It's my understanding that Aristotle believed 1) that gravity is a constant force toward the center of the earth, and 2) forces cause objects to move but not accelerate. It seems to me if those are both true then the same object dropped from two heights would experience the same force and, upon arriving at the ground, hit it at the same speed with the same force. Did Aristotle have a resolution for this puzzle?
Of the medieval physicists who studied this question, it is hard to say which of their arguments is more "Aristotelian," as some physicists in circa the 13th and following centuries were influenced more by Averroes ("The Commentator") than others, or by the Nominalists more so than by the Thomists or Scotists, etc. In other words, there are several interpretations of Aristotle on this point.
One popular interpretation is due to one of the greatest physicists of that era, Jean Buridan (1295-1358), rector of the University of Paris. He is known for his impetus theory, impetus being similar to what we would call momentum today (cf. John Philoponus, circa 6th cen., who held a similar theory). Moody's Dictionary of Scientific Biography entry on Buridan gives a good summary:
The Questions composed by Buridan on problems raised in Aristotle’s Physics and De caelo et mundo exhibit his application of these criteria of scientific method and evidence to the critical evaluation of Aristotle’s theories and arguments and to the diverse interpretations of them offered by Greek, Moslem, and Christian scholastic commentators. The general scheme and conceptual framework of analysis, within which Aristotle’s physics and cosmology are formulated, is accepted by Buridan as the working hypothesis, so to speak, of natural philosophy. But the scheme is not sacrosanct, and Buridan not infrequently entertains alternative assumptions as being not only logically possible but also possibly preferable in accounting for the observed phenomena. While the authority of Aristotle had often been challenged on the ground that his positions contradicted Christian doctrine, it had come, in Buridan’s time, to be challenged on grounds of inadequacy as a scientific account of observed facts. Buridan’s major significance in the historical development of physics arises from just such a challenge with respect to Aristotle’s dynamic theory of local motion and from his proposal of an alternative dynamics which came to be known as the impetus theory.
An obvious weakness of Aristotle’s dynamics is its inability to account for projectile motions, such as the upward motion of a stone thrown into the air after it has left the hand of the thrower. According to the assumptions of Aristotelian physics, such a motion, being violent and contrary to the natural movement of the stone toward the earth, required an external moving cause continuously in contact with it. Since the only body in contact with it is the air, Aristotle supposed that in some way the air pushes or pulls such a body upward. This feeble explanation drew criticism in antiquity and from medieval Moslem commentators and gave rise to a theory that the violent action of the thrower impresses on the stone a temporary disposition, of a qualitative sort, which causes it to move for a short time in the direction contrary to its nature. This disposition was called an impressed virtue (virtus impressa), and it was held to be self-expending and quickly used up because of its separation from its source. Franciscus de Marchia, a Franciscan theologian who taught at Paris around 1322, gave a full presentation of this theory, and it is likely that Buridan was influenced by it.
In treating of the problem of projectile motion in his Questions on Aristotle’s Physics (VIII, question 12), Buridan expounded Aristotle’s theory of propulsion by the air and rejected it with arguments similar to those that Marchia had used. His own solution was in some respects like that of Marchia, but in one crucial point it was strikingly different. The tendency of the projectile to continue moving in the direction in which it is propelled, which Buridan calls impetus rather than virtus impressa, is described as a permanent power of motion, which would continue unchanged if it were not opposed by the gravity of the projectile and the resistance of the air. “This impetus,” he says in another discussion given in his Questions on the Metaphysics, “would endure forever [ad infinitum] if it were not diminished and corrupted by an opposed resistance or by something tending to an opposed motion.”[Qu. in Metaph. II, Qu. 1, (1518) m fol. 73r.]
The suggestion given here of the inertial principle fundamental to modern mechanics is striking, as are some further uses that Buridan makes of the impetus concept in explaining the accelerated velocity of free fall, the vibration of plucked strings, the bouncing of balls, and the everlasting rotational movements ascribed to the celestial spheres by Greek astronomy. Buridan defines impetus in a quantitative manner, as a function of the “quantity of matter” of the body and of the velocity of its motion; thus, he seems to conceive of impetus as equivalent to what in classical mechanics is called momentum, defined as the product of mass and velocity. In treating the action of gravity in the case of freely falling bodies, Buridan construes this action as one imparting successive increments of impetus to the body during its fall.
It must be imagined that a heavy body acquires from its primary mover, namely from its gravity, not merely motion, but also, with that motion, a certain impetus such as is able to move that body along with the natural constant gravity. And because the impetus is acquired commensurately with motion, it follows that the faster the motion, the greater and stronger is the impetus. Thus the heavy body is moved initially only by its natural gravity, and hence slowly; but it is then moved by that same gravity as well as by the impetus already acquired, same gravity as well as by the impetus already acquired, and thus it is… continuously accelerated to the end.[Qu. De caelo et mundo (1942), 180.]
The effect of a force, such as gravity, is thus conceived of as a production of successive increments of impetus, or of velocity in the mass acted upon, throughout the fall. It is a short step from this to the modern definition of force as that which changes the velocity of the body acted upon, implying the correlative principle that a body in uniform motion is under the action of no force. Buridan does not quite take this step, since he retains the Aristotelian assumption that a constant cause must produce a constant effect, and ascribes the increase in velocity to the addition of impetus as an added cause acting along with the gravity.
Yet his theory obviously requires a distinction between impetus as a “conserving cause” of motion and gravity as a “producing cause” of the motion conserved by the impetus; his failure to draw the consequence of this distinction was perhaps because he did not attempt a mathematical analysis involving the concept of instantaneous velocities added continuously with time. Whether Buridan construed the acceleration as uniform with respect to time elapsed, or with respect to distance traversed, is not clear. He probably regarded the two functions as equivalent, a view that, however impossible from a mathematical point of view, was retained into the seventeenth century, when Descartes and Galileo (in his letter to Sarpi of 604) sought to prove that velocity increases in proportion to time elapsed from the premise that velocity increases in direct proportion to distance of fall.
Buridan’s concept of impetus is further distinguished from the modern inertial concept by the fact that he construes rotational motion at uniform angular velocity as due to a rotational impetus analogous to the rectilinear impetus involved in projectile motion. Galileo did likewise, and was in this respect nearer to Buridan than to Newton. But Buridan makes a striking use of his impetus concept, in its rotational sense, by arguing that since the celestial spheres posited by the astronomers encounter no external resistance to the rotational movements and have no internal tendency toward a place of rest (such as heavy and light bodies have), their uniform rotational motions are purely inertial and require no causes acting on them to maintain their motions. There is, therefore, no need to posit immaterial intelligences as unmoved movers of the heavenly spheres, in the manner that Aristotle and his commentators supposed. “For it could be said that God, in creating the world, set each celestial orb in motion… and, in setting them in motion, he gave them an impetus capable of keeping them in motion without there being any need of his moving them any more.”[Qu De caelo et mundo (1942), 180.] It was in this way, Buridan adds, that God rested on the seventh day and committed the motions of the bodies he had created to those bodies themselves.
It is clear that Buridan’s impetus theory marked a significant step toward the dynamics of Galileo and Newton, and an important stage in the gradual dissolution of Aristotelian physics and cosmology. Buridan did not, however, exploit the potentially revolutionary implications of his analysis of projectile motion and gravitational acceleration, or generalize his impetus theory into a theory of universal inertial mechanics. Thus, in discussing the argument of Aristotle against the possibility of motion in a void, Buridan accepted the principle that the velocity of a natural motion in a corporeal medium is determined by the ratio of the motive force to the resisting force of the medium, so that if there were no resisting medium, the motion would be instantaneous. This is scarcely consistent with the analysis of gravitational acceleration as finite increments of impetus given to the falling body by its gravity, and Buridan made no effort to harmonize these two different approaches within a common theory.
For an excellent historical summary of the medieval physicists' various interpretations of Aristotle's Physics (and De Cælo) regarding this question, see:
- Pierre Maurice Marie Duhem, Études sur Léonard de Vinci, ceux qu’il a lus et ceux qui l’ont lu, vol. 3: Les Précurseurs Parisians de Galilée [Galileo's Parisian Precursors] (Paris: A. Hermann, 1913).
That 3rd vol. is on Galileo's precursors and is standalone. The question you ask was hotly debated in the 13th centuries onward, preceding Galileo. An English translation of it is coming out in Springer's Boston Studies in the Philosophy and History of Science in circa 2018.
A more popular, but still scholarly overview of the medievals' interpretations of Aristotle's physics is:
- James Hannam, God’s Philosophers: How the Medieval World Laid the Foundations of Modern Science (London: Icon Books, 2009).
Regarding motion in Aristotle's Natural Philosophy, it is classified as either natural or violent.
The fall of an heavy body is a natural motion because it is due to its intrinsic property : the heaviness. The body is "aiming at" reaching its natural place.
De Caelo, Book I, 269b18-270a12. Let us then apply the term ‘heavy’ to that which naturally moves towards the centre, and ‘light’ to that which moves naturally away from the centre. The heaviest thing will be that which sinks to the bottom of all things that move downward, and the lightest that which rises to the surface of everything that moves upward.
Physics, Book IV, 215a24-215a27. We see the same weight or body moving faster than another for two reasons, either because there is a difference in what it moves through, as between water, air, and earth, or because, other things being equal, the moving body differs from the other owing to excess of weight or of lightness.
De caelo, Book I, 273b27-274a18. A given weight moves a given distance in a given time; a weight which is as great and more moves the same distance in a less time, the times being in inverse proportion to the weights. For instance, if one weight is twice another, it will take half as long over a given movement.
See also : Aristotle: Motion and its Place in Nature.
For Aristotelian accounts of free fall, see medieval Theory of impetus :
introduced by John Philoponus in the 6th century and elaborated by Nur ad-Din al-Bitruji at the end of the 12th century, but was only established in western scientific thought by Jean Buridan in the 14th century.
For a modern point of view, see : Carlo Rovelli, Aristotle’s Physics : a Physicist’s Look (2014) :
Quantitative precision is not very common in Aristotle, who is interested in the causal and qualitative aspects of phenomena.
Science for Aristotle is not what we are accustomed to : measurement, experiment, prediction.
It is more : observation of empirical facts and search for "general" explanation.
Thus, in Aristotle's physics (and all subsequent developmements of Aristotelian science) there is no measure of speed of fall, nor of "force of percussion".
Aristotle does not explain the discrepancy with empirical evidence, nor he describes it.
For Aristotle, gravitation was not a force. It was a property of the body, just as hardness or some color is a property of the body.