The Schwarzschild radius (sometimes historically referred to as the gravitational radius ) is the radius of a sphere such that, if all the mass of an object were to be compressed within that sphere, the escape velocity from the surface of the sphere would equal the speed of light. An example of an object where the mass is within its Schwarzschild radius is a black hole. Once a stellar remnant collapses to or below this radius, light cannot escape and the object is no longer directly visible, thereby forming a black hole. It is a characteristic radius associated with every quantity of mass. The Schwarzschild radius was named after the German astronomer Karl Schwarzschild, who calculated this exact solution for the theory of general relativity in 1916. History[edit] In 1916, Karl Schwarzschild obtained the exact solution to Einstein's field equations for the gravitational field outside a non-rotating, spherically symmetric body (see Schwarzschild metric). Using the definition , the solution contained a term of the form ; where the value of making this term singular has come to be known as the . The physical significance of this, and whether this singularity could ever occur in nature, was debated for many decades; a general acceptance of the possibility of a black hole did not occur until the second half of the 20th century. Parameters[edit] The Schwarzschild radius of an object is proportional to the mass. Accordingly, the Sun has a Schwarzschild radius of approximately 3.0 km (1.9 mi), whereas Earth's is only about 9.0 mm. The observable universe's mass has a Schwarzschild radius of approximately 13.7 billion light years. Formula[edit] The Schwarzschild radius is the limiting maximum radius of a massive object at which the escape velocity reaches it's maximum limit (the speed of light, c). If an object is thrown up from the surface of a massive object at velocity v, its kinetic energy slowly transforms into potential energy, and then back as the object falls back to the surface. Escape velocity is the limiting minimum velocity at which the object continues to slow but never stop until it reaches an infinite distance. So, it's total positive kinetic energy and negative potential energy is greater than or equal to zero (i.e. KE = PE). Therefore, escape velocity can be calculated (from KE = PE) as: Therefore, at maximum escape velocity (speed of light, c), Schwarzschild radius becomes directly proportional to mass as: where: s is the Schwarzschild radius; G is the gravitational constant; M is the mass of the object; c is the speed of light in vacuum. The proportionality constant, 2/2, is approximately km /☉. An object of any density can be large enough to fall within its own Schwarzschild radius, is the volume of the object; is its density. Black hole classification by Schwarzschild radius[edit] Any object whose radius is smaller than its Schwarzschild radius is called a black hole. The surface at the Schwarzschild radius acts as an event horizon in a non-rotating body (a rotating black hole operates slightly differently). Neither light nor particles can escape through this surface from the region inside, hence the name "black hole". Black holes can be classified based on their Schwarzschild radius, or equivalently, by their density. As the radius is linearly related to mass, and the enclosed volume to the third power of radius, the mass density of such volumes at the low end of the mass scale is much higher than that of the larger black holes. The volume enclosed in the event horizon of the most massive black holes has a mass density lower than main sequence stars. Supermassive black hole[edit] A supermassive black hole (SMBH) is the largest type of black hole, though there are few official criteria on how such an object is considered so, on the order of hundreds of thousands to billions of solar masses. (Supermassive black holes up to 21 billion (2.1 × 1010) ☉ have been detected, such as NGC 4889.) Unlike stellar mass black holes, supermassive black holes have low densities if you assume that the Schwarzschild radius is the outer edge of the black hole (note that this assumption is in contrast to the typical assumption that a black hole is a singularity, and therefore has zero radial extent). Under this assumption, the average density of a supermassive black hole can be less than the density of water. The Schwarzschild radius of a body is proportional to its mass and therefore to its volume, assuming that the body has a constant mass-density. In contrast, the physical radius of the body is proportional to the cube root of its volume. Therefore, as the body accumulates matter at a given fixed density (in this example, 103kg/m3, the density of water), its Schwarzschild radius will increase more quickly than its physical radius. When a body of this density has grown to around 136 million solar masses (1.36 × 108) ☉, its physical radius would be overtaken by its Schwarzschild radius, and thus it would form a supermassive black hole. It is thought that supermassive black holes like these do not form immediately from the singular collapse of a cluster of stars. Instead they may begin life as smaller, stellar-sized black holes and grow larger by the accretion of matter, or even of other black holes. The Schwarzschild radius of the supermassive black hole at the Galactic Center would be approximately 13.3 million kilometres. Stellar black hole[edit] Stellar black holes have much greater densities than supermassive black holes. If one accumulates matter at nuclear density (the density of the nucleus of an atom, about 1018kg/m3; neutron stars also reach this density), such an accumulation would fall within its own Schwarzschild radius at about 3 ☉ and thus would be a stellar black hole. Primordial black hole[edit] A small mass has an extremely small Schwarzschild radius. A mass similar to Mount Everest has a Schwarzschild radius much smaller than a nanometre. Its average density at that size would be so high that no known mechanism could form such extremely compact objects. Such black holes might possibly be formed in an early stage of the evolution of the universe, just after the Big Bang, when densities were extremely high. Therefore these hypothetical miniature black holes are called primordial black holes. In gravitational time dilation[edit] Gravitational time dilation near a large, slowly rotating, nearly spherical body, such as the Earth or Sun can be reasonably approximated using the Schwarzschild radius as follows: tr is the elapsed time for an observer at radial coordinate "r" within the gravitational field; t is the elapsed time for an observer distant from the massive object (and therefore outside of the gravitational field); r is the radial coordinate of the observer (which is analogous to the classical distance from the center of the object); s is the Schwarzschild radius. The results of the Pound–Rebka experiment in 1959 were found to be consistent with predictions made by general relativity. By measuring Earth’s gravitational time dilation, this experiment indirectly measured Earth’s Schwarzschild radius. In Newtonian gravitational fields[edit] The Newtonian gravitational field near a large, slowly rotating, nearly spherical body can be reasonably approximated using the Schwarzschild radius as follows: and Therefore on dividing above by below: g is the gravitational acceleration at radial coordinate "r"; s is the Schwarzschild radius of the gravitating central body; r is the radial coordinate; c is the speed of light in vacuum. On the surface of the Earth: In Keplerian orbits[edit] Therefore, but (derived above) r is the orbit radius; s is the Schwarzschild radius of the gravitating central body; v is the orbital speed; c is the speed of light in vacuum. a is the semi-major axis; T is the orbital period. For the Earth orbiting the Sun: Relativistic circular orbits and the photon sphere[edit] The Keplerian equation for circular orbits can be generalized to the relativistic equation for circular orbits by accounting for time dilation in the velocity term: This final equation indicates that an object orbiting at the speed of light would have an orbital radius of 1.5 times the Schwarzschild radius. This is a special orbit known as the photon sphere. See also[edit] Classification of black holes by type: A classification of black holes by mass: Using these values, one can calculate a mass estimate of 6.3715e14 kg. One can calculate the Schwarzschild radius: 2 * 6.6738e-11 m3 kg−1 s−2 * 6.3715e14 kg / (299 792 458 m s−1)2 = 9.46e-13 m, or 9.46e-4 nm.

]]>Newton's second law Newton's second law shows how an object will be affected if an external force does act upon it. This law states that This means that force = momentum / time . Momentum = mass × velocity , and acceleration = velocity / time , and so Newton's second law can be stated as force = mass × acceleration . Newton's third law Newton's third law states that the force on an object is always due to another object; all forces act in pairs that are equal in magnitude and opposite in direction. This is why you feel recoil when you strike an object, and why you do not fall through the Earth due to the pull of gravity. The conservation of momentum The combination of Newton's second and third laws shows that momentum must be conserved. This means that the total momentum of two objects will remain the same before and after a collision. This is because if F = ma and F = -F , then ma = -ma , and so mv / t = -mv / t . Here is force, is mass, is acceleration, and is velocity. Newton's law of universal gravitation Newton's law of universal gravitation states that every mass attracts every other mass in the universe, and the gravitational force between two bodies is proportional to the product of their masses, and inversely proportional to the square of the distance between them. Spherical objects like planets and stars act as if all of their mass is concentrated at their centre, and so the distance between objects should include the distance to the centre of both objects. Newton stated that the force of gravity is always attractive, works instantaneously at a distance, and has an infinite range. Most importantly, it affects everything with mass - and has nothing to do with an object's charge or chemical composition. This means that it can account for both the downwards force caused by the pull of the Earth - as described by Galileo - and the force that causes the planets to orbit the Sun - as described by Kepler. Newton's law of gravitation shows that objects with different masses fall at the same rate when combined with his second law of motion. This is because an object's acceleration due to the force of gravity only depends on the mass of the object that is pulling it: if F = m1a and F = G m1m2 / r2 , then m1a = G , and so a = Gm2 / r2 . Newton's law of gravitation, here is a constant that is the same for everything in the universe. Image credit: modified from Dna-Dennis. Here m1 is the mass of the less massive object (e.g. a feather or hammer), and m2 is the mass of the more massive object (e.g. a planet). This means that a feather and hammer will all fall at the same rate if they are dropped in the same place.

]]>One of the questions I get most often from my readers is this: Since gravity pulls on things proportional to their mass, and since the Higgs field is responsible for giving everything its mass, there obviously must be a deep connection between the Higgs and gravity… right? It’s a very reasonable guess, but — it turns out to be completely wrong. The problem is that this statement combines a 17th century notion of gravity, long ago revised, with an overly simplified version of a late-20th century notion of where masses of various particles comes from. I’ve finally produced the Higgs FAQ version 2.0, intended for non-experts with little background in the subject, and as part of that, I’ve answered this question. But since the question is so common, I thought I’d also put the answer in a post of its own. As preface, let me bring out my professorial training and correct the question above with a red pen: Since gravity pulls on things proportional to their mass to a combination of their energy and momentum, and since the Higgs field is responsible of giving everything not everything, just the known elementary particles excepting the Higgs particle itself its mass, there obviously must be a deep connection between the Higgs and gravity… right? wrong. Now let me explain these corrections one by one. When you first learn about gravity in school, you learn Newton’s law: that the force of gravity between two objects, one of mass M1 and one of mass M2, has a strength proportional to the product M1 M2. But that was true before Einstein. It turns out that Newton’s law needs to be revised: the Einsteinian statement of the law is (roughly) that for two objects that are slow-moving (i.e. their speed relative to one another is much less than c, the speed of light) and have energy E1 and E2, the gravitational force between them has a strength proportional to the product E1 E2. How are these two statements, the Newtonian and the Einsteinian, consistent? They are consistent because Einstein and his followers established that for any ordinary object, the relation between its energy E, momentum p and mass M [sometimes called “rest mass”, but just called `mass’ by particle physicists] is For a slow-moving object, p ≈ Mv (where v is the object’s velocity) and pc ≈ Mvc is much smaller than Mc2. And therefore

]]>To begin with, the speed of gravity has not been measured directly in the laboratory—the gravitational interaction is too weak, and such an experiment is beyond present technological capabilities. The "speed of gravity" must therefore be deduced from astronomical observations, and the answer depends on what model of gravity one uses to describe those observations. In the simple newtonian model, gravity propagates instantaneously: the force exerted by a massive object points directly toward that object's present position. For example, even though the Sun is 500 light seconds from the Earth, newtonian gravity describes a force on Earth directed towards the Sun's position "now, " not its position 500 seconds ago. Putting a "light travel delay" (technically called "retardation") into newtonian gravity would make orbits unstable, leading to predictions that clearly contradict Solar System observations. In general relativity, on the other hand, gravity propagates at the speed of light; that is, the motion of a massive object creates a distortion in the curvature of spacetime that moves outward at light speed. This might seem to contradict the Solar System observations described above, but remember that general relativity is conceptually very different from newtonian gravity, so a direct comparison is not so simple. Strictly speaking, gravity is not a "force" in general relativity, and a description in terms of speed and direction can be tricky. For weak fields, though, one can describe the theory in a sort of newtonian language. In that case, one finds that the "force" in GR is not quite central—it does not point directly towards the source of the gravitational field—and that it depends on velocity as well as position. The net result is that the effect of propagation delay is almost exactly cancelled, and general relativity very nearly reproduces the newtonian result. This cancellation may seem less strange if one notes that a similar effect occurs in electromagnetism. If a charged particle is moving at a constant velocity, it exerts a force that points toward its present position, not its retarded position, even though electromagnetic interactions certainly move at the speed of light. Here, as in general relativity, subtleties in the nature of the interaction "conspire" to disguise the effect of propagation delay. It should be emphasized that in both electromagnetism and general relativity, this effect is not put in ad hoc but comes out of the equations. Also, the cancellation is nearly exact only for constant velocities. If a charged particle or a gravitating mass suddenly accelerates, the change in the electric or gravitational field propagates outward at the speed of light. Since this point can be confusing, it's worth exploring a little further, in a slightly more technical manner. Consider two bodies—call them A and B—held in orbit by either electrical or gravitational attraction. As long as the force on A points directly towards B and vice versa, a stable orbit is possible. If the force on A points instead towards the retarded (propagation-time-delayed) position of B, on the other hand, the effect is to add a new component of force in the direction of A's motion, causing instability of the orbit. This instability, in turn, leads to a change in the mechanical angular momentum of the A-B system. But total angular momentum is conserved, so this change can only occur if some of the angular momentum of the A-B system is carried away by electromagnetic or gravitational radiation. Now, in electrodynamics, a charge moving at a constant velocity does not radiate. Technically, the lowest-order radiation is dipole radiation, and the radiated power depends on the second time derivative of the electric dipole moment; two time derivatives give acceleration. So, to the extent that A's motion can be approximated as motion at a constant velocity, A cannot lose angular momentum. For the theory to be consistent, there must therefore be compensating terms that partially cancel the instability of the orbit caused by retardation. This is exactly what happens; a calculation shows that the force on A points not towards B's retarded position, but towards B's "linearly extrapolated" retarded position. In general relativity, roughly speaking, a mass moving at a constant acceleration does not radiate. Here, the lowest order radiation is quadrupole radiation, and the radiated power depends on the third time derivative of the mass quadrupole moment. (The full picture is slightly more complex, since one cannot have a single, isolated accelerating mass; whatever it is that causes the acceleration also has a gravitational field, and its field must be taken into account.) For consistency, just as in the case of electromagnetism, a cancellation of the effect of retardation must occur, but it must now be even more complete—that is, it must hold to a higher power of /c. This is exactly what one finds when one solves the equations of motion in general relativity. While current observations do not yet provide a direct model-independent measurement of the speed of gravity, a test within the framework of general relativity can be made by observing the binary pulsar PSR 1913+16. The orbit of this binary system is gradually decaying, and this behavior is attributed to the loss of energy due to escaping gravitational radiation. But in any field theory, radiation is intimately related to the finite velocity of field propagation, and the orbital changes due to gravitational radiation can equivalently be viewed as damping caused by the finite propagation speed. (In the discussion above, this damping represents a failure of the "retardation" and "noncentral, velocity-dependent" effects to completely cancel.)

]]>[Textbook disclaimers are down, but not out. This satirical look at "only a theory" disclaimers imagines what might happen if advocates applied the same logic to the theory of gravitation that they do to the theory of evolution.] All physics textbook should include this warning label: This textbook contains material on Gravity. Universal Gravity is a theory, not a fact, regarding the natural law of attraction. This material should be approached with an open mind, studied carefully, and critically considered. The Universal Theory of Gravity is often taught in schools as a fact, when in fact it is not even a good theory. First of all, no one has measured gravity for every atom and every star. It is simply a religious belief that it is "universal". Secondly, school textbooks routinely make false statements. For example, "the moon goes around the earth." If the theory of gravity were true, it would show that the sun's gravitational force on the moon is much stronger than the earth's gravitational force on the moon, so the moon would go around the sun. Anybody can look up at night and see the obvious gaps in gravity theory. The existence of tides is often taken as a proof of gravity, but this is logically flawed. Because if the moon's "gravity" were responsible for a bulge underneath it, then how can anyone explain a high tide on the opposite side of the earth at the same time? Anyone can observe that there are two — not one — high tides every day. It is far more likely that tides were given us by an Intelligent Creator long ago and they have been with us ever since. In any case, the fact that there are two high tides falsifies gravity. There are numerous other flaws. For example, astronomers, who seem to have a fetish for gravity, tell us that the moon rotates on its axis but at the same time it always presents the same face to the earth. This is patently absurd. Moreover, if gravity were working on the early earth, then earth would have been bombarded out of existence by falling asteroids, meteors, comets, and other space junk. Furthermore, gravity theory suggests that the planets have been moving in orderly orbits for millions and millions of years, which wholly contradicts the Second Law of Thermodynamics. Since everything in the Universe tends to disorder according to the Second Law, orderly orbits are impossible. This cannot be resolved by pointing to the huge outpouring of energy from the sun. In fact, it is known that the flux of photons from the sun and the "solar wind" actually tends to push earth away.

]]>What is the difference between a scientific hypothesis, theory, and law? When reading scientific articles (and many of the articles on From Quarks to Quasars), you will see the terms hypothesis, theory, and law used to describe something. In the scientific community these words have very specific definitions. For laypeople, sometimes these definitions get confusing because many time these words are used differently in a colloquial context. So, what does it mean when you call something a hypothesis, a theory, or a law? Hypothesis: A hypothesis is a reasonable guess based on what you know or observe. Hypotheses (plural of hypothesis) are proven and disproven all of the time. Hypotheses play a strong role in the scientific method where you formulate a question, create a hypothesis, make a testable prediction, test, and then analyze the data. Even then, a hypothesis needs to be tested and retested many times before it is generally accepted in the scientific community as being true. Example: You observe that, upon waking up each morning, your trashcan is overturned with trash spread around the yard. You form a hypothesis that raccoons are responsible. Through testing, the results will either support or refute your hypothesis. Theory: A scientific theory consists of one or more hypotheses that have been supported with repeated testing. Theories are one of the pinnacles of science and are widely accepted in the scientific community as being true. To remain a theory, it must never be shown to be wrong; if it is, the theory is disproven (this also happens). Theories can also evolve. This means the old theory wasn’t wrong, but it wasn’t complete either. Here are some examples. When Sir Isaac Newton discovered the theory of gravity and wrote laws that explained the motions of objects, he was not wrong; but he wasn’t fully right either. Einstein later discovered the theories of special and general relativity and this creates a more complete theory of gravity. In fact, when you stay far below the speed of light, many of the equations in general and special relativity give you Newton’s equations. NASA, for the record, uses Newton’s equations when planning missions for their spacecraft. Overturning a theory – Steady State vs Big Bang What happens when you have two theories that contradict each other, as is the case with the Steady State and Big Bang theories? For a very brief summery on these theories. the Steady State theory says the universe is Steady and doesn’t change whereas the Big Bang theory says the universe started at some point in time in a ‘big bang’. In this case, scientists make observations, hypothesis and testable predictions to figure out which one is right (Example: I observe the universe is expanding, I hypothesize there was a beginning, I test by doing the math). Eventually, either one theory is overturned completely (as is the case with Steady State vs Big Bang) or the correct aspects of each theory are combined to form a new theory. In either case, the theories then need to withstand the rigors of testing and retesting. After a theory proves itself overtime, it is accepted into the scientific community as being correct. In many cases, these theories are the groundwork on which other theories are built on. An example is general/special relativity, these theories lay the foundation for many, many other theories and equations (such as Hubble’s law and the Schwarzschild radius). If relativity were ever overturned, that would be very bad (but, also good because it means science advanced). Note: In cases like relativity, since the math always works out, the likelihood of that happening is very, very small. Rather, relativity will probably be proven a smaller piece in a lager more complete theory scientists hypothesize about called Grand Unification – but that is a post for another time. Law: Scientific laws are short, sweet, and always true. Many times laws are expressed in a single expression. Laws cannot ever be shown to be wrong (that is why there are many theories and few laws). Laws are accepted as being universal and are the cornerstones of science. If a law were ever to be shown false, then any science built on that law would also be wrong; then the domino effect would have a new (and devastating) meaning. Laws generally rely on a concise mathematical equation

]]>American political personality Bill O’Reilly once famously said, “Tide goes in, tide goes out—never a miscommunication. You can’t explain that.” While he probably can’t explain that, scientists can: The tides are formed by gravitational forces exerted unevenly on the Earth by the moon (video). The Earth’s gravitational pull has quite an effect on the moon as well. And since the moon doesn’t have a liquid ocean, the Earth’s tidal forces are manifested in other, strange ways. A crack in the lunar surface, called a “lobate scarp, ” formed by the shrinking of the moon.(NASA/LRO/Arizona State University/Smithsonian Institution) In 2010, researchers examined a number of images from NASA’s Lunar Reconnaissance Orbiter (LRO) and found 14 small cracks on the moon’s surface—most less than 6.2 miles (10 kilometers) long. The researchers concluded that these faults were the result of the moon, ever so slowly, shrinking in size. As the moon’s liquid core cools, it solidifies, and its volume decreases. The core contracts and the moon’s solid crust “buckles, ” forming the cracks. Since then, LRO has found over 3, 000 more of these cracks. Researchers expected them to be randomly distributed across the moon, as they are on other planets and their satellites—but that’s not what they found. “There is a pattern in the orientations of the thousands of faults, and it suggests something else is influencing their formation, something that’s also acting on a global scale, ” said Tom Watters, Smithsonian senior scientist, in a press release. “That something is the Earth’s gravitational pull.” While the moon’s gravity might cause our tides to rise and fall, the Earth’s gravity is causing the moon’s crust to essentially rise and fall. (NASA/LRO/Arizona State University/Smithsonian Institution) The researchers observed that the cracks tended to run east-west toward the lunar poles, and north-south closer to the moon’s equator—both consistent with the Earth’s tidal forces in those areas. “The agreement between the mapped fault orientations and the fault orientations predicted by the modeled tidal and contractional forces is pretty striking, ” Watters said. He and his team .

]]>States that the gravitational force between two objects is proportional to the product of their masses and inversely proportional to the square of separation between them. This equation is a result of Isaac Newton's Law of Universal Gravitation, which states that quantities of matter attract other matter to it. The proportionality constant in the equation is called the Universal Gravitational Constant. The value of that constant was determined experimentally by Henry Cavendish in 1798. This Universal Gravitation Equation originally applied to point masses but was extended to masses of finite size with the assumption that their mass was concentrated at their center of mass...

]]>Particle physics usually has a hard time competing with politics and celebrity gossip for headlines, but the Higgs boson has garnered some serious attention. That's exactly what happened on July 4, 2012, though, when scientists at CERN announced that they'd found a particle that behaved the way they expect the Higgs boson to behave. Maybe the famed boson's grand and controversial nickname, the "God Particle, " has kept media outlets buzzing. Then again, the intriguing possibility that the Higgs boson is responsible for all the mass in the universe rather captures the imagination, too. Or perhaps we're simply excited to learn more about our world, and we know that if the Higgs boson does exist, we'll unravel the mystery a little more. In order to truly understand what the Higgs boson is, however, we need to examine one of the most prominent theories describing the way the cosmos works: the standard model . The model comes to us by way of particle physics , a field filled with physicists dedicated to reducing our complicated universe to its most basic building blocks. It's a challenge we've been tackling for centuries, and we've made a lot of progress. First we discovered atoms, then protons, neutrons and electrons, and finally quarks and leptons (more on those later). But the universe doesn't only contain matter; it also contains forces that act upon that matter. The standard model has given us more insight into the types of matter and forces than perhaps any other theory we have. Here's the gist of the standard model, which was developed in the early 1970s: Our entire universe is made of 12 different matter particles and four forces [source: European Organization for Nuclear Research]. Among those 12 particles, you'll encounter six quarks and six leptons. Quarks make up protons and neutrons, while members of the lepton family include the electron and the electron neutrino , its neutrally charged counterpart. Scientists think that leptons and quarks are indivisible; that you can't break them apart into smaller particles. Along with all those particles, the standard model also acknowledges four forces: gravity, electromagnetic, strong and weak. As theories go, the standard model has been very effective, aside from its failure to fit in gravity. Armed with it, physicists have predicted the existence of certain particles years before they were verified empirically. Unfortunately, the model still has another missing piece - the Higgs boson. What is it, and why is it necessary for the universe the standard model describes to work? Let's find out.

]]>A painting of Sir Isaac Newton by Sir Godfrey Kneller, dated to 1689. Credit: Sir Godfrey Kneller Sir Isaac Newton's three laws of motion describe the motion of massive bodies and how they interact. While Newton’s laws may seem obvious to us today, more than three centuries ago they were considered to be revolutionary. Newton was one of the most influential scientists of all time. His ideas became the basis for modern physics. He studied optics, astronomy and math — he invented calculus. (German mathematician Gottfried Leibniz is also credited with developing it independently at about the same time.) Newton is perhaps best known for his work in studying gravity and the motion of planets. Urged on by astronomer Edmond Halley, Newton published his laws in 1687, in his seminal work “Philosophiæ Naturalis Principia Mathematica” (Mathematical Principles of Natural Philosophy) in which he formalized the description of how massive bodies move under the influence of external forces. In formulating his three laws, Newton simplified his treatment of massive bodies by considering them to be mathematical points with no size or rotation. This allowed him to ignore factors such as friction, air resistance, temperature, material properties, etc., and concentrate on phenomena that can be described solely in terms of mass, length and time. Consequently, the three laws cannot be used to describe precisely the behavior of large rigid or deformable objects; however, in many cases they provide suitably accurate approximations. Newton’s laws pertain to the motion of massive bodies in an inertial reference frame , sometimes called a Newtonian reference frame, although Newton himself never described such a reference frame. An inertial reference frame can be described as a 3-dimensional coordinate system that is either stationary or in uniform linear motion., i.e., it is not accelerating or rotating. He found that motion within such an inertial reference frame could be described by 3 simple laws. The First Law of Motion states, “A body at rest will remain at rest, and a body in motion will remain in motion unless it is acted upon by an external force.” This simply means that things cannot start, stop, or change direction all by themselves. It takes some force acting on them from the outside to cause such a change. This property of massive bodies to resist changes in their state of motion is sometimes called inertia. The Second Law of Motion describes what happens to a massive body when it is acted upon by an external force. It states, “The force acting on an object is equal to the mass of that object times its acceleration.” This is written in mathematical form as F = ma, where F is force, m is mass, and a is acceleration. The bold letters indicate that force and acceleration are vectorquantities, which means they have both magnitude and direction. The force can be a single force, or it can be the vector sum of more than one force, which is the net force after all the forces are combined. When a constant force acts on a massive body, it causes it to accelerate, i.e., to change its velocity, at a constant rate. In the simplest case, a force applied to an object at rest causes it to accelerate in the direction of the force. However, if the object is already in motion, or if this situation is viewed from a moving reference frame, that body might appear to speed up, slow down, or change direction depending on the direction of the force and the directions that the object and reference frame are moving relative to each other. The Third Law of Motion states, “For every action, there is an equal and opposite reaction.” This law describes what happens to a body when it exerts a force on another body. Forces always occur in pairs, so when one body pushes against another, the second body pushes back just as hard. For example, when you push a cart, the cart pushes back against you; when you pull on a rope, the rope pulls back against you; when gravity pulls you down against the ground, the ground pushes up against your feet; and when a rocket ignites its fuel behind it, the expanding exhaust gas pushes on the rocket causing it to accelerate. If one object is much, much more massive than the other, particularly in the case of the first object being anchored to the Earth, virtually all of the acceleration is imparted to the second object, and the acceleration of the first object can be safely ignored. For instance, if you were to throw a baseball to the west, you would not have to consider that you actually caused the rotation of the Earth to speed up ever so slightly while the ball was in the air. However, if you were standing on roller skates, and you threw a bowling ball forward, you would start moving backward at a noticeable speed. The three laws have been verified by countless experiments over the past three centuries, and they are still being widely used to this day to describe the kinds of objects and speeds that we encounter in everyday life. They form the foundation of what is now known as classical mechanics, which is the study of massive objects that are larger than the very small scales addressed by quantum mechanics and that are moving slower than the very high speeds addressed by relativistic mechanics. Jim Lucas is a freelance writer and editor specializing in physics, astronomy and engineering. He is general manager of Lucas Technologies.

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