= Falling bodies and lunar motion as tests of gravity
One motivating laboratory demonstration compares two balls initially at the same height. A switch releases one vertically when the other leaves a horizontal track; arranging their paths to meet gives a collision as the readout of equal downward <displacement> over equal <time>. Equal initial height and synchronized release control the comparison. This tests the local independence of horizontal motion and <free fall>, under nearly constant <gravitational acceleration>; it does not measure an <inverse-square law>.<The Feynman Lectures on Physics, Volume I by Richard Feynman and others/Chapter 7: The Theory of Gravitation>[§7–4, figure 7–3: synchronized release and midair collision]{ref}
A complementary astronomical comparison uses the <Moon>'s distance and <orbital period> to infer inward <centripetal acceleration>, $a=4\pi^2r/T^2$, and compares it with surface <gravitational acceleration> scaled by $(R/r)^2$. The approximately sixtyfold distance ratio gives the approximately $1/3600$ prediction. The inference links terrestrial <free fall> to a lunar <orbit>. Distance calibration matters; the <circular orbit> approximation and the <Sun>'s <tidal force> limit this elementary comparison.<The Feynman Lectures on Physics, Volume I by Richard Feynman and others/Chapter 7: The Theory of Gravitation>[§7–4: lunar distance, period, and the inverse-square comparison]{ref}
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