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In
Newtonian physics Classical mechanics is a physical theory describing the motion of macroscopic objects, from projectiles to parts of machinery, and astronomical objects, such as spacecraft, planets, stars, and galaxies. For objects governed by classical mec ...
, free fall is any motion of a body where
gravity In physics, gravity () is a fundamental interaction which causes mutual attraction between all things with mass or energy. Gravity is, by far, the weakest of the four fundamental interactions, approximately 1038 times weaker than the stro ...
is the only
force In physics, a force is an influence that can change the motion of an object. A force can cause an object with mass to change its velocity (e.g. moving from a state of rest), i.e., to accelerate. Force can also be described intuitively as a ...
acting upon it. In the context of
general relativity General relativity, also known as the general theory of relativity and Einstein's theory of gravity, is the geometric theory of gravitation published by Albert Einstein in 1915 and is the current description of gravitation in modern physics ...
, where gravitation is reduced to a space-time curvature, a body in free fall has no force acting on it. An object in the technical sense of the term "free fall" may not necessarily be falling down in the usual sense of the term. An object moving upwards might not normally be considered to be falling, but if it is subject to only the force of gravity, it is said to be in free fall. The
Moon The Moon is Earth's only natural satellite. It is the fifth largest satellite in the Solar System and the largest and most massive relative to its parent planet, with a diameter about one-quarter that of Earth (comparable to the width of ...
is thus in free fall around the
Earth Earth is the third planet from the Sun and the only astronomical object known to harbor life. While large volumes of water can be found throughout the Solar System, only Earth sustains liquid surface water. About 71% of Earth's sur ...
, though its
orbital speed In gravitationally bound systems, the orbital speed of an astronomical body or object (e.g. planet, moon, artificial satellite, spacecraft, or star) is the speed at which it orbits around either the barycenter or, if one body is much more mas ...
keeps it in very far orbit from the
Earth's surface Earth is the third planet from the Sun and the only astronomical object known to harbor life. While large volumes of water can be found throughout the Solar System, only Earth sustains liquid surface water. About 71% of Earth's surface ...
. In a roughly uniform
gravitational field In physics, a gravitational field is a model used to explain the influences that a massive body extends into the space around itself, producing a force on another massive body. Thus, a gravitational field is used to explain gravitational pheno ...
gravity acts on each part of a body approximately equally. When there are no other forces, such as the
normal force In mechanics, the normal force F_n is the component of a contact force that is perpendicular to the surface that an object contacts, as in Figure 1. In this instance '' normal'' is used in the geometric sense and means perpendicular, as oppos ...
exerted between a body (e.g. an
astronaut An astronaut (from the Ancient Greek (), meaning 'star', and (), meaning 'sailor') is a person trained, equipped, and deployed by a human spaceflight program to serve as a commander or crew member aboard a spacecraft. Although generally r ...
in orbit) and its surrounding objects, it will result in the sensation of
weightlessness Weightlessness is the complete or near-complete absence of the sensation of weight. It is also termed zero gravity, zero G-force, or zero-G. Weight is a measurement of the force on an object at rest in a relatively strong gravitational fie ...
, a condition that also occurs when the gravitational field is weak (such as when far away from any source of gravity). The term "free fall" is often used more loosely than in the strict sense defined above. Thus, falling through an
atmosphere An atmosphere () is a layer of gas or layers of gases that envelop a planet, and is held in place by the gravity of the planetary body. A planet retains an atmosphere when the gravity is great and the temperature of the atmosphere is low. A ...
without a deployed
parachute A parachute is a device used to slow the motion of an object through an atmosphere by creating drag or, in a ram-air parachute, aerodynamic lift. A major application is to support people, for recreation or as a safety device for aviators, w ...
, or lifting device, is also often referred to as ''free fall''. The
aerodynamic Aerodynamics, from grc, ἀήρ ''aero'' (air) + grc, δυναμική (dynamics), is the study of the motion of air, particularly when affected by a solid object, such as an airplane wing. It involves topics covered in the field of fluid dyn ...
drag forces in such situations prevent them from producing full weightlessness, and thus a skydiver's "free fall" after reaching
terminal velocity Terminal velocity is the maximum velocity (speed) attainable by an object as it falls through a fluid ( air is the most common example). It occurs when the sum of the drag force (''Fd'') and the buoyancy is equal to the downward force of grav ...
produces the sensation of the body's weight being supported on a cushion of air.


History

In the Western world prior to the 16th century, it was generally assumed that the speed of a falling body would be proportional to its weight—that is, a 10 kg object was expected to fall ten times faster than an otherwise identical 1 kg object through the same medium. The ancient Greek philosopher
Aristotle Aristotle (; grc-gre, Ἀριστοτέλης ''Aristotélēs'', ; 384–322 BC) was a Greek philosopher and polymath during the Classical period in Ancient Greece. Taught by Plato, he was the founder of the Peripatetic school of ...
(384–322 BC) discussed falling objects in ''
Physics Physics is the natural science that studies matter, its fundamental constituents, its motion and behavior through space and time, and the related entities of energy and force. "Physical science is that department of knowledge which ...
'' (Book VII), one of the oldest books on
mechanics Mechanics (from Ancient Greek: μηχανική, ''mēkhanikḗ'', "of machines") is the area of mathematics and physics concerned with the relationships between force, matter, and motion among physical objects. Forces applied to objec ...
(see
Aristotelian physics Aristotelian physics is the form of natural science described in the works of the Greek philosopher Aristotle (384–322 BC). In his work ''Physics'', Aristotle intended to establish general principles of change that govern all natural bodies, b ...
). Although, in the 6th century,
John Philoponus John Philoponus (Greek: ; ; c. 490 – c. 570), also known as John the Grammarian or John of Alexandria, was a Byzantine Greek philologist, Aristotelian commentator, Christian theologian and an author of a considerable number of philosophical tr ...
challenged this argument and said that, by observation, two balls of very different weights will fall at nearly the same speed. In 12th-century Iraq,
Abu'l-Barakāt al-Baghdādī Abu'l-Barakāt Hibat Allah ibn Malkā al-Baghdādī ( ar, أبو البركات هبة الله بن ملكا البغدادي; c. 1080 – 1164 or 1165 CE) was an Islamic philosopher, physician and physicist of Jewish descent from Baghdad, Iraq. ...
gave an explanation for the
gravitational acceleration In physics, gravitational acceleration is the acceleration of an object in free fall within a vacuum (and thus without experiencing drag). This is the steady gain in speed caused exclusively by the force of gravitational attraction. All bodie ...
of falling bodies. According to
Shlomo Pines Shlomo Pines (; ; August 5, 1908 in Charenton-le-Pont – January 9, 1990 in Jerusalem) was an Israeli scholar of Jewish and Islamic philosophy, best known for his English translation of Maimonides' ''Guide of the Perplexed''. Biography Pines ...
, al-Baghdādī's theory of motion was "the oldest negation of Aristotle's fundamental dynamic law amely, that a constant force produces a uniform motion nd is thus ananticipation in a vague fashion of the fundamental law of
classical mechanics Classical mechanics is a physical theory describing the motion of macroscopic objects, from projectiles to parts of machinery, and astronomical objects, such as spacecraft, planets, stars, and galaxies. For objects governed by classi ...
amely, that a force applied continuously produces acceleration" According to a tale that may be apocryphal, in 1589–92 Galileo dropped two objects of unequal mass from the Leaning Tower of Pisa. Given the speed at which such a fall would occur, it is doubtful that Galileo could have extracted much information from this experiment. Most of his observations of falling bodies were really of bodies rolling down ramps. This slowed things down enough to the point where he was able to measure the time intervals with
water clock A water clock or clepsydra (; ; ) is a timepiece by which time is measured by the regulated flow of liquid into (inflow type) or out from (outflow type) a vessel, and where the amount is then measured. Water clocks are one of the oldest time- ...
s 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 1589–92, Galileo wrote ''
De Motu Antiquiora ''De Motu Antiquiora'' ("The Older Writings on Motion"), or simply ''De Motu'', is Galileo Galilei's early written work on motion. It was written largely between 1589 and 1592, but was not published until 1687, after his death. It was never publis ...
'', an unpublished manuscript on the motion of falling bodies.


Examples

Examples of objects in free fall include: * A
spacecraft A spacecraft is a vehicle or machine designed to fly in outer space. A type of artificial satellite, spacecraft are used for a variety of purposes, including communications, Earth observation, meteorology, navigation, space colonization, ...
(in space) with propulsion off (e.g. in a continuous orbit, or on a suborbital trajectory (
ballistics Ballistics is the field of mechanics concerned with the launching, flight behaviour and impact effects of projectiles, especially ranged weapon munitions such as bullets, unguided bombs, rockets or the like; the science or art of designing a ...
) going up for some minutes, and then down). * An object dropped at the top of a
drop tube In physics and materials science, a drop tower or drop tube is a structure used to produce a controlled period of weightlessness for an object under study. Air bags, polystyrene pellets, and magnetic or mechanical brakes are sometimes used to ...
. * An object thrown upward or a person jumping off the ground at low speed (i.e. as long as air resistance is negligible in comparison to weight). Technically, an object is in free fall even when moving upwards or instantaneously at rest at the top of its motion. If gravity is the only influence acting, then the acceleration is always downward and has the same magnitude for all bodies, commonly denoted g. Since all objects fall at the same rate in the absence of other forces, objects and people will experience
weightlessness Weightlessness is the complete or near-complete absence of the sensation of weight. It is also termed zero gravity, zero G-force, or zero-G. Weight is a measurement of the force on an object at rest in a relatively strong gravitational fie ...
in these situations. Examples of objects not in free-fall: * Flying in an aircraft: there is also an additional force of
lift Lift or LIFT may refer to: Physical devices * Elevator, or lift, a device used for raising and lowering people or goods ** Paternoster lift, a type of lift using a continuous chain of cars which do not stop ** Patient lift, or Hoyer lift, mobil ...
. * Standing on the ground: the gravitational force is counteracted by the
normal force In mechanics, the normal force F_n is the component of a contact force that is perpendicular to the surface that an object contacts, as in Figure 1. In this instance '' normal'' is used in the geometric sense and means perpendicular, as oppos ...
from the ground. * Descending to the Earth using a parachute, which balances the force of gravity with an aerodynamic drag force (and with some parachutes, an additional lift force). The example of a falling skydiver who has not yet deployed a parachute is not considered free fall from a physics perspective, since they experience a
drag force In fluid dynamics, drag (sometimes called air resistance, a type of friction, or fluid resistance, another type of friction or fluid friction) is a force acting opposite to the relative motion of any object moving with respect to a surrounding flu ...
that equals their weight once they have achieved
terminal velocity Terminal velocity is the maximum velocity (speed) attainable by an object as it falls through a fluid ( air is the most common example). It occurs when the sum of the drag force (''Fd'') and the buoyancy is equal to the downward force of grav ...
(see below). 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 Mass is an intrinsic property of a body. It was traditionally believed to be related to the quantity of matter in a physical body, until the discovery of the atom and particle physics. It was found that different atoms and different ele ...
. With air resistance acting on an object that has been dropped, the object will eventually reach a terminal velocity, which is around 53 m/s (190 km/h or 118 mph) for a human skydiver. The terminal velocity depends on many factors including mass,
drag coefficient In fluid dynamics, the drag coefficient (commonly denoted as: c_\mathrm, c_x or c_) is a dimensionless quantity that is used to quantify the drag or resistance of an object in a fluid environment, such as air or water. It is used in the drag e ...
, 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). Free fall was demonstrated on the moon by astronaut
David Scott David Randolph Scott (born June 6, 1932) is an American retired test pilot and NASA astronaut who was the seventh person to walk on the Moon. Selected as part of the third group of astronauts in 1963, Scott flew to space three times and ...
on August 2, 1971. He simultaneously released a hammer and a feather from the same height above the moon's surface. The hammer and the feather both fell at the same rate and hit the surface at the same time. This demonstrated Galileo's discovery that, in the absence of air resistance, all objects experience the same acceleration due to gravity. On the Moon, however, the
gravitational acceleration In physics, gravitational acceleration is the acceleration of an object in free fall within a vacuum (and thus without experiencing drag). This is the steady gain in speed caused exclusively by the force of gravitational attraction. All bodie ...
is approximately 1.63 m/s2, or only about 16 that on Earth.


Free fall in Newtonian mechanics


Uniform gravitational field without air resistance

This is the "textbook" case of the vertical motion of an object falling a small distance close to the surface of a planet. It is a good approximation in air as long as the force of gravity on the object is much greater than the force of air resistance, or equivalently the object's velocity is always much less than the terminal velocity (see below). :v(t)=v_-gt\, :y(t)=v_t+y_-\fracgt^2 where :v_\, is the initial velocity (m/s). :v(t)\, is the vertical velocity with respect to time (m/s). :y_\, is the initial altitude (m). :y(t)\, is the altitude with respect to time (m). :t\, is time elapsed (s). :g\, is the acceleration due to
gravity In physics, gravity () is a fundamental interaction which causes mutual attraction between all things with mass or energy. Gravity is, by far, the weakest of the four fundamental interactions, approximately 1038 times weaker than the stro ...
(9.81 m/s2 near the surface of the earth). If the initial velocity is zero, then the distance fallen from the initial position will grow as the square of the elapsed time. Moreover, because the odd numbers sum to the perfect squares, the distance fallen in successive time intervals grows as the odd numbers. This description of the behavior of falling bodies was given by Galileo.


Uniform gravitational field with air resistance

This case, which applies to skydivers, parachutists or any body of mass, m, and cross-sectional area, A, with
Reynolds number In fluid mechanics, the Reynolds number () is a dimensionless quantity that helps predict fluid flow patterns in different situations by measuring the ratio between inertial and viscous forces. At low Reynolds numbers, flows tend to be dom ...
well above the critical Reynolds number, so that the air resistance is proportional to the square of the fall velocity, v, has an equation of motion :m\frac=mg - \frac \rho C_ A v^2 \, , where \rho is the
air density The density of air or atmospheric density, denoted '' ρ'', is the mass per unit volume of Earth's atmosphere. Air density, like air pressure, decreases with increasing altitude. It also changes with variation in atmospheric pressure, temperature a ...
and C_ is the
drag coefficient In fluid dynamics, the drag coefficient (commonly denoted as: c_\mathrm, c_x or c_) is a dimensionless quantity that is used to quantify the drag or resistance of an object in a fluid environment, such as air or water. It is used in the drag e ...
, assumed to be constant although in general it will depend on the Reynolds number. Assuming an object falling from rest and no change in air density with altitude, the solution is: : v(t) = v\tanh\left(\frac\right), where the
terminal speed Terminal velocity is the maximum velocity (speed) attainable by an object as it falls through a fluid (air is the most common example). It occurs when the sum of the drag force (''Fd'') and the buoyancy is equal to the downward force of grav ...
is given by :v_=\sqrt \, . The object's speed versus time can be integrated over time to find the vertical position as a function of time: :y = y_0 - \frac \ln \cosh\left(\frac\right). Using the figure of 56 m/s for the terminal velocity of a human, one finds that after 10 seconds he will have fallen 348 metres and attained 94% of terminal velocity, and after 12 seconds he will have fallen 455 metres and will have attained 97% of terminal velocity. However, when the air density cannot be assumed to be constant, such as for objects falling from high altitude, the equation of motion becomes much more difficult to solve analytically and a numerical simulation of the motion is usually necessary. The figure shows the forces acting on meteoroids falling through the Earth's upper atmosphere.
HALO jump High-altitude military parachuting, or military free fall (MFF), is a method of delivering military personnel, military equipment, and other military supplies from a transport aircraft at a high altitude via free-fall parachute insertion. Tw ...
s, including
Joe Kittinger Joseph William Kittinger II (July 27, 1928 – December 9, 2022) served as a United States Air Force (USAF) officer from 1950 to 1978. He was a fighter pilot who earned Command Pilot status and retired as a colonel. He held the world record for ...
's and
Felix Baumgartner Felix Baumgartner (; born 20 April 1969) is an Austrian skydiver, daredevil and BASE jumper. He is widely known for jumping to Earth from a helium balloon from the stratosphere on 14 October 2012 and landing in New Mexico, United States, as par ...
's record jumps, also belong in this category.


Inverse-square law gravitational field

It can be said that two objects in space orbiting each other in the absence of other forces are in free fall around each other, e.g. that the Moon or an artificial satellite "falls around" the Earth, or a planet "falls around" the Sun. Assuming spherical objects means that the equation of motion is governed by
Newton's law of universal gravitation Newton's law of universal gravitation is usually stated as that every particle attracts every other particle in the universe with a force that is proportional to the product of their masses and inversely proportional to the square of the distan ...
, with solutions to the gravitational two-body problem being elliptic orbits obeying
Kepler's laws of planetary motion In astronomy, Kepler's laws of planetary motion, published by Johannes Kepler between 1609 and 1619, describe the orbits of planets around the Sun. The laws modified the heliocentric theory of Nicolaus Copernicus, replacing its circular orb ...
. This connection between falling objects close to the Earth and orbiting objects is best illustrated by the thought experiment,
Newton's cannonball Newton's cannonball was a thought experiment Isaac Newton used to hypothesize that the force of gravity was universal, and it was the key force for planetary motion. It appeared in his posthumously published 1728 work ''De mundi systemate'' (also ...
. The motion of two objects moving radially towards each other with no
angular momentum In physics, angular momentum (rarely, moment of momentum or rotational momentum) is the rotational analog of linear momentum. It is an important physical quantity because it is a conserved quantity—the total angular momentum of a closed syst ...
can be considered a special case of an elliptical orbit of eccentricity (
radial elliptic trajectory In astrodynamics or celestial mechanics, an elliptic orbit or elliptical orbit is a Kepler orbit with an eccentricity of less than 1; this includes the special case of a circular orbit, with eccentricity equal to 0. In a stricter sense, i ...
). This allows one to compute the
free-fall time The free-fall time is the characteristic time that would take a body to collapse under its own gravitational attraction, if no other forces existed to oppose the collapse. As such, it plays a fundamental role in setting the timescale for a wide vari ...
for two point objects on a radial path. The solution of this equation of motion yields time as a function of separation: :t(y)= \sqrt \left(\sqrt + \arccos \right), where :t is the time after the start of the fall :y is the distance between the centers of the bodies :y_0 is the initial value of y :\mu = G(m_1 + m_2) is the
standard gravitational parameter In celestial mechanics, the standard gravitational parameter ''μ'' of a celestial body is the product of the gravitational constant ''G'' and the mass ''M'' of the bodies. For two bodies the parameter may be expressed as G(m1+m2), or as GM whe ...
. Substituting y = 0 we get the
free-fall time The free-fall time is the characteristic time that would take a body to collapse under its own gravitational attraction, if no other forces existed to oppose the collapse. As such, it plays a fundamental role in setting the timescale for a wide vari ...
. The separation as a function of time is given by the inverse of the equation. The inverse is represented exactly by the analytic power series: : y( t ) = \sum_^ \left _\lim__\left( __ ___\frac_\left[ ____r^n_\left(_\frac_(_\arcsin(_\sqrt_)_-_\sqrt_)_ ___\right)^ __\right\right) _\right.html" ;"title=" r^n \left( \frac ( \arcsin( \sqrt ) - \sqrt ) \right)^ \right"> \lim_ \left( \frac \left[ r^n \left( \frac ( \arcsin( \sqrt ) - \sqrt ) \right)^ \right\right) \right"> r^n \left( \frac ( \arcsin( \sqrt ) - \sqrt ) \right)^ \right"> \lim_ \left( \frac \left[ r^n \left( \frac ( \arcsin( \sqrt ) - \sqrt ) \right)^ \right\right) \right Evaluating this yields: :y(t)=y_0 \left( x - \frac x^2 - \fracx^3 - \fracx^4 - \fracx^5 - \fracx^6 - \fracx^7 - \cdots \right) \ , where x = \left[\frac \left( \frac- t \sqrt \right) \right]^.


Free fall in general relativity

In general relativity, an object in free fall is subject to no force and is an inertial body moving along a geodesics in general relativity, geodesic. Far away from any sources of space-time curvature, where
spacetime In physics, spacetime is a mathematical model that combines the three dimensions of space and one dimension of time into a single four-dimensional manifold. Spacetime diagrams can be used to visualize relativistic effects, such as why differ ...
is flat, the Newtonian theory of free fall agrees with general relativity. Otherwise the two disagree; e.g., only general relativity can account for the
precession Precession is a change in the orientation of the rotational axis of a rotating body. In an appropriate reference frame it can be defined as a change in the first Euler angle, whereas the third Euler angle defines the rotation itself. In oth ...
of orbits, the
orbital decay Orbital decay is a gradual decrease of the distance between two orbiting bodies at their closest approach (the periapsis) over many orbital periods. These orbiting bodies can be a planet and its satellite, a star and any object orbiting it, or ...
or inspiral of compact binaries due to
gravitational waves Gravitational waves are waves of the intensity of gravity generated by the accelerated masses of an orbital binary system that propagate as waves outward from their source at the speed of light. They were first proposed by Oliver Heaviside i ...
, and the relativity of direction (
geodetic precession The geodetic effect (also known as geodetic precession, de Sitter precession or de Sitter effect) represents the effect of the curvature of spacetime, predicted by general relativity, on a vector carried along with an orbiting body. For example, ...
and
frame dragging Frame-dragging is an effect on spacetime, predicted by Albert Einstein's general theory of relativity, that is due to non-static stationary distributions of mass–energy. A stationary field is one that is in a steady state, but the masses cau ...
). 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 The Eötvös experiment was a famous physics experiment that measured the correlation between inertial mass and gravitational mass, demonstrating that the two were one and the same, something that had long been suspected but never demonstrated with ...
, is the basis of the
equivalence principle In the theory of general relativity, the equivalence principle is the equivalence of gravitational and inertial mass, and Albert Einstein's observation that the gravitational "force" as experienced locally while standing on a massive body (su ...
, from which basis Einstein's theory of general relativity initially took off.


See also

*
Equations for a falling body Lection 0 A set of equations describing the trajectories of objects subject to a constant gravitational force under normal Earth-bound conditions. Assuming constant acceleration ''g'' due to Earth’s gravity, Newton's law of universal gravitati ...
*
G-force The gravitational force equivalent, or, more commonly, g-force, is a measurement of the type of force per unit mass – typically acceleration – that causes a perception of weight, with a g-force of 1 g (not gram in mass measur ...
*
High-altitude military parachuting High-altitude military parachuting, or military free fall (MFF), is a method of delivering military personnel, military equipment, and other military supplies from a transport aircraft at a high altitude via free-fall parachute insertion. Two ...
*
Micro-g environment The term micro-g environment (also μg, often referred to by the term microgravity) is more or less synonymous with the terms '' weightlessness'' and ''zero-g'', but emphasising that g-forces are never exactly zero—just very small (on the ...
* Reduced-gravity aircraft *
Terminal velocity Terminal velocity is the maximum velocity (speed) attainable by an object as it falls through a fluid ( air is the most common example). It occurs when the sum of the drag force (''Fd'') and the buoyancy is equal to the downward force of grav ...
*
Weightlessness Weightlessness is the complete or near-complete absence of the sensation of weight. It is also termed zero gravity, zero G-force, or zero-G. Weight is a measurement of the force on an object at rest in a relatively strong gravitational fie ...


References


External links


Freefall formula calculator
an educational website {{Authority control Gravity Articles containing video clips