I am who I am.
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Calculus is something quite simple and yet it has an inexplicable and unreasonable effectiveness. It can be taught to school children and they can use it to solve a very large set of problems.
In this case you could summarise calculus as the mathematics of things that change, but I doubt that the audience would be any the wiser.
The analysis of functions of variability.
1. As @evan_au pointed out in the reference, there is thought to be at least one black hole, just not necessarily a super-massive one at the centre.Thanks for the reply, you're clearly very smart (I'm not being facetious). However, I take issue with your overuse of the spacebar. The attached file illustrates what I'm talking about. It's guys like you that are causing chaos on our forums... Get your act together.
2. Gravity is complicated. Even Newtonian gravity is complicated. We can find good solutions for what is called the two-body problem, which literally just involves two bodies and gravity acting between them. We can even make a bit of progress with a three-body problem, however you get to four-bodies and the whole thing is just a "pig" ("pig" just means difficult). Most of the "solutions" or information about multi-body problems are just obtained from simulations and numerical approximation techniques and not from any analytical or exact solutions to the problem.
Having a super-massive black hole at the centre of a galaxy is one easy way to have a stable structure that is a galaxy. In a numerical approximation, the whole thing does behave a lot like a two body problem for everything close to the black hole. You have the body you are considering (planet or star etc.) and the only other body of any importance is the black hole because nothing else has the mass to compete with that and so you can just neglect it.
We don't know for certain that the Triangulum Galaxy doesn't have a SMBH at it's centre but let's assume it doesn't. Then it just is another possible solution (a distribution of the diffuse matter like Hydrogen gas and the more dense bodies like planets in the system) for the multi-body problem that produces a stable structure like a galaxy. There are going to be quite a few solutions.
3. When analysing structures like galaxies and the orbit of certain things, one of the approximations that can be used is just to draw a circle (well a 3-D spherical surface) around the point which the body seems to orbit out to a radius that is the radius of its orbit (well more or less if it's elliptical or odd shaped) and assume that there is a roughly uniform distribution of mass outside of that sphere. We have results like the shell theorem which suggest the only thing(s) providing a net gravitational pull on that body and hence influencing the orbit of that body is the mass inside of that sphere. I haven't seen the data for the Triangulum galaxy but I'm fairly confident that these are the sorts of techniques that would have been used to suggest that there wasn't much mass (e.g. a SMBH) on the interior of some of the orbiting objects you mentioned ("...its core stars orbit slowly..."). However, the core of the galaxy is not the only thing holding the galaxy together. As you look at objects further out, that circle (or 3-D spherical surface - but for a fairly flat galaxy it's just a flat circle that you'll be interested in) which is the boundary of their orbit is much bigger. This means there is more mass on the interior of that circle and hence much more that can be binding them.
4. I'm not sure exactly what you meant with the sentence about binding and attracting stars in some H2 dense regions. If you meant attracting H2 gas so as to form a new star.... well stellar formation is accelerated by all sorts of processes and conditions. Hydrogen gas might be getting driven into where these stars are forming rather than merely being attracted by the mass of whatever seed for a star was already there. Also Hydrogen gas isn't all that heavy or "massive" is the correct term . You don't need a lot of mass in your seed for a new star to attract some hydrogen gas, especially if the gas is already close to it. The rate of star production is likely to be much more of an indication of the density or availability of H2 gas in that region rather than any indication that there is a lot of mass in that region.
David asks:Yes, because it is actually possible to stop them.
If you became aware that a significant-sized asteroid was likely to collide with the Earth in the not-too-distant future (say months rather than years) would you tell your colleagues or tell government officials or tell the world? Or would you just sell the family home and have a great holiday (assuming post Covid-19 conditions)?
What would you do?