The lack of a strong gravitational pull has caused any water the moon may have had to leak out into space over the 4.6 billion years that it has been in existence.
I'd like to know the meaning of "over" in the sentence.
The lack of a strong gravitational pull has caused any water the moon may have had to leak out into space over the 4.6 billion years that it has been in existence.
I'd like to know the meaning of "over" in the sentence.
The sentence reads correctly, to me, in idiomatic American English.
In that context, the use of the word "over" is a kind of short-hand for the more extended phrase "over the course of", meaning that a process or occurrence is happening continually while some amount of time passes.
Both of the synonyms "during" and "throughout" are appropriate interpretations, but "more than" is not appropriate.
If you drop either of the first two synonyms into the sentence in place of "over", they work, although some nuance of meaning or intent is lost or shifted.
The lack of a strong gravitational pull has caused any water the moon may have had to leak out into space during the 4.6 billion years that it has been in existence.
The lack of a strong gravitational pull has caused any water the moon may have had to leak out into space throughout the 4.6 billion years that it has been in existence.
The above examples are proper, with slightly different shadings to the meaning.
Using "more than" in place of "over" would suggest that the water has leaked out to a greater extent than the years have leaked out - it would be fairly nonsensical to a native speaker.
The lack of a strong gravitational pull has caused any water the moon may have had to leak out into space more than the 4.6 billion years that it has been in existence.
That doesn't work.
However, there's an unexplored variant that can include "more than", and be proper, but it would not replace "over". This:
The lack of a strong gravitational pull has caused any water the moon may have had to leak out into space over the more than 4 billion years that it has been in existence.
That usage still employs the word "over" in the same manner as your original example, but "more than" is used as a modifier of the following number, to suggest that there's some uncertainty about the exact duration, but there is at least a known minimum amount of time.
I, for one, can certainly see how the mixed uses demonstrated in that last example can lead to confusion. The structure of English is notoriously messy.
Note that the use of the "definite article" "the" between "over" and "4.6 billion" has a strong determinant effect on the interpretation of the word "over" in that sentence. Without the definite article, it would read as somewhat vague in its intent, and poorly constructed.
The lack of a strong gravitational pull has caused any water the moon may have had to leak out into space over 4.6 billion years that it has been in existence.
Omitting "the" is not really optional, and would identify the speaker as not being a native speaker, making its presence a shibboleth. (Or it may perhaps only show that they did not proof-read the sentence.) The difference is subtle, but important.
My background is that I am a native speaker of American English, born and raised in California, with some college, and I have a parent who is a published author. Other than that, I'm afraid I'm not well versed enough in technical grammar to cite a specific rule. However, substitution of synonyms can often clear up the intent of a word, by elimination.