there are two competing theories because theorists in astrophysics can't quite come up with a model that actually forms planets. what you've described is right in an overall qualitative picture, but then to get it right quantiativley is much more difficult.
the competing theories you mentioned, as well, are to do with the gas giant planets (e.g. jupiter, saturn and much much larger). each theory has its plusses and minuses:
for example, core accretion theories (the second one you mentioned) are able to form cores similar to our own jupiters and saturns as far as mettalicity and chemical abundances. however, most models have this process taking orders of magnitude longer than the time available (e.g. before the young protostar disperses its disk). the gravitational instability model (the first one you mentioned) has the advantage of being able to form planets on a more reasonable time scale, but it is not clear that it can find the right chemical abundances.
the problem is far from solved!
unfortuantely, i don't know much about the theories of forming terrestrial sized rocky planets like the one in this article.
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there are two competing theories because theorists in astrophysics can't quite come up with a model that actually forms planets. what you've described is right in an overall qualitative picture, but then to get it right quantiativley is much more difficult. the competing theories you mentioned, as well, are to do with the gas giant planets (e.g. jupiter, saturn and much much larger). each theory has its plusses and minuses: for example, core accretion theories (the second one you mentioned) are able to form cores similar to our own jupiters and saturns as far as mettalicity and chemical abundances. however, most models have this process taking orders of magnitude longer than the time available (e.g. before the young protostar disperses its disk). the gravitational instability model (the first one you mentioned) has the advantage of being able to form planets on a more reasonable time scale, but it is not clear that it can find the right chemical abundances. the problem is far from solved! unfortuantely, i don't know much about the theories of forming terrestrial sized rocky planets like the one in this article.