Since episode 9, we know we can understand turning points in dynamics by going from two mechanical quantities to three. The three pairs of the trio are associated with three lines intersecting at what we called a “proper” event. But as we saw in the last episode, there are a lot of cases out there, where only two mechanical quantities have been identified, resulting in an incomplete or “pseudo-event.” These pseudo-events are begging to be fully “mechanized”. We've done this on a couple of examples related to droplets in the last episode and we've seen how a complete mechanical picture always offers new opportunities to connect the dots between apparently disparate phenomena. Because these two cases may have seemed anecdotal to some viewers unfamiliar with the world of capillary flows, today we'll address an example that will speak to all. It is time to come back to the most famous intersection in science: the bridge between Kepler's law of orbital motion and Galileo's law of free fall. We saw in episode 6 how Newton approached this intersection, by mechanizing Kepler, and by connecting the scale of the crossover to the size of the earth. With Newton's insight, is this intersection understood solely from mechanical parameters? No it isn't, and such unfinished business deserves our close attention.
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