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I know that planets can form through accretion, bulging up from $0$ to their final mass $\mathrm{M_{planet}}$ at $\mathrm{M}(t_f)$. I know that when studying Planetary formation and migration theories, sometimes this $\mathrm{M}$ function gets modelled, e.g., as a $\propto \tanh{(k\cdot t)}$ function. What I do not know and I'd like to ask you is:

  • What kind of assumptions are we throwing in (proto-) planet formation models, e.g., to describe $\mathrm{M = M}(t)$? Is this well studied? Is planetary formation being studied through N-body simulations or similars?

Context: I'm not sure if we could constrain enough with experimental data. I don't know it at all though. But at the same time, it just comes to my mind that N-body simulations starting from "simple enough" statements could help model $d\mathrm{M}/dt$ for instance. I wondered if planet caracterization through N-body "accretion simulations" is (was) a subject or not? Closed? In development? What are the problems that are being solved on this? Related

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    $\begingroup$ below a certain size you cannot speak of a planet, but you usually must look at mass or size distributions. One often looks at $<\dot{M}>$, but looking at the growth of a single particle / planetesimal or body often makes little sense, unless we already entered the phase of run-away growth when you can actually speak already of proto-planets instead of only planetesimals (and when looking at $<\dot{M}>$ starts to make less sense). $\endgroup$
    – planetmaker
    Commented Feb 15 at 22:02
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    $\begingroup$ In short, this is a well-studied problem, but one with many nonlinearities, free parameters and unknown unknowns in it. Any specific flavour of planet formation theory that fits the meager constraints we have will still have trouble of fitting a unique function, as you suggested, due to the nonlinear nature of multiple processes going into planet formation theory. As to what might help you in reading further, I am confused. You seem to know some fundamentals, yet you ask about fundamentals? Do you want to read up on some basic literature? $\endgroup$
    – AtmosphericPrisonEscape
    Commented Feb 22 at 8:27
  • $\begingroup$ @AtmosphericPrisonEscape Not only reading but more like overviewing the state of the art on the topic, the main problems and branches with questions and/or methods to assess/answer. I could go and look for enough basic literature but as this is not a topic I know deeply, I'm more prone to have a "biased idea" towards it, for instance because of selecting not enough articles as samples. That'd be a path to understand more about computational methods as a tool to find answers, without getting lost in rabbit holes, details, or too much discussion $\endgroup$
    – nuwe
    Commented Feb 22 at 18:59
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    $\begingroup$ The state of the art is summarized in the current Protostars & Planets 7 chapters, ppvii.org/chapter-list/index.html most of the chapters there are only listed not linked, so you'll have to just google them or find them on the ADS ui.adsabs.harvard.edu via first author and title. Spoiler: There is a lot to know, even the PP7 reviews are thousands of pages in the end. You might want to start with something simpler, e.g. Armitage's Book on Planet formation gives many starting points (most less thorough than others). Or to go for an (outdated) classic, Safronov's book from 1962. $\endgroup$
    – AtmosphericPrisonEscape
    Commented Feb 23 at 2:47
  • $\begingroup$ Too broad. Needs focus. $\endgroup$
    – ProfRob
    Commented Mar 1 at 13:46

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