Physics is the ONLY thing that can give us an estimate for that number.
Why physics and not simple observation?
If you were a 19th century physicist contemplating emission lines from a star, you could observe and record them in detail. But without an understanding of how molecular bonds absorb quanta, much of which gradually accumulated during the first half of the 20th century, your 19th century physics would be dead in the water trying to estimate the locations and strengths of those lines.