Why use "the" in "than the 3.5bn years ago"?

Previous studies suggested that volcanic activity on The Moon ended about 3.5bn years ago. The analysis of recently collected rocks, however, have lead scientists to suspect volcanic activity ended after the accepted 3.5hn years.

"the" refers to the previous estimate, 3.5bn years.

This is so because "3.5 bn years" is determined by the that-clause (that is the estimate derived…) and that it is a unique possibility.

• This is not the bundle (that) they showed to you. (unique)
• This is not a bundle (that) they showed to you. (not unique)

The determination can result from other circumstances.

• This is during the first hour on the job. It is for the second hour that you need to use new tools.

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Addition prompted by user Jack Rowntree's answer

In my opinion, Jack Rowntree does detect a problem in the formulation of the proposed sentence, and if I failed to give sufficient thought to it as I read the sentence, I feel now that his remarks make it stand out enough to address it, which I wouldn't have done had I not disagreed to a certain extent with him.

This number of years is a means to define a date; a point in time is what we have to specify since the key word is "until"; we do that not by means of a date since for such times way back in the geological times and still further back, dates are rather meaningless, unless it would be rather that there is no established usage; instead it is done by means of a span of time with the convention that the inferior limit of that span is the point or date referred to; however, in order to establish a correspondence in time for that inferior limit the superior limit must be fixed. You can fix it in several ways, by choosing a reference point, an event, a period if an approximate date is sufficient. Here, this is accomplished by a reference to the present in general (which is again an approximation but sufficiently good since even several decades do not matter in this question); the term to fix that reference is "ago". As Jack Rowntree notices the formulation is unusual or at least it doesn't have the feel of proper syntax. This is correct in my opinion since the term in the comparison is not a simple term but "3.5 bn years ago"; as "the" does not bear upon "ago" there is not a well defined term for the comparison; this is highlighted in Jack Rowntree's answer. As he shows, an apparent solution is to suppress "ago".

• Researchers hope rocks collected here will confirm that volcanic activity on the Moon continued until far more recently than the 3.5bn years that is the estimate derived from studies of currently available samples.

However, that does not define a date but a span of time and this is not proper. If keeping the article, the only way out towards normal syntax is in an addition of terms.

• Researchers hope rocks collected here will confirm that volcanic activity on the Moon continued until far more recently than the point 3.5bn years ago, that is the estimate derived from studies of currently available samples.

There is also, according to Jack Rowntree the possibility of doing away with the article and I agree entirely with that.

• Researchers hope rocks collected here will confirm that volcanic activity on the Moon continued until far more recently than 3.5bn years ago, (that/which) is the estimate derived from studies of currently available samples.

The phrases "3.5bn years ago" and "the estimate derived from studies of currently available samples" are in apposition to each other - both refer to the same thing.

You can leave out the first "the" by separating the two phrases with a comma:

... until far more recently than 3.5bn years ago, the estimate derived from studies of currently available samples.

Or you can make the second phrase into a relative clause explaining the meaning of "3.5bn years ago", replacing "that" with "which":

...until far more recently than 3.5bn years ago, which is the estimate derived from studies of currently available samples.

IMO the original quotation would be acceptable and easily understood in spoken English, but the grammar seems a bit careless for written English. It seems to me as if a speaker was going to say

...until far more recently than the estimate derived from studies of currently available samples.

but then added the extra information about the numerical value of the estimate (3.5bn years) in the "wrong place" in the complete sentence.

If someone asks me how many bananas I have, and I say "I think I have seven", and then they ask me how many oranges I have, and I say "I think I have seven", the number "seven" has appeared twice, but it's not the same seven. They refer to different things and might be obtained from different sources and have different levels of certainty. If you ask me "Do you have the same number of bananas as oranges?", I might say "I don't think so": even though my estimates for them are the same, I might be unsure enough of each that I think there's a good chance that they aren't the same. And I can talk about them separately. For instance, I can say "The first seven comes from knowing that I bought ten yesterday, and my roommate has a habit of eating three bananas each day. The second seven comes from the fact that I picked some oranges and they filled up my bag, and my bag holds about seven oranges." This is a perfectly coherent statement. So numbers can act like nouns in this sense, and we can talk about particular ones, and they can take definite articles when we're referring back to previously specified ones.

This feels wrong to me.

The below feels OK:

than the 3.5bn years [no ago] that is the estimate derived from studies of currently available samples.

As does:

than [no the] 3.5bn years ago, (that/which) is the estimate derived from studies of currently available samples.

Specifically, I would say *the* 3.5bn years ago basically feels wrong in the original. The definite article brings focus to the years themselves, ago/in the past, rather than the idea of a stated estimate. The next clause still uses is to refer to the concept of said estimate, but the previous definite article has primed us to think about years plural. I'm sure I've never seen that phrasing written or spoken. I would advise against using it.