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At least for some planets (Venus, Jupiter and Saturn) you can consult the gear ration which were recently recovered:

 https://pmc.ncbi.nlm.nih.gov/articles/PMC7955085/

for Antikythera Mechanism. In general, you can do the following. Write the necessary ratio (from a modern exact source) and 

expand it to a continued fraction. Step 1: take integer part. Step 2: take the reciprocal of the remainder.

3. Repeat Step 1, then Step 2, as many times as convenient. stop the procedure at some step. You obtain an ordinary fraction.

This fraction is the best possible rational approximation of your number with given denominator.