I know it doesn't, but I say you can use maths to prove whatever you like.
So, 'maths' as an answer, is not satisfactory to me.
AFAIK, all this discussion is in the realms of hypothesis.
It is. It's just currently the best hypothesis, and it's refined to better match observation over time. For example, the impact with Theia was originally thought to be a glancing blow by a planet spinning similarly to earth, but more recent simulations indicate it was a head-on collision and that Theia had relatively little angular momentum. This hypothesis does make predictions about the moon's core that are falsifiable but it may be some time before we figure out a way to make the necessary measurements.
You're technically right, but only when compared against the exact way the comment you're replying to was phrased. Scientists don't just write down whatever equations give them the answers they feel like getting that day, they first figure out which equations give correct answers, and then use only those.
The stability of ring systems can be worked out using the same old laws that Newton figured out, which describe inertia and gravity. They can then be tested in particular by observing rings around other planets, and in general by every observation that confirms Newton's laws.
> AFAIK, all this discussion is in the realms of hypothesis.
it is unfortunate that you are being downvoted. I have been increasingly taking note of things that "science" says that the general public then takes for granted as fact, when they're entirely unfalsifiable, unprovable, and just conjecture. of course there is nothing wrong with conjecture, and especially nothing wrong with mathematically-backed conjecture. but there is a huge gulf between making conjectures about Earth possibly having had rings in the past and accepting as fact that Earth most certainly had rings in the past.
it seems to me that a big part of this is the (at least contemporary) human "need" to be absolutely sure about everything. most people come away from reading e.g. this comments thread either "knowing" that Earth definitely had rings in the past, or rejecting the rhetoric here and believing Earth never had rings. few people allow themselves the "mental gray area" of not really believing or disbelieving something, instead leaving that "did the Earth ever have rings or not" factoid field in their mental database with the value of "idk, maybe?"
once you start training yourself to embrace this "mental gray area" for unprovable (or merely unproven) facts, you start to notice a lot of things that many people take for granted as being absolutely True, when in fact there is ample possibility for them to be False. another example is the composition of the Earth's core—there's all sorts of ways we can inductively determine this, but ultimately we don't definitively know what the Truth of the matter is.
this "lack of 'mental gray area'" phenomenon is what leads to many people today taking not just proven scientific research as gospel, but also all sorts of theories and conjectures and unproven hypotheses. how many ardently atheist "science-believers" literally believe in the existence of dark matter, because "the science says so" (even if that's not really the case)? awhile ago I posted a comment on this website about how an atheist friend of mine believed that a government policy definitely had no downsides or issues because a social "science" Study had been done saying no such issues existed, and he took this just as equally As Gospel as he would F=ma—it's Science, Scientists say so, so therefore it must be True—as though the world were a computer simulation and Scientists are reading the assembly language and/or database entries that comprise the totality of the Universe verbatim. intuitively realizing that this explicitly is not and cannot be True has really opened my eyes to the nature of how many (most?) people take lots of scientific conjecture and theory and social "science" as Accepted Fact, and how that's Probably Not The Best Way To Go About Things.
The way I put it sometimes, is that people don't know what 'knowing' is. It is an epistemological question. Individuals seem to think 'we' can know something - or that knowing is a group activity! That you can accept authoritative sources without personally verifying it AND call it knowledge.
Really, they are just hypotheses, or beliefs. There is actually no difference between these beliefs and religion that I can see... but people are so adamant that science is not religion!
It's funny to watch.
Earth having rings is not really special. In fact right now we have "dust moons" orbiting us. Any large-scale impactor is going to create rings of orbiting debris. The question is how much mass was in orbit and how long it took for the amount of mass in orbit to return to an average amount. Rings are quite ephemeral things despite their striking visuals.