I'm trying to understand if it is ok to use the indefinite article in this sentence.
The solar system belongs to a group of 100,000 million stars called the Milky Way.
First of all, yes, it's okay.
To me it sounds as if there were many groups of 100,000 stars called the Milky Way, and the solar system just belongs to one of these groups.
That isn't how it sounds to native speakers.
Taking into account that there is only one group of stars called the Milky Way, wouldn't it be more logical to say
The solar system belongs to the group of 100,000 million stars (which is) called the Milky Way.
No, 'logical' isn't the right word. What you're asking is whether it would make more
sense. The answer is it would make sense but you will have changed the meaning (the 'reference').
I understand very well how article usage can be a very difficult thing to grasp for Russian speakers, so with this in mind, this is how I suggest you begin to think about this sentence:
a group of 100 billion stars [This is an indefinite noun phrase]
called the Milky Way [This is a modifying phrase which in some way 'defines' the noun phrase it modifies]
I believe it's the transition from indefinite to definite that is causing you problems in this case.
If I were to convey the idea in question, I'd write something like:
The solar system belongs to the Milky Way, a group of about 100 billion stars.
Sounds a bit clearer to me.
Yes, that's very clear and well expressed.
The textbook's version seems to be combining two sentences into one:
The solar system belongs to a group of 100 billion stars. + The group is called the Milky Way.
Not really. The textbook version is certainly combining the propositional content (what they're saying) of the two sentences, but it isn't really combining the two sentences grammatically speaking.
Which resulted in some ambiguity, in my opinion.
Like I said, there isn't any ambiguity to a native speaker.
As a learner of English (and a teacher for my kids), I'm trying to find as much logic in the language as possible, to make the learning process easier
And this evening I found myself in a tight corner trying to explain to my daughter why the indefinite article has been used when the second part sort of asked for the definite article.
I really admire your efforts but I'm not surprised you had trouble explaining this. Even as a native-speaking user who has spent the majority of his life reading around the subject of sense and reference, I have great trouble explaining things like this too!
Yes, I guess they meant 100 billion
Yes, they did.