Free fall
In classical mechanics, free fall is any motion of a body where gravity is the only force acting upon it.
In a roughly uniform gravitational field gravity acts on each part of a body approximately equally.
In the context of general relativity, where gravitation is reduced to a space-time curvature, a body in free fall has no force acting on it.
Although, in the 6th century, John Philoponus challenged this argument and said that, by observation, two balls of very different weights will fall at nearly the same speed.
[1] In 12th-century Iraq, Abu'l-Barakāt al-Baghdādī gave an explanation for the gravitational acceleration of falling bodies.
According to Shlomo Pines, al-Baghdādī's theory of motion was "the oldest negation of Aristotle's fundamental dynamic law [namely, that a constant force produces a uniform motion], [and is thus an] anticipation in a vague fashion of the fundamental law of classical mechanics [namely, that a force applied continuously produces acceleration].
"[2] According to a tale that may be apocryphal, in 1589–1592 Galileo dropped two objects of unequal mass from the Leaning Tower of Pisa.
This slowed things down enough to the point where he was able to measure the time intervals with water clocks and his own pulse (stopwatches having not yet been invented).
He repeated this "a full hundred times" until he had achieved "an accuracy such that the deviation between two observations never exceeded one-tenth of a pulse beat."
In 1589–1592, Galileo wrote De Motu Antiquiora, an unpublished manuscript on the motion of falling bodies.
Near the surface of the Earth, an object in free fall in a vacuum will accelerate at approximately 9.8 m/s2, independent of its mass.
The terminal velocity depends on many factors including mass, drag coefficient, and relative surface area and will only be achieved if the fall is from sufficient altitude.
A typical skydiver in a spread-eagle position will reach terminal velocity after about 12 seconds, during which time they will have fallen around 450 m (1,500 ft).
This demonstrated Galileo's discovery that, in the absence of air resistance, all objects experience the same acceleration due to gravity.
This is the "textbook" case of the vertical motion of an object falling a small distance close to the surface of a planet.
Assuming spherical objects means that the equation of motion is governed by Newton's law of universal gravitation, with solutions to the gravitational two-body problem being elliptic orbits obeying Kepler's laws of planetary motion.
In general relativity, an object in free fall is subject to no force and is an inertial body moving along a geodesic.
Far away from any sources of space-time curvature, where spacetime is flat, the Newtonian theory of free fall agrees with general relativity.
The experimental observation that all objects in free fall accelerate at the same rate, as noted by Galileo and then embodied in Newton's theory as the equality of gravitational and inertial masses, and later confirmed to high accuracy by modern forms of the Eötvös experiment, is the basis of the equivalence principle, from which basis Einstein's theory of general relativity initially took off.
