Possible to derive an approximation of G from a Saros ?

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Isaacsname
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I recently read a paper titled : " The Saros cycle: obtaining eclipse periodicity from Newton's laws "

My question is, more or less: " Is it possible to obtain an approximation of G by observing Saros periodicity ? "

I'm currently studying the derivations of the Lunar , Solar, and Stellar calendars, dating back to Babylonian / Chaldean / Sumerian astronomy, and was curious about this after discovering something intriguing in Newton's work

Thanks,
Isaac
 
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If you scale up all masses by a factor of 2 and reduce G by a factor of 2, nothing changes in orbital mechanics (neglecting general relativity). You cannot, unless you have an independent way to estimate the mass of objects - but then you don't need Saros cycles, then the simple orbital period is sufficient.