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Galaxy Without Any Dark Matter Baffles Astronomers (arstechnica.com)
A distant galaxy that appears completely devoid of dark matter has baffled astronomers and deepened the mystery of the universe's most elusive substance. The Guardian reports: The absence of dark matter from a small patch of sky might appear to be a non-problem, given that astronomers have never directly observed dark matter anywhere. However, most current theories of the universe suggest that everywhere that ordinary matter is found, dark matter ought to be lurking too, making the newly observed galaxy an odd exception. Dark matter's existence is inferred from its gravitational influence on visible objects, which suggests it dominates over ordinary matter by a ratio of 5:1. Some of the clearest evidence comes from tracking stars in the outer regions of galaxies, which consistently appear to be orbiting faster than their escape velocity, the threshold speed at which they ought to break free of the gravitational binds holding them in place and slingshot into space. This suggests there is unseen, but substantial, mass holding stars in orbit. In the Milky Way there is about 30 times more dark matter than normal matter. The latest observations focused on an ultra-diffuse galaxy -- ghostly galaxies that are large but have hardly any stars -- called NGC 1052-DF2. The team tracked the motions of 10 bright star clusters and found that they were traveling way below the velocities expected. The velocities gave an upper estimate for the galactic mass of 400 times lower than expected. The researchers described their discovery in the journal Nature.
... in other ways. I remember reading a paper that explained exactly that away very nicely. I can't find it anymore, but I know it was mentioned in the Scientific American, many years ago.
Our math still does not fit reality, especially energy-wise, but not because of the rotation of galaxies.
It's just that in pop-sci, "dark matter/energy" is commonly presented as if our theories were right and it was just our observations of the universe that are wrong, when in reality, "dark matter/energy" is merely a convenient identifier for the discrepancy and is merely saying "we don't know yet". Implying that, obviously, it's our theories that are still wrong.
So saying "without any dark matter" is already highly questionable. Rather, this galaxy might help us fix our silly theories, to match the cold hard reality that we simply observe. Not the other way around.
You are wrong. Dark matter and dark energy are used as they are the only things that help explain our observations of nature.
Yes our theories are still wrong. They will be until we can describe everything - something not likely to ever happen. That's science. What you are doing is hand waving without understanding the basics.
I am not GP, but:
"Dark matter and dark energy are used as they are the only things"
That statement is completely false. "Only" isn't a science word (it requires you disprove all other theories, even theories you haven't had yet), and neither of those claims is proven or even likely, given they don't address even currently understood data.
"hand waving without understanding the basics"
i.e. to paraphrase you make the claim that "dark matter and dark energy" are the basics of science, and that they are set in stone, and deeper understand requires knownledge/acceptance of these basics.
Again this is not science. You will likely have to throw away a lot of theories built on false logic (e.g. QM, standard model, mass/gravity) if the current understanding of these hit a dead end. You cannot say "this theory is broken, yet must form the basis of better theories", because that's nonsense logic. A broken theory is broken, it must be wrong.
"You are wrong"
And acceptance of mistakes is necessary for science, i.e. you might be wrong.
Really the danger to science is people like you. You learn things as though they're true, you build your careers based on this, and when experiments point to faults, you gloss over the failure and defend the broken model. It's more religion than science.
There are enough unrelated discrepancies in our observations, that can all be explained by dark matter or dark energy (making up a consistent fraction of the universe in all cases), that I think it's safe to say there's probably something to it. Especially when we know the Standard Model in particle physics is flawed, and many extensions happen to contain viable dark matter candidates.
For dark matter specifically, I would say the smoking gun is the aptly named Bullet Cluster. Two galaxies colliding, ordinary matter interacts and gets slowed, dark matter doesn't interact and gets separated from the ordinary matter, and then the dark matter and ordinary matter components can be observed separately (ordinary matter from ordinary photons, dark matter from its gravitational lensing effect on photons coming from galaxies behind the cluster).
There is a very promising theory by a Dutch theoretician (paper here), which can explain the observations without the need for dark energy / matter. I have seen the presentation of his work, and, as far as my understanding, it is based on idea that gravity is an emergent force, so-called entropic gravity Drupal.
Dark matter has always struck me as a kludge.
Astrophysicist (but not a cosmologist) here: this is true! In its favour, though, this makes "dark matter" an umbrella term that covers any phenomenon that fits the data. It might be stray, undetected, planet-sized objects; it might be some exotic neutrino variant; it might be little clumps of antiquarks; it might be one of any number of things. All these possibilities are referred to under the term "dark matter".
On the particular possibilities you mention:
Our current theory of gravity does not apply on the scales we are observing, i.e., the theory is incomplete.
This is certainly possible, and some theorists work on it. My understanding, though, is that these approaches postulate energy (with an equivalent mass) resulting from large-scale gravitational fields; that is, you can think of this as a form of dark matter that arises from the gravitational field itself.
This sort of approach has trouble explaining the formation of small-scale dark-matter halos, which depend on some kind of dark-matter self-interaction. It's also incompatible with the example in this article: if "dark matter" results directly from gravitational fields, how can you have a galaxy without it?
Physical laws are not constant. e are looking at very distant objects, and seeing them in the distant past. Perhaps universal constants are not, in fact, constant across large spans of space and/or time.
If this were the case, we'd expect the rotation curves of nearby galaxies to be well-behaved, while more distant galaxies would show gradually increasing evidence for the influence of "dark matter". We don't see that. There are theories that fundamental constants do change over time - I've seen some interesting tests for the speed of light changing based on gamma-ray absorption spectra - but they don't work as an alternative explanation to dark matter.
Please, note that there is are some very powerful distinctions between practical engineering and the predictive power of science.
There are but literally every bit of engineering is based on scientific evidence. Whether or not the person doing the engineering fully and properly understands that science does not make it less true. Engineering doesn't work unless it is based on the ability of science to make predictions. There is science independent of engineering but not the other way around.
People sometimes call engineering "applied science". I think that definition is incomplete. I think it is "applied science with economic and temporal constraints". Engineering is science applied to practical tasks within the constraints of a budget and with a deadline.