assume success.

Sorry, the onus is on you to prove your theory. The hint is - if you try, you'll find you can't do it.

RealityCheckFleetfootFair point but they did that a century ago, both LET and SR are self-consistent theories and match the relevant observations. Now it's your turn.

What you claim is that motion relative to causes clocks to slow down by a certain amount. The MMX observationally produces a null result when moving relative to the same which means the speed of light is invariant. The onus is on you to explain that null result, and since you use the same clock slowing factor as used by LET, I think you will find you have to have the same formula for length contraction to achieve that.

RealityCheckMMX also proves photons don't couple to space, hence 'expanding space' of big bang supposedly 'stretching photons' is NOT valid conclusion from reality, no matter what standard theory claims! :)

FleetfootThere is no "hence" in what you say, just an ad hoc assumption but no matter, LET was always empirical.

Ah, the penny drops, your "hence" is justified this time but that's a different model originally proposed by Ritz in 1908. It was clearly disproved by Sagnac in 1913 (although other observations such as binary star systems made it untenable before it was published).

I hadn't realised you were cherry-picking phenomena from different conflicting models, clock slowing doesn't happen in Ritz's "ballistic" theory but Sagnac rules it out with or without that effect.

RealityCheckFleetfootThat's a common mistake, there are doppler effects if viewed from the lab but in the Sagnac experiment, the interferometer is also on the table and rotating at the same rate as the source so there is no Doppler between them. If there were, the fringes would move at a common rate but they are actually static.

The interferometer actually measures the phase difference, not frequency and if Ritz's theory were correct, there would be no shift (if neither distance nor speed relative to the source are changed, neither is the time delay hence the phase on arrival). In reality, there is a fringe shift proportional to the angular velocity which cannot be explained by Doppler. Again, this is common knowledge if you do a little research, it's been known since 1913.

The effect is used in optical gyroscopes in aircraft and inertial navigation systems and could not exist if the ballistic model were correct.

RealityCheckFleetfootExcellent, no disagreement there then.

That's a bit ambiguously stated but I think you have it the wrong way round, in reality, the beam going the same way as the rotation is retarded because it has farther to travel (in the lab frame). They both travel the same distance in the rotating frame hence ballistic theory predicts no phase difference.

That would cancel it out in all the models so doesn't give any new information, what you need to do is explain (show by calculation) why there is a fringe shift in Sagnac's setup.

RealityCheckFleetfootExplaining the existing results remains your first challenge, if you can't do that, you don't have a base from which to extend the experiment.

I'm getting very busy organising some events next month too, it's been fun. Good luck.

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