Physics
Gravity
Gravity is a fundamental force of nature that causes objects with mass to be attracted to each other. It is responsible for the motion of planets, stars, and galaxies, as well as the falling of objects on Earth. According to the theory of general relativity, gravity is the result of the curvature of spacetime caused by mass and energy.
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12 Key excerpts on "Gravity"
- Thais Russomano, Gustavo Dalmarco, Felipe Prehn Falcao(Authors)
- 2022(Publication Date)
- Springer(Publisher)
Compared to the other three fundamental interactions in nature, gravitation is the weakest one. It, however, acts over great distances and is always present. Gravitation is interpreted differently by classic mechanics, relativity, and quantum physics. In classic mechanics, gravitation arises out of the force of Gravity. In general relativity, it is the mass that curves space time, not a force. In quantum Gravity theories, the gravitation is the postulated carrier of the gravitational force, time space itself is envisioned as discrete in nature, or both. The gravitational attraction of the Earth endows objects with weight that causes them to fall to the ground when dropped (the Earth also moves toward the object but only by an infinitesimal amount). FIGURE 1.1: The gravitational force keeps the planets in orbit about the sun (http://en.wikipedia .org/wiki/Gravity). GENERAL CONCEPTS IN PHYSICS—DEFINITION OF PHYSICAL TERMS 3 The Universal Law of Gravitation was postulated by the English physicist and mathemati- cian Sir Isaac Newton (1642–1727). There is a popular story that the origin of this theory happened when Newton was sitting under a tree and an apple fell on his head. This is almost certainly not an exact truth, with embellishment of details, as what happens in most legends. Probably, the more correct version of the story is that Newton, upon observing (or imagining!) an apple fall from a tree, began to think that the apple is accelerated because its velocity changes from zero as it is hanging on the tree then moves toward the ground. He then considered that the same force that pulled the apple toward the Earth is the same one that makes the Moon to orbit our planet. Newton’s theory of how a celestial body can orbit another celestial body can be illustrated by his well-known example shown in Figure 1.2. Suppose that a cannon ball is fired horizontally from a high mountain on top of the Earth.
eBook - PDFGravity from the Ground Up
An Introductory Guide to Gravity and General Relativity
- Bernard Schutz(Author)
- 2003(Publication Date)
- Cambridge University Press(Publisher)
For example, the balance between attraction and repulsion among the different charges that make up, say, a piece of wood gives it rigidity: try to stretch it and the electrons resist being pulled away from the protons; try to compress it and the electrons resist being squashed up against other electrons. Gravity allows no such fine balances, and we shall see that this means that bodies in which Gravity plays a dominant role cannot be rigid. Instead of achieving equilibrium, they have a strong tendency to collapse, sometimes even to black holes. These two facts about Gravity, that it is ever-present and always attractive, might make it easy to take it for granted. It seems to be just part of the background, a constant and rather boring feature of our world. But nothing could be further from the truth. Precisely because it penetrates everywhere and cannot be cancelled out, it 2 Chapter 1. Gravity on Earth is the engine of the Universe. All the unexpected and exciting discoveries of modern astronomy – quasars, pulsars, neutron stars, black holes – owe their existence to Gravity. It binds together the gases of a star, the stars of a galaxy, and even galaxies into galaxy clusters. It has governed the formation of stars and it regulates the way stars create chemical elements of which we are made. On a grand scale, it controls the expansion of the Universe. Nearer to home, it holds planets in orbit about the Sun and satellites about the Earth. The study of Gravity, therefore, is in a very real sense the study of practically everything from the surface of the Earth out to the edge of the Universe. But it is even more: it is the study of our own history and evolution right back to the Big Bang. Because Gravity is everywhere, our study of Gravity in this book will take us everywhere, as far away in distance and as far back in time as we have scientific evidence to guide us.
- David Halliday, Jearl Walker, Patrick Keleher, Paul Lasky, John Long, Judith Dawes, Julius Orwa, Ajay Mahato, Peter Huf, Warren Stannard, Amanda Edgar, Liam Lyons, Dipesh Bhattarai(Authors)
- 2020(Publication Date)
- Wiley(Publisher)
Although the gravitational force is still not fully understood, the starting point in our understanding of it lies in the law of gravitation of Isaac Newton. Newton’s law of gravitation Before we get to the equations, let’s just think for a moment about something that we take for granted. We are held to the ground just about right, not so strongly that we have to crawl to get to school (though an occasional exam may leave you crawling home) and not so lightly that we bump our heads on the ceiling when we take a step. It is also just about right so that we are held to the ground but not to each other (that would be awkward in any classroom) or to the objects around us (the phrase ‘catching a bus’ would then take on a new meaning). The attraction obviously depends on how much ‘stuff’ there is in ourselves and other objects: Earth has lots of ‘stuff’ and produces a big attraction, but another person has less ‘stuff’ and produces a smaller (even negligible) attraction. Moreover, this ‘stuff’ always attracts other ‘stuff’, never repelling it (or a hard sneeze could put us into orbit). In the past people obviously knew that they were being pulled downward (especially if they tripped and fell over), but they figured that the downward force was unique to Earth and unrelated to the apparent movement of astronomical bodies across the sky. But in 1665, 23‐year‐old Isaac Newton recognised that this force is responsible for holding the Moon in its orbit. Indeed, he showed that every body in the universe attracts every other body. This tendency of bodies to move towards one another is called gravitation, and the ‘stuff’ that is involved is the mass of each body. If the myth were true that a falling apple inspired Newton to his law of gravitation, then the attraction is between the mass of the apple and the mass of Pdf_Folio:241 CHAPTER 13 Gravitation 241 Earth. It is appreciable because the mass of Earth is so large, but even then it is only about 0.8 N.
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- 2014(Publication Date)
- Learning Press(Publisher)
Thus general relativity predicted that the Universe had to be non-static—it had to either expand or contract. The expansion of the universe discovered by Edwin Hubble in 1929 confirmed this prediction. Gravity and quantum mechanics In the decades after the discovery of general relativity it was realized that general relativity is incompatible with quantum mechanics. It is possible to describe Gravity in the framework of quantum field theory like the other fundamental forces, such that the attractive force of Gravity arises due to exchange of virtual gravitons, in the same way as the electromagnetic force arises from exchange of virtual photons. This reproduces general relativity in the classical limit. However, this approach fails at short distances of the order of the Planck length, where a more complete theory of quantum Gravity (or a new approach to quantum mechanics) is required. Many believe the complete theory to be string theory, or more currently M-theory, and, on the other hand, it may be a background independent theory such as loop quantum Gravity or causal dynamical triangulation. Specifics Earth's Gravity Every planetary body (including the Earth) is surrounded by its own gravitational field, which exerts an attractive force on all objects. Assuming a spherically symmetrical planet (a reasonable approximation), the strength of this field at any given point is proportional to the planetary body's mass and inversely proportional to the square of the distance from the center of the body. The strength of the gravitational field is numerically equal to the acceleration of objects under its influence, and its value at the Earth's surface, denoted g , is approximately expressed below as the standard average. g = 9.81 m/s 2 = 32.2 ft/s 2 This means that, ignoring air resistance, an object falling freely near the Earth's surface increases its velocity by 9.81 m/s (32.2 ft/s or 22 mph) for each second of its descent.
- Peter Kosso(Author)
- 2017(Publication Date)
- Cambridge University Press(Publisher)
1 Introduction: What to Expect from a Science of Gravity Gravity dominates our lives and attracts our attention like no other force of nature. First thing in the morning, just getting up and out of bed, lifting your head from the pillow and dropping your feet to the floor, it’s Gravity that works with you and works against you, and you know it. You will spend your day opposing and cooperating with Gravity, lifting the coffee pot, pouring the coffee, and so on. There is no up or down without Gravity. This most basic direction is defined, not by some cosmic or even planetary coordinate system, but by the force of attraction between the Earth and things. The force is generally directed toward the center of the spherical planet; that’s down. The other direction is up. A builder deter- mines that a wall is vertical by using a plumb-line, a mass hanging free in the field of Gravity. And for all of us, getting up in the morning amounts to changing our orientation in the gravitational field from horizontal to vertical, from lying down to standing up. Gravity is the force we all notice and the one we can all identify explicitly. This is despite the fact that physicists describe Gravity as the weakest of the four funda- mental forces in nature. The electromagnetic force is responsible for holding the atoms and molecules together in everything we touch, but this is largely overlooked as we go about our days. Two versions of nuclear force are responsible for stabi- lizing the core of matter, the atomic nucleus, or in some cases for destabilizing it, perhaps the start of the process of heating your coffee if your electricity comes from a nuclear power plant. But the nuclear glue holds at such short range as to go un- detected unless you know what to look for. It’s only Gravity that we all experience and we all know. The force of Gravity is always attractive. It is a force pulling together any two things that have mass.
No longer available |Learn more- (Author)
- 2014(Publication Date)
- Learning Press(Publisher)
Moreover, he refused to even offer a hypothesis as to the cause of this force on grounds that to do so was contrary to sound science. He lamented that philosophers have hitherto attempted the search of nature in vain for the source of the gravitational force, as he was convinced by many reasons that there were causes hitherto unknown that were fundamental to all the phenomena of nature. These fundamental phenomena are still under investigation and, though hypotheses abound, the definitive answer has yet to be found. And in Newton's 1713 General Scholium in the second edition of Principia : I have not yet been able to discover the cause of these properties of Gravity from phenomena and I feign no hypotheses... It is enough that Gravity does really exist and acts according to the laws I have explained, and that it abundantly serves to account for all the motions of celestial bodies. Einstein's solution These objections were rendered moot by Einstein's theory of general relativity, in which gravitation is an attribute of curved spacetime instead of being due to a force propagated between bodies. In Einstein's theory, masses distort spacetime in their vicinity, and other ________________________ WORLD TECHNOLOGIES ________________________ particles move in trajectories determined by the geometry of spacetime. This allowed a description of the motions of light and mass that was consistent with all available observations. In general relativity, the gravitational force is a fictitious force due to the curvature of spacetime, because the gravitational acceleration of a body in free fall is due to its world line being a geodesic of spacetime. Newton's laws of motion Newton's First and Second laws, in Latin, from the original 1687 edition of the Principia Mathematica. Newton's laws of motion are three physical laws that form the basis for classical mechanics. They describe the relationship between the forces acting on a body and its motion due to those forces.
Available until 25 Jan |Learn more- Tai L. Chow(Author)
- 2013(Publication Date)
- CRC Press(Publisher)
No prediction can be made from a definition! The second law acquires real significance only when the force is independently defined. But completely describing the specific independent properties of force is not a trivial task. Everyone has an intuitive feeling for the concept of a force. We can take force, like length, as a primitive concept and define it operationally in terms of, for example, the compression or expansion of a “standard” spring by some specific amount. Then Newton’s laws of motion are laws, and so are the laws of theories of special forces. Most of the forces that are found in nature are now well understood. There are only four basic forces: strong nuclear, electromagnetic, gravitational, and weak nuclear. Of these four, only the elec-tromagnetic and gravitational forces properly belong to the domain of classical mechanics. All other apparently different forces in the classical domain are manifestations of either electromagnetic or gravitational force. As an example, the friction force between two bodies ultimately results from an electrostatic force between the charged particles that make up the atoms of the bodies. 29 Newtonian Mechanics © 2010 Taylor & Francis Group, LLC Gravitational interaction is a property of all bodies whether they are electrically charged or neutral and is determined only by the masses of the bodies. In Chapter 6 on central force motion, we shall learn how Newton deduced the law of gravitation from Kepler’s three laws of planetary motion. He found that the gravitational force between two particles is inversely proportional to the square of the distance between them and proportional to the product of the masses of the two particles.
eBook - PDF- Anthony Wolbarst(Author)
- 2005(Publication Date)
- Medical Physics Publishing(Publisher)
4. MASS, MOTION, AND FORCE 49 they are, and how they relate to one another. But when all is said and done, the cruel reality is that we don’t really know why they are the way they are, or where they come from, or whether they are the same in other universes. If we ever did manage to explain everything in terms or quarks or strings or whatever, then we’d have to start worrying full-time about who ordered them. (And the Greeks thought Sisyphus had a hard time of it!) Like Time, Love, Consciousness, and I Love Lucy reruns, the forces of Nature just are, and that’s about all you can really say about them. The first of the forces to be understood at all was the grav- itational. By positing a particular functional form for the gravitational force and calling upon his Second Law, Newton was able to describe quantitatively the parabolic trajectory of a thrown object, the swinging of a pendulum, and the elliptic paths of the planets around the Sun. The Second Law of Motion, Equation (4.2), reveals how the motion of an object is affected by the application of any kind of force whatsoever, so let’s focus it on the particularly simple and familiar situation of an apple dangling loosely from a tree. The gravitational force on the apple is proportional to its mass, m, a claim that can be expressed as F grav mg. (4.3) The more massive the apple (which depends on how many atoms it contains and what kinds), the more the Earth pulls downward on it. The constant of proportionality g is measured to be 9.8 m/s 2 . [The units of the other terms in Equation (4.3) reveal that the units of g must be m/s 2 .] The apple has not fallen yet because the tree pulls upward on it with exactly the same force, so that the net force on it is zero. For now. EXERCISE 4–6. A 3-kg basket is sitting on the ground. How much force is the Earth exerting on it? How much force must you apply to lift it? EXERCISE 4–7.
eBook - PDF- Fulvio Melia(Author)
- 2018(Publication Date)
- Princeton University Press(Publisher)
3 THE THEORY OF Gravity The question “Why does matter have mass?” may seem com- pletely redundant, for we often take it for granted that we have a commonsense understanding of what mass and weight must be. Some may say that our everyday experience makes these concepts self-evident. In fact, they are not, and therein lies one of the main reasons for our struggle, since the time of Aristotle, to come to grips with what Gravity is and why objects behave the way they do in the presence of other matter. We cannot even hope to fathom what it must be like near an object as big as the Sun, let alone one that is millions of times “more massive,” until we understand the force—Gravity—that gives them such a powerful influence on their environment. (Incidentally, the concept of Gravity as a “force” is itself subject to review when we consider the general theory of rel- ativity.) In this chapter, we will examine the evolution of thought that has brought us to a rather comprehensive (yet still incom- plete!) theory, whose main prediction is the existence of objects that have collapsed completely unto themselves. We are appar- ently dealing with one of these at the galactic center. 3.1 WHAT IS MASS? By now all of us have an intuition that Gravity is associated with mass: in simple terms, Gravity is an attractive force that any mate- rial object exerts on any other. However, we must be very precise 51 52 Chapter 3 about what we mean by this, for our experience with common phenomena makes us aware of mass in two quite distinct ways. We all remember from high school that matter is made up of a very large number of smaller constituents called atoms, or on a slightly larger scale, combinations of atoms in the form of molecules. Water, for example, is the compound H 2 O, meaning that two hydrogen atoms (H) combine with one oxygen atom (O) to form a molecule of this substance.
eBook - PDFQuantum Themes: The Charms Of The Microworld
The Charms of the Microworld
- Thanu Padmanabhan(Author)
- 2009(Publication Date)
- World Scientific(Publisher)
Chapter 6 Matters of Gravity Earlier on, in Chapter 2, we described several features of Gravity and noted that it is somewhat of an odd-man-out amongst the forces of nature. In Chapters 3 and 4 we introduced the principles of quantum theory and showed how they are universal in the sense that they are applicable in the description of all the laws of nature. Just as laws of electrodynamics got modified to a description based on quantum electrodynamics — when the principles of quantum theory are brought in — one would have expected the description of Gravity to get modified into something, which we could call quantum Gravity, when we bring in the same principles. Nowhere do the peculiarities of Gravity play a greater role than in frus-trating the attempts of the physicists to combine the principles of quantum theory and Gravity. As a result, we do not yet have a quantum theory of Gravity but only a plethora of candidate models and imaginative ideas. There are, however, strong indications that bringing together the princi-ples of quantum theory and Gravity will usher a new revolution in physics possibly more dramatic than the relativistic or quantum revolutions and thus, will enrich our knowledge of nature. In this chapter, we shall describe several aspects of these issues. 6.1 This peculiar thing called Gravity In the good old days of Newton, Gravity was just a force like the electromag-netic force. Forces act between particles and make them move in space and time. The special theory of relativity changed the way we look at space and time but did not really modify our fundamental ideas of dynamics. The de-scription of electromagnetic force, for example, is perfectly consistent with the principles of special relativity. The force acted between charged parti-171 172 Quantum Themes: The Charms of the Microworld cles and made them move.
No longer available |Learn more- (Author)
- 2014(Publication Date)
- Learning Press(Publisher)
This formula was powerful enough to stand as the basis for all subsequent descriptions of motion within the solar system until the twentieth century. During that time, sophisticated methods of perturbation analysis were invented to calculate the deviations of orbits due to the influence of multiple bodies on a planet, moon, comet, or asteroid. The formalism was exact enough to allow mathematicians to predict the existence of the planet Neptune before it was observed. It was only the orbit of the planet Mercury that Newton's Law of Gravitation seemed not to fully explain. Some astrophysicists predicted the existence of another planet (Vulcan) that would explain the discrepancies; however, despite some early indications, no such planet could be found. When Albert Einstein finally formulated his theory of general relativity (GR) he turned his attention to the problem of Mercury's orbit and found that his theory added a correction which could account for the discrepancy. This was the first time that Newton's Theory of Gravity had been shown to be less correct than an alternative. Since then, and so far, general relativity has been acknowledged as the theory which best explains Gravity. In GR, gravitation is not viewed as a force, but rather, objects moving freely in gravitational fields travel under their own inertia in straight lines through curved space-time – defined as the shortest space-time path between two space-time events. From the perspective of the object, all motion occurs as if there were no gravitation whatsoever. It is only when observing the motion in a global sense that the curvature of space-time can be observed and the force is inferred from the object's curved path. Thus, the straight line path in space-time is seen as a curved line in space, and it is called the ballistic trajectory of the object. For example, a basketball thrown from the ground moves in a parabola, as it is in a uniform gravitational field.
- Daniel Fleisch, Julia Kregenow(Authors)
- 2013(Publication Date)
- Cambridge University Press(Publisher)
To help with that process, we’ll write “expanded” versions of some of the important equations in this book, of which you can see an exam-ple in Figure 2.1 . As you can see, in an expanded equation, the meaning and units of each term are readily available in a text block with an arrow pointing to the relevant term. After the figure, you’ll find additional explanations of the 41 42 Gravity F g = G m 1 m 2 R 2 mass 2 (kg) mass 1 (kg) Distance from the center of mass 1 to the center of mass 2 (m) The universal gravitational constant (N m 2 /kg 2 ) Force of Gravity between mass 1 and mass 2 (N) Figure 2.1 Newton’s Law of Gravity. terms as well as examples of how to apply the equation using both the absolute method and the ratio method. 2.1.1 Description of terms in the Gravity equation Whenever you encounter an equation such as that shown in Figure 2.1 , it’s a good idea to make sure you understand not only the meaning (and units) of each term, but also what the placement and powers of those terms are telling you. The force of Gravity, F g , appears on the left side of this equation in units of newtons (N). The force occurs between two objects such as those shown in Figure 2.2 ; each object produces the gravitational force F g on the other. Here are detailed descriptions of each of the terms on the right side of the Gravity equation: G The first term is G , the universal gravitational constant. 1 To the best of sci-entists’ knowledge, this constant has the same value throughout the known Universe, and that value in SI units is 6 . 67 × 10 − 11 N m 2 / kg 2 . m 1 , m 2 The variables in the numerator of the fraction, m 1 and m 2 , represent the amount of mass (in units of kilograms) in each of the two objects for which the force of Gravity is being calculated. Most astronomy texts use lowercase “ m ,” as we have here, as a variable (a placeholder for an unspeci-fied quantity) to represent mass.
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