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I only recently looked into the etymology of the word "disturb", which means "per-turb", completely (through, thoroughly) + disturb, which translated into "disturb greatly in mind".

My question is that how did the word "pertubation" get the meaning of "small changes" as in "perturbation in Jupiter's orbital" and "perturbation theory" in physics?

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    It seems, that the meaning conveyed by the prefix "per-" was been dropped for both senses of the word you list: MW With its per- prefix, perturb meant originally "thoroughly upset", though today the word has lost most of its intense edge. Perturb and perturbation are often used by scientists, usually when speaking of a change in their data indicating that something has affected some normal process.
    – katatahito
    Commented Jun 25, 2019 at 4:54
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    "Perturb" has a scientific meaning and an everyday meaning, as any good dictionary will show (e.g. Merriam-Webster); this isn't uncommon in English. The same is true of "perturbation" (looking at usage examples in a dictionary will make this clearer than the definition alone). A good etymological dictionary will trace the changing meaning of both words.
    – Stuart F
    Commented Jun 25, 2019 at 9:16
  • @Stuart F Thanks! Could you recommand a good etymology dictionary where the changes of these two words were traced? I could not find such dictionaires and I am hoping that you could point some directions!
    – wooohooo
    Commented Jun 25, 2019 at 12:46
  • @katatahito Interesting point! My guess is that words in academia use tend to "loose edge", as in "permutation" in math is less than "completely change", but I could not find more examples to testify it. If the meaning of perturbation is already weakened in 14.C. then probably that's how the word purtabation picked up the meaning of "small change".
    – wooohooo
    Commented Jun 25, 2019 at 12:52
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    Although the previously mentioned notation from Merriam-Webster indicates etymological origins, neither perturbation nor perturb have current definitions (at least at M-W) that indicate either small or great change; in fact, the quantity of change is not assumed in any way. What is your source for thinking that either word does have such a current meaning, in any context? Commented Jun 25, 2019 at 18:24

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When you consider that Jupiter is the largest planet in the Solar System (more than 1,300 Earths could fit inside it; all the other planets could fit inside it), anything that can cause at-all-detectable changes in Jupiter's orbit is by definition not a small disturbance: "perturbance" fits.

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    Sorry @Raven I do not agree with you. A purturbation is to consider the effects of two interactions relatively. Thus the pertubation, however big it is independently, is small compared to the interaction between the sun and the Jupiter, which is why the perturbation theory works at all.
    – wooohooo
    Commented Jun 25, 2019 at 12:58

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