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Over the years, I have often heard statements like: "Newton's laws became really famous because they proved to be very useful in shipbuilding and during the Industrial Revolution."

Have you ever come across something similar?

Assuming that to be the case, do you know any of the first real use cases of Newtonian physics?

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  • $\begingroup$ Aside from, well, Newton? $\endgroup$
    – Jon Custer
    Commented Jul 30 at 21:51
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    $\begingroup$ Honestly speaking... I don't think Newton was the first to use Newtonian physics in current matured form. He didn't even use the idea of a vector and acceleration, look into Principia. I read an article which said that he'd had misconceptions about differences between centripetal and centrifugal forces. $\endgroup$
    – Lukasz Skowron
    Commented Jul 31 at 8:20
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    $\begingroup$ You saying that Newton "didn't even use the idea of a vector and acceleration" ??? I don't think you can back that up: both those are expressly in the Principia. What's your source? $\endgroup$
    – terry-s
    Commented Jul 31 at 20:56
  • $\begingroup$ I was reading many pages of Principia and never seen word vector or acceleration. He is using those concepts as if there are intuituive to him, but never expresses them in mature format. $\endgroup$
    – Lukasz Skowron
    Commented Aug 2 at 6:47
  • $\begingroup$ Euler wrote first $\mathbf F=m\mathbf a$ not so long after Newton, so that might be what you are looking for $\endgroup$
    – Mauricio
    Commented Aug 3 at 10:56

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The first real uses of Newtonian physics are due to Newton himself. In his principia, he

  1. Derived Kepler's laws from the law of gravitation,

  2. Determined the first correct approximation for the shape of the Earth, after the sphere.

  3. Explained the tides.

  4. Partially explained the inequalities of the Moon motion.

  5. Explained the motion of comets which enabled Halley to predict the return of the Halley comet.

These are his most famous achievements, but there were plenty of others. Further development of this occupied many mathematicians for the rest of 18th century, and more. All this had very substantial applications to real life, first of all to navigation.

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  • $\begingroup$ Thanks! Can you guide where to look for applications in navigation of that? Do you know anyone particular aside Newton? $\endgroup$
    – Lukasz Skowron
    Commented Aug 2 at 6:57
  • $\begingroup$ Application of 2 to map making is evident, application of 3 to navigation is also clear. Concerning 4, look for the "method of lunar distances" on Google, beginning with Wikipedia article. Of course, a lot of additional development of Newton's discoveries was necessary before all this really could be applied in practice. This development occupied most of the 18 century. $\endgroup$
    – Alexandre Eremenko
    Commented Aug 2 at 13:39
  • $\begingroup$ It's an unfounded myth that Newton used Newton's dynamical laws to compute orbits of comets. Newton and Halley obtained Flamsteed's observations and fitted a parabola to that data. Newton and Halley used purely geometric methods not dynamical methods. You can confirm this fact by looking at the Prop.41, Prob.21 in Book 3. $\endgroup$
    – zeynel
    Commented Aug 3 at 15:18
  • $\begingroup$ @zeynel: Halley's comet moves on an elliptic orbit, not parabolic (otherwise it would not return). And that comets move according to Kepler's laws, is a consequence of the universal gravitation, I do not think it was known or accepted before Newton. $\endgroup$
    – Alexandre Eremenko
    Commented Aug 4 at 12:51

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