Isaac Newton suggested that there are forces of mutual attraction between any bodies in nature. These forces are called by gravitational forces or forces of universal gravity. The force of unnatural gravity manifests itself in space, solar system and on Earth.
Law of Gravity
Newton generalized the laws of motion celestial bodies and found out that the force \(F\) is equal to:
\[ F = G \dfrac(m_1 m_2)(R^2) \]
where \(m_1\) and \(m_2\) are the masses of interacting bodies, \(R\) is the distance between them, \(G\) is the proportionality coefficient, which is called gravitational constant. The numerical value of the gravitational constant was experimentally determined by Cavendish by measuring the force of interaction between lead balls.
The physical meaning of the gravitational constant follows from the law of universal gravitation. If \(m_1 = m_2 = 1 \text(kg)\), \(R = 1 \text(m) \) , then \(G = F \) , i.e. the gravitational constant is equal to the force with which two bodies of 1 kg each are attracted at a distance of 1 m.
Numerical value:
\(G = 6.67 \cdot() 10^(-11) N \cdot() m^2/ kg^2 \) .
The forces of universal gravity act between any bodies in nature, but they become noticeable at large masses (or if at least the mass of one of the bodies is large). The law of universal gravitation is satisfied only for material points and balls (in this case, the distance between the centers of the balls is taken as the distance).
Gravity
A particular type of universal gravitational force is the force of attraction of bodies towards the Earth (or to another planet). This force is called gravity. Under the influence of this force, all bodies acquire free fall acceleration.
In accordance with Newton's second law \(g = F_T /m\) , therefore, \(F_T = mg \) .
If M is the mass of the Earth, R is its radius, m is the mass of a given body, then the force of gravity is equal to
\(F = G \dfrac(M)(R^2)m = mg \) .
The force of gravity is always directed towards the center of the Earth. Depending on the height \(h\) above surface of the Earth And geographical latitude body position acceleration free fall takes on different meanings. On the Earth's surface and in mid-latitudes, the acceleration of gravity is 9.831 m/s 2 .
Body weight
The concept of body weight is widely used in technology and everyday life.
Body weight denoted by \(P\) . The unit of weight is newton (N). Since weight is equal to the force with which the body acts on the support, then, in accordance with Newton’s third law, the largest weight of the body is equal to the reaction force of the support. Therefore, in order to find the weight of the body, it is necessary to determine what the support reaction force is equal to.
In this case, it is assumed that the body is motionless relative to the support or suspension.
The weight of a body and the force of gravity differ in nature: the weight of a body is a manifestation of the action of intermolecular forces, and the force of gravity is of a gravitational nature.
The state of a body in which its weight is zero is called weightlessness. The state of weightlessness is observed in an airplane or spacecraft when moving with free fall acceleration, regardless of the direction and value of the speed of their movement. Outside earth's atmosphere when turning off jet engines on spaceship Only the force of universal gravity acts. Under the influence of this force, the spaceship and all the bodies in it move with the same acceleration, therefore a state of weightlessness is observed in the ship.
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In his declining years he spoke about how he discovered law of universal gravitation.
When young Isaac walked in the garden among the apple trees on his parents' estate, he saw the moon in the daytime sky. And next to him an apple fell to the ground, falling from its branch.
Since Newton was working on the laws of motion at that very time, he already knew that the apple fell under the influence of the Earth's gravitational field. And he knew that the Moon is not just in the sky, but revolves around the Earth in orbit, and, therefore, it is affected by some kind of force that keeps it from breaking out of orbit and flying in a straight line away into outer space. This is where the idea came to him that perhaps the same force makes the apple fall to the ground and the Moon remain in Earth orbit.
Before Newton, scientists believed that there were two types of gravity: terrestrial gravity (acting on Earth) and celestial gravity (acting in the heavens). This idea was firmly entrenched in the minds of people of that time.
Newton's insight was that he combined these two types of gravity in his mind. From this historical moment, the artificial and false separation of the Earth and the rest of the Universe ceased to exist.
This is how the law of universal gravitation was discovered, which is one of the universal laws of nature. According to the law, all material bodies attract each other, and the magnitude of the gravitational force does not depend on chemical and physical properties bodies, on the state of their motion, on the properties of the environment where the bodies are located. Gravity on Earth is manifested, first of all, in the existence of gravity, which is the result of the attraction of any material body by the Earth. The term associated with this “gravity” (from Latin gravitas - heaviness) , equivalent to the term "gravity".
The law of gravity states that the force of gravitational attraction between two material points of mass m1 and m2, separated by a distance R, is proportional to both masses and inversely proportional to the square of the distance between them.
The very idea of the universal force of gravity was repeatedly expressed before Newton. Previously, Huygens, Roberval, Descartes, Borelli, Kepler, Gassendi, Epicurus and others thought about it.
According to Kepler's assumption, gravity is inversely proportional to the distance to the Sun and extends only in the ecliptic plane; Descartes considered it the result of vortices in the ether.
There were, however, guesses with a correct dependence on distance, but before Newton no one was able to clearly and mathematically conclusively connect the law of gravity (a force inversely proportional to the square of the distance) and the laws of planetary motion (Kepler's laws).
In his main work "Mathematical Principles of Natural Philosophy" (1687)
Isaac Newton derived the law of gravitation based on Kepler's empirical laws known at that time.
He showed that:
- the observed movements of the planets indicate the presence of a central force;
- conversely, the central force of attraction leads to elliptical (or hyperbolic) orbits.
Unlike the hypotheses of its predecessors, Newton's theory had a number of significant differences. Sir Isaac published not only the supposed formula of the law of universal gravitation, but actually proposed a complete mathematical model:
- law of gravitation;
- law of motion (Newton's second law);
- system of methods for mathematical research (mathematical analysis).
Taken together, this triad is sufficient for a complete study of the most complex movements of celestial bodies, thereby creating the foundations of celestial mechanics.
But Isaac Newton left open question about the nature of gravity. The assumption about the instantaneous propagation of gravity in space (i.e., the assumption that with a change in the positions of bodies the gravitational force between them instantly changes), which is closely related to the nature of gravity, was also not explained. For more than two hundred years after Newton, physicists proposed various ways to improve Newton's theory of gravity. Only in 1915 these efforts were crowned with success by the creation Einstein's general theory of relativity , in which all these difficulties were overcome.
Aristotle argued that massive objects fall to the ground faster than light ones.
Galileo showed at the beginning of the 17th century that all objects fall “equally.” And around the same time, Kepler wondered what made the planets move in their orbits. Maybe it's magnetism? Isaac Newton, working on "", reduced all these movements to the action of a single force called gravity, which obeys simple universal laws.
Galileo experimentally showed that the distance traveled by a body falling under the influence of gravity is proportional to the square of the time of fall: a ball falling within two seconds will travel four times as far as the same object within one second. Galileo also showed that speed is directly proportional to the time of fall, and from this he deduced that a cannonball flies along a parabolic trajectory - one of the types of conic sections, like the ellipses along which, according to Kepler, the planets move. But where does this connection come from?
When Cambridge University closed during the Great Plague in the mid-1660s, Newton returned to the family estate and formulated his law of gravity there, although he kept it secret for another 20 years. (The story of the falling apple was unheard of until eighty-year-old Newton told it after a large dinner party.)
He suggested that all objects in the Universe generate a gravitational force that attracts other objects (just as an apple is attracted to the Earth), and this same gravitational force determines the trajectories along which stars, planets and other celestial bodies move in space.
In his declining days, Isaac Newton told how this happened: he was walking along apple orchard on his parents' estate and suddenly saw the moon in the daytime sky. And right there, before his eyes, an apple came off the branch and fell to the ground. Since Newton was working on the laws of motion at that very time, he already knew that the apple fell under the influence of the Earth's gravitational field. He also knew that the Moon does not just hang in the sky, but rotates in orbit around the Earth, and, therefore, it is affected by some kind of force that keeps it from breaking out of orbit and flying in a straight line away, into open space. Then it occurred to him that perhaps it was the same force that made both the apple fall to the ground and the Moon remain in orbit around the Earth.
Inverse square law
Newton was able to calculate the magnitude of the Moon’s acceleration under the influence of Earth’s gravity and found that it was thousands of times less than the acceleration of objects (the same apple) near the Earth. How can this be if they move under the same force?
Newton's explanation was that the force of gravity weakens with distance. An object on the Earth's surface is 60 times closer to the center of the planet than the Moon. The gravity around the Moon is 1/3600, or 1/602, that of an apple. Thus, the force of attraction between two objects - be it the Earth and an apple, the Earth and the Moon, or the Sun and a comet - is inversely proportional to the square of the distance separating them. Double the distance and the force decreases by a factor of four, triple it and the force becomes nine times less, etc. The force also depends on the mass of the objects - the greater the mass, the stronger the gravity.
The law of universal gravitation can be written as a formula:
F = G(Mm/r 2).
Where: the force of gravity is equal to the product greater mass M and less mass m divided by the square of the distance between them r 2 and multiplied by the gravitational constant, denoted capital letter G(lowercase g stands for gravity-induced acceleration).
This constant determines the attraction between any two masses anywhere in the Universe. In 1789 it was used to calculate the mass of the Earth (6·1024 kg). Newton's laws are excellent at predicting forces and motions in a system of two objects. But when you add a third, everything becomes significantly more complicated and leads (after 300 years) to the mathematics of chaos.
Newton's classical theory of gravity (Newton's Law of Universal Gravitation)- a law describing gravitational interaction within the framework of classical mechanics. This law was discovered by Newton around 1666. It says that strength F (\displaystyle F) gravitational attraction between two material points of mass m 1 (\displaystyle m_(1)) And m 2 (\displaystyle m_(2)), separated by distance R (\displaystyle R), is proportional to both masses and inversely proportional to the square of the distance between them - that is:
F = G ⋅ m 1 ⋅ m 2 R 2 (\displaystyle F=G\cdot (m_(1)\cdot m_(2) \over R^(2)))
Here G (\displaystyle G)- gravitational constant equal to 6.67408(31)·10 −11 m³/(kg·s²) :.
Encyclopedic YouTube
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✪ Introduction to the law of universal Newton's gravity
✪ Law of Gravity
✪ physics LAW OF UNIVERSAL GRAVITY 9th grade
✪ About Isaac Newton ( Short story)
✪ Lesson 60. The law of universal gravitation. Gravitational constant
Subtitles
Now let's learn a little about gravity, or gravitation. As you know, gravity, especially in a beginner or even in a fairly advanced course of physics, is a concept that can be calculated and the basic parameters that determine it, but in fact, gravity is not entirely understandable. Even if you are familiar with the general theory of relativity, if you are asked what gravity is, you can answer: it is the curvature of space-time and the like. However, it is still difficult to get an intuition as to why two objects, simply because they have so-called mass, are attracted to each other. At least for me it's mystical. Having noted this, let us begin to consider the concept of gravity. We will do this by studying Newton's law of universal gravitation, which is valid for most situations. This law states: the force of mutual gravitational attraction F between two material points with masses m₁ and m₂ is equal to the product of the gravitational constant G by the mass of the first object m₁ and the second object m₂, divided by the square of the distance d between them. This is a fairly simple formula. Let's try to transform it and see if we can get some results that are familiar to us. We use this formula to calculate the acceleration of gravity near the Earth's surface. Let's draw the Earth first. Just to understand what we are talking about. This is our Earth. Let's say we need to calculate the gravitational acceleration acting on Sal, that is, on me. Here I am. Let's try to apply this equation to calculate the magnitude of the acceleration of my fall to the center of the Earth, or to the center of mass of the Earth. The quantity indicated by the capital letter G is the universal gravitational constant. Once again: G is the universal gravitational constant. Although, as far as I know, although I am not an expert on this matter, it seems to me that its value can change, that is, it is not a real constant, and I assume that when different dimensions its magnitude varies. But for our purposes, as well as in most physics courses, it is a constant, a constant equal to 6.67 * 10^(−11) cubic meters divided by a kilogram per second squared. Yes, its dimension looks strange, but it is enough for you to understand that these are conventional units necessary to, as a result of multiplying by the masses of objects and dividing by the square of the distance, obtain the dimension of force - newton, or kilogram per meter divided by second squared. So there's no need to worry about these units: just know that we'll have to work with meters, seconds, and kilograms. Let's substitute this number into the formula for force: 6.67 * 10^(−11). Since we need to know the acceleration acting on Sal, m₁ is equal to the mass of Sal, that is, me. I wouldn’t like to expose how much I weigh in this story, so let’s leave this mass as a variable, denoting ms. The second mass in the equation is the mass of the Earth. Let's write down its meaning by looking at Wikipedia. So, the mass of the Earth is 5.97 * 10^24 kilograms. Yes, the Earth is more massive than Sal. By the way, weight and mass are different concepts. So, the force F is equal to the product of the gravitational constant G by the mass ms, then by the mass of the Earth, and divide all this by the square of the distance. You may object: what is the distance between the Earth and what stands on it? After all, if objects touch, the distance is zero. It is important to understand here: the distance between two objects in this formula is the distance between their centers of mass. In most cases, a person's center of mass is located about three feet above the surface of the Earth, unless the person is very tall. Anyway, my center of mass may be three feet above the ground. Where is the center of mass of the Earth? Obviously in the center of the Earth. What is the radius of the Earth? 6371 kilometers, or approximately 6 million meters. Since the height of my center of mass is about one millionth the distance to the center of mass of the Earth, it can be neglected in this case. Then the distance will be equal to 6 and so on, like all other quantities, you need to write it in standard form - 6.371 * 10^6, since 6000 km is 6 million meters, and a million is 10^6. We write, rounding all fractions to the second decimal place, the distance is 6.37 * 10^6 meters. The formula contains the square of the distance, so let's square everything. Let's try to simplify now. First, let's multiply the values in the numerator and move forward the variable ms. Then the force F is equal to the entire mass of Sal top part, let's calculate it separately. So 6.67 times 5.97 equals 39.82. 39.82. This work significant parts, which should now be multiplied by 10 to the required degree. 10^(−11) and 10^24 have the same base, so to multiply them it is enough to add the exponents. Adding 24 and −11, we get 13, resulting in 10^13. Let's find the denominator. It is equal to 6.37 squared times 10^6 also squared. As you remember, if a number written as a power is raised to another power, then the exponents are multiplied, which means that 10^6 squared is equal to 10 to the power of 6 multiplied by 2, or 10^12. Next, we calculate the square of 6.37 using a calculator and get... Square 6.37. And it's 40.58. 40.58. All that remains is to divide 39.82 by 40.58. Divide 39.82 by 40.58, which equals 0.981. Then we divide 10^13 by 10^12, which is equal to 10^1, or just 10. And 0.981 times 10 is 9.81. After simplification and simple calculations, we found that the gravitational force near the Earth’s surface acting on Sal is equal to Sel’s mass multiplied by 9.81. What does this give us? Is it now possible to calculate gravitational acceleration? It is known that force is equal to the product of mass and acceleration, therefore the gravitational force is simply equal to the product of Sal’s mass and gravitational acceleration, which is usually denoted lowercase letter g. So, on the one hand, the force of gravity is equal to 9.81 times Sal's mass. On the other hand, it is equal to Sal’s mass per gravitational acceleration. Dividing both sides of the equation by Sal’s mass, we find that the coefficient 9.81 is the gravitational acceleration. And if we included in the calculations the full record of units of dimension, then, having reduced the kilograms, we would see that gravitational acceleration is measured in meters divided by a second squared, like any acceleration. You can also notice that the resulting value is very close to the one we used when solving problems about the motion of a thrown body: 9.8 meters per second squared. This is impressive. Let's do another quick gravity problem because we have a couple of minutes left. Let's say we have another planet called Baby Earth. Let the radius of the Baby rS be half the radius of the Earth rE, and its mass mS is also equal to half the mass of the Earth mE. What will be the force of gravity acting here on any object, and how much less is it less than the force of gravity? Although, let's leave the problem for next time, then I'll solve it. See you. Subtitles by the Amara.org community
Properties of Newtonian gravity
In Newtonian theory, each massive body generates a force field of attraction towards this body, which is called a gravitational field. This field is potential, and the function of gravitational potential for a material point with mass M (\displaystyle M) is determined by the formula:
φ (r) = − G M r . (\displaystyle \varphi (r)=-G(\frac (M)(r)).)IN general case, when the density of the substance ρ (\displaystyle \rho ) distributed randomly, satisfies the Poisson equation:
Δ φ = − 4 π G ρ (r) . (\displaystyle \Delta \varphi =-4\pi G\rho (r).)The solution to this equation is written as:
φ = − G ∫ ρ (r) d V r + C , (\displaystyle \varphi =-G\int (\frac (\rho (r)dV)(r))+C,)Where r (\displaystyle r) - distance between volume element d V (\displaystyle dV) and the point at which the potential is determined φ (\displaystyle \varphi ), C (\displaystyle C) - arbitrary constant.
The force of attraction acting in a gravitational field on a material point with mass m (\displaystyle m), is related to the potential by the formula:
F (r) = − m ∇ φ (r) . (\displaystyle F(r)=-m\nabla \varphi (r).)A spherically symmetrical body creates the same field outside its boundaries as a material point of the same mass located in the center of the body.
The trajectory of a material point in a gravitational field created by a much larger material point obeys Kepler's laws. In particular, planets and comets in the Solar System move in ellipses or hyperbolas. The influence of other planets, which distorts this picture, can be taken into account using perturbation theory.
Accuracy of Newton's law of universal gravitation
An experimental assessment of the degree of accuracy of Newton's law of gravitation is one of the confirmations of the general theory of relativity. Experiments on measuring the quadrupole interaction of a rotating body and a stationary antenna showed that the increment δ (\displaystyle \delta ) in the expression for the dependence of the Newtonian potential r − (1 + δ) (\displaystyle r^(-(1+\delta))) at distances of several meters is within (2 , 1 ± 6 , 2) ∗ 10 − 3 (\displaystyle (2.1\pm 6.2)*10^(-3)). Other experiments also confirmed the absence of modifications in the law of universal gravitation.
Newton's law of universal gravitation in 2007 was tested at distances smaller than one centimeter (from 55 microns to 9.53 mm). Taking into account the experimental errors, no deviations from Newton's law were found in the studied range of distances.
Precision laser ranging observations of the Moon's orbit confirm the law of universal gravitation at the distance from the Earth to the Moon with precision 3 ⋅ 10 − 11 (\displaystyle 3\cdot 10^(-11)).
Connection with the geometry of Euclidean space
The fact of equality with very high accuracy 10 − 9 (\displaystyle 10^(-9)) exponent of the distance in the denominator of the expression for the force of gravity to the number 2 (\displaystyle 2) reflects the Euclidean nature of the three-dimensional physical space of Newtonian mechanics. In three-dimensional Euclidean space, the surface area of a sphere is exactly proportional to the square of its radius
Historical sketch
The very idea of the universal force of gravity was repeatedly expressed before Newton. Previously, Epicurus, Gassendi, Kepler, Borelli, Descartes, Roberval, Huygens and others thought about it. Kepler believed that gravity is inversely proportional to the distance to the Sun and extends only in the ecliptic plane; Descartes considered it to be the result of vortices in the ether. There were, however, guesses with a correct dependence on distance; Newton, in a letter to Halley, mentions Bulliald, Wren and Hooke as his predecessors. But before Newton, no one was able to clearly and mathematically conclusively connect the law of gravity (a force inversely proportional to the square of the distance) and the laws of planetary motion (Kepler’s laws).
- law of gravitation;
- law of motion (Newton's second law);
- system of methods for mathematical research (mathematical analysis).
Taken together, this triad is sufficient for a complete study of the most complex movements of celestial bodies, thereby creating the foundations of celestial mechanics. Before Einstein, no fundamental amendments to this model were needed, although the mathematical apparatus turned out to be necessary to significantly develop.
Note that Newton's theory of gravity was no longer, strictly speaking, heliocentric. Already in the two-body problem, the planet rotates not around the Sun, but around general center gravity, since not only the Sun attracts the planet, but the planet also attracts the Sun. Finally, it became clear that it was necessary to take into account the influence of the planets on each other.
During the 18th century, the law of universal gravitation was the subject of active debate (supporters of the Descartes school opposed it) and thorough checks. By the end of the century, it became generally accepted that the law of universal gravitation makes it possible to explain and predict the movements of celestial bodies with great accuracy. Henry Cavendish in 1798 carried out a direct test of the validity of the law of gravity in terrestrial conditions, using extremely sensitive torsion balances. An important step was the introduction by Poisson in 1813 of the concept of gravitational potential and the Poisson equation for this potential; this model made it possible to study the gravitational field with an arbitrary distribution of matter. After this, Newton's law began to be regarded as a fundamental law of nature.
At the same time, Newton's theory contained a number of difficulties. The main one is the inexplicable long-range action: the force of attraction was transmitted incomprehensibly through completely empty space, and infinitely quickly. Essentially, Newton's model was purely mathematical, without any physical content. Moreover, if the Universe, as was then assumed, is Euclidean and infinite, and at the same time average density matter in it is non-zero, then a gravitational paradox arises. IN late XIX century, another problem was discovered: the discrepancy between the theoretical and observed displacement of the perihelion of Mercury.
Further development
General theory of relativity
For more than two hundred years after Newton, physicists proposed various ways to improve Newton's theory of gravity. These efforts were crowned with success in 1915, with the creation of Einstein's general theory of relativity, in which all these difficulties were overcome. Newton's theory, in full agreement with the correspondence principle, turned out to be an approximation of a more general theory, applicable when two conditions are met:
In weak stationary gravitational fields, the equations of motion become Newtonian (gravitational potential). To prove this, we show that the scalar gravitational potential in weak stationary gravitational fields satisfies the Poisson equation
Δ Φ = − 4 π G ρ (\displaystyle \Delta \Phi =-4\pi G\rho ).It is known (Gravitational potential) that in this case the gravitational potential has the form:
Φ = − 1 2 c 2 (g 44 + 1) (\displaystyle \Phi =-(\frac (1)(2))c^(2)(g_(44)+1)).Let us find the component of the energy-momentum tensor from the gravitational field equations of the general theory of relativity:
R i k = − ϰ (T i k − 1 2 g i k T) (\displaystyle R_(ik)=-\varkappa (T_(ik)-(\frac (1)(2))g_(ik)T)),Where R i k (\displaystyle R_(ik))- curvature tensor. For we can introduce the kinetic energy-momentum tensor ρ u i u k (\displaystyle \rho u_(i)u_(k)). Neglecting quantities of the order u/c (\displaystyle u/c), you can put all the components T i k (\displaystyle T_(ik)), except T 44 (\displaystyle T_(44)), equal to zero. Component T 44 (\displaystyle T_(44)) equal to T 44 = ρ c 2 (\displaystyle T_(44)=\rho c^(2)) and therefore T = g i k T i k = g 44 T 44 = − ρ c 2 (\displaystyle T=g^(ik)T_(ik)=g^(44)T_(44)=-\rho c^(2)). Thus, the gravitational field equations take the form R 44 = − 1 2 ϰ ρ c 2 (\displaystyle R_(44)=-(\frac (1)(2))\varkappa \rho c^(2)). Due to the formula
R i k = ∂ Γ i α α ∂ x k − ∂ Γ i k α ∂ x α + Γ i α β Γ k β α − Γ i k α Γ α β β (\displaystyle R_(ik)=(\frac (\partial \ Gamma _(i\alpha )^(\alpha ))(\partial x^(k)))-(\frac (\partial \Gamma _(ik)^(\alpha ))(\partial x^(\alpha )))+\Gamma _(i\alpha )^(\beta )\Gamma _(k\beta )^(\alpha )-\Gamma _(ik)^(\alpha )\Gamma _(\alpha \beta )^(\beta ))value of the curvature tensor component R 44 (\displaystyle R_(44)) can be taken equal R 44 = − ∂ Γ 44 α ∂ x α (\displaystyle R_(44)=-(\frac (\partial \Gamma _(44)^(\alpha ))(\partial x^(\alpha )))) and since Γ 44 α ≈ − 1 2 ∂ g 44 ∂ x α (\displaystyle \Gamma _(44)^(\alpha )\approx -(\frac (1)(2))(\frac (\partial g_(44) )(\partial x^(\alpha )))), R 44 = 1 2 ∑ α ∂ 2 g 44 ∂ x α 2 = 1 2 Δ g 44 = − Δ Φ c 2 (\displaystyle R_(44)=(\frac (1)(2))\sum _(\ alpha )(\frac (\partial ^(2)g_(44))(\partial x_(\alpha )^(2)))=(\frac (1)(2))\Delta g_(44)=- (\frac (\Delta \Phi )(c^(2)))). Thus, we arrive at the Poisson equation:
Δ Φ = 1 2 ϰ c 4 ρ (\displaystyle \Delta \Phi =(\frac (1)(2))\varkappa c^(4)\rho ), Where ϰ = − 8 π G c 4 (\displaystyle \varkappa =-(\frac (8\pi G)(c^(4))))Quantum gravity
However general theory relativity is not the final theory of gravity, since it unsatisfactorily describes gravitational processes on quantum scales (at distances on the order of the Planck distance, about 1.6⋅10 −35). The construction of a consistent quantum theory of gravity is one of the most important unsolved problems of modern physics.
From the point of view of quantum gravity, gravitational interaction occurs through the exchange of virtual gravitons between interacting bodies. According to the uncertainty principle, the energy of a virtual graviton is inversely proportional to the time of its existence from the moment of emission by one body to the moment of absorption by another body. The lifetime is proportional to the distance between the bodies. Thus, at short distances, interacting bodies can exchange virtual gravitons with short and long wavelengths, and at large distances only long-wave gravitons. From these considerations we can obtain the law inverse proportionality Newtonian potential versus distance. The analogy between Newton's law and Coulomb's law is explained by the fact that the graviton mass, like the mass
Obi-Wan Kenobi said that strength holds the galaxy together. The same can be said about gravity. Fact: Gravity allows us to walk on the Earth, the Earth to revolve around the Sun, and the Sun to move around the supermassive black hole at the center of our galaxy. How to understand gravity? This is discussed in our article.
Let us say right away that you will not find here a uniquely correct answer to the question “What is gravity.” Because it simply doesn't exist! Gravity is one of the most mysterious phenomena, over which scientists are puzzling and still cannot fully explain its nature.
There are many hypotheses and opinions. There are more than a dozen theories of gravity, alternative and classical. We will look at the most interesting, relevant and modern ones.
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Gravity is a physical fundamental interaction
There are 4 fundamental interactions in physics. Thanks to them, the world is exactly what it is. Gravity is one of these interactions.
Fundamental interactions:
- gravity;
- electromagnetism;
- strong interaction;
- weak interaction.
On this moment The current theory that describes gravity is GTR (general relativity). It was proposed by Albert Einstein in 1915-1916.
However, we know that it is too early to talk about the ultimate truth. After all, several centuries before the appearance of general relativity in physics, Newton’s theory dominated to describe gravity, which was significantly expanded.
Within the framework of GTO on this moment it is impossible to explain and describe all issues related to gravity.
Before Newton, it was widely believed that gravity on earth and gravity in heaven were different things. It was believed that the planets move according to their own ideal laws, different from those on Earth.
Newton discovered the law of universal gravitation in 1667. Of course, this law existed even during the time of dinosaurs and much earlier.
Ancient philosophers thought about the existence of gravity. Galileo experimentally calculated the acceleration of gravity on Earth, discovering that it is the same for bodies of any mass. Kepler studied the laws of motion of celestial bodies.
Newton managed to formulate and generalize the results of his observations. Here's what he got:
Two bodies attract each other with a force called gravitational force or gravity.
Formula for the force of attraction between bodies:
G is the gravitational constant, m is the mass of bodies, r is the distance between the centers of mass of bodies.
What physical meaning gravitational constant? It is equal to the force with which bodies with masses of 1 kilogram each act on each other, being at a distance of 1 meter from each other.
According to Newton's theory, every object creates a gravitational field. The accuracy of Newton's law has been tested at distances less than one centimeter. Of course, for small masses these forces are insignificant and can be neglected.
Newton's formula is applicable both for calculating the force of attraction of planets to the sun and for small objects. We simply do not notice the force with which, say, the balls on a billiard table are attracted. Nevertheless, this force exists and can be calculated.
The force of attraction acts between any bodies in the Universe. Its effect extends to any distance.
Newton's law of universal gravitation does not explain the nature of the force of gravity, but establishes quantitative laws. Newton's theory does not contradict GTR. It is quite enough to solve practical problems on an Earth scale and to calculate the movement of celestial bodies.
Gravity in general relativity
Despite the fact that Newton's theory is quite applicable in practice, it has a number of disadvantages. The law of universal gravitation is mathematical description, but does not give an idea of the fundamental physical nature of things.
According to Newton, the force of gravity acts at any distance. And it works instantly. Considering that the fastest speed in the world is the speed of light, there is a discrepancy. How can gravity act instantly at any distance, when it takes light not an instant, but several seconds or even years to overcome them?
Within the framework of general relativity, gravity is considered not as a force that acts on bodies, but as a curvature of space and time under the influence of mass. Thus, gravity is not a force interaction.
What is the effect of gravity? Let's try to describe it using an analogy.
Let's imagine space in the form of an elastic sheet. If you put a light one on it tennis ball IR, the surface will remain flat. But if you place a heavy weight next to the ball, it will press a hole on the surface, and the ball will begin to roll towards the large, heavy weight. This is “gravity”.
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Discovery of gravitational waves
Gravitational waves were predicted by Albert Einstein back in 1916, but they were discovered only a hundred years later, in 2015.
What are gravitational waves? Let's draw an analogy again. If you throw a stone into calm water, circles will appear on the surface of the water from where it falls. Gravitational waves are the same ripples, disturbances. Just not on the water, but in world space-time.
Instead of water there is space-time, and instead of a stone, say, a black hole. Any accelerated movement of mass generates a gravitational wave. If the bodies are in a state of free fall, when a gravitational wave passes, the distance between them will change.
Since gravity is a very weak force, detecting gravitational waves has been associated with great technical difficulties. Modern technologies made it possible to detect a burst of gravitational waves only from supermassive sources.
A suitable event for detecting a gravitational wave is the merger of black holes. Unfortunately or fortunately, this happens quite rarely. Nevertheless, scientists managed to register a wave that literally rolled across the space of the Universe.
To record gravitational waves, a detector with a diameter of 4 kilometers was built. During the passage of the wave, vibrations of mirrors on suspensions in a vacuum and the interference of light reflected from them were recorded.
Gravitational waves confirmed the validity of general relativity.
Gravity and elementary particles
In the standard model, each interaction is responsible for certain elementary particles. We can say that particles are carriers of interactions.
The graviton, a hypothetical massless particle with energy, is responsible for gravity. By the way, in our separate material, read more about the Higgs boson, which has caused a lot of noise, and other elementary particles.
Finally, here are some interesting facts about gravity.
10 facts about gravity
- To overcome the force of Earth's gravity, a body must have a speed of 7.91 km/s. This is the first escape velocity. It is enough for a body (for example, a space probe) to move in orbit around the planet.
- To escape the Earth's gravitational field, the spacecraft must have a speed of at least 11.2 km/s. This is the second escape velocity.
- The objects with the strongest gravity are black holes. Their gravity is so strong that they even attract light (photons).
- You will not find the force of gravity in any equation of quantum mechanics. The fact is that when you try to include gravity in the equations, they lose their relevance. This is one of the most important issues modern physics.
- The word gravity comes from the Latin “gravis”, which means “heavy”.
- The more massive the object, the stronger the gravity. If a person who weighs 60 kilograms on Earth weighs himself on Jupiter, the scales will show 142 kilograms.
- NASA scientists are trying to develop a gravity beam that will allow objects to be moved without contact, overcoming the force of gravity.
- Astronauts in orbit also experience gravity. More precisely, microgravity. They seem to fall endlessly along with the ship they are in.
- Gravity always attracts and never repels.
- The black hole, the size of a tennis ball, attracts objects with the same force as our planet.
Now you know the definition of gravity and can tell what formula is used to calculate the force of attraction. If the granite of science is pressing you to the ground stronger than gravity, contact our student service. We will help you study easily under the heaviest loads!