= Free fall
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Free fall is motion under <gravity> alone: there is no supporting <normal force>, engine thrust or appreciable <drag force>. In the <Newtonian mechanics> model, a <test particle> of <mass> $m$ obeys $m\ddot{\mathbf r}=m\mathbf g(\mathbf r)$, hence $\ddot{\mathbf r}=\mathbf g(\mathbf r)$. The <mass> cancels. Bodies released at the same <position> with the same <velocity> follow the same path in this model, even if their <gravitational weights> differ. https://www1.grc.nasa.gov/beginners-guide-to-aeronautics/free-falling-objects/[NASA Glenn: free-falling objects and the cancellation of mass]{ref}
A dropped stone is one example; a coasting satellite is another. Free fall does not require motion straight down or decreasing distance to the attracting body. An ideal <circular orbit> has constant radius while its <velocity> continually turns under <centripetal acceleration>. The <circular orbit as continuous free fall> connects the familiar drop with orbital motion.
Near a surface, treating the <gravitational acceleration> as constant gives a useful first prediction. Over larger heights, the <inverse-square law> changes the acceleration during the fall. <Radial free fall from rest> uses <conservation of mechanical energy> to account for that change exactly, within the specified <Newtonian gravitational field>. The contrast matters: the simplest formula is an approximation to a physical model, rather than a law with the same numerical $g$ everywhere.
History also makes the idealization tangible. Galileo's \i[Two New Sciences] (1638), Third Day, Theorem II, derives distance proportional to the square of time for uniformly accelerated motion from rest; its first corollary gives successive distances in the ratios $1,3,5,7,\ldots$ over equal time intervals. This is a kinematic statement, predating the gravitational <inverse-square law>. https://galileoandeinstein.phys.virginia.edu/tns_draft/tns_160to243.html[Galileo, Two New Sciences, Third Day, Theorem II and Corollary I; Crew and de Salvio's 1914 translation, pp. 174–176]{ref}
On Apollo 15's final lunar surface excursion, David Scott released a hammer and a feather together. The near-<vacuum> removed the large difference in <drag force> familiar on Earth. NASA's report describes their arrival together within the accuracy of the release; this demonstration illustrates the <free fall> prediction without establishing infinite experimental precision. https://science.nasa.gov/resource/the-apollo-15-hammer-feather-drop/[NASA's original footage and Joe Allen's account in the Apollo 15 Preliminary Science Report, p. 2-11]{ref}
\Video[https://www.youtube.com/watch?v=oYEgdZ3iEKA]
{title=NASA footage of David Scott's Apollo 15 hammer-and-feather free-fall demonstration}
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