Our Sun has a mass of 1.99 × 10 27 tons - 330 thousand times heavier than the Earth. But this is far from the limit. The heaviest star discovered, R136a1, weighs as much as 256 Suns. A, the star closest to us, barely exceeded a tenth of the height of our star. The mass of a star can vary astonishingly - but is there a limit to it? And why is it so important to astronomers?
Mass is one of the most important and unusual characteristics of a star. From it, astronomers can accurately determine the age of the star and its future fate. Moreover, the massiveness determines the strength of the gravitational compression of the star - the main condition for the star’s core to “ignite” in a thermonuclear reaction and the beginning. Therefore, mass is a passing criterion for the category of stars. Objects that are too light, like , will not be able to really shine - and too heavy ones go into the category of extreme objects of the type.
And at the same time, scientists can barely calculate the mass of the star - the only star whose mass is known exactly is ours. Our Earth helped bring such clarity. Knowing the mass of the planet and its speed, you can calculate the mass of the star itself based on Kepler’s Third Law, modified famous physicist Isaac Newton. Johannes Kepler discovered the connection between the distance from a planet to a star and speed full turn planets around the star, and Newton supplemented his formula with the masses of the star and the planet. A modified version of Kepler's Third Law is often used by astronomers - not only to determine the mass of stars, but also of other space objects, components together .
For now we can only guess about distant luminaries. The most advanced (in terms of accuracy) is the method for determining mass star systems. Its error is “only” 20–60%. This inaccuracy is critical for astronomy - if the Sun were 40% lighter or heavier, life on Earth would not have arisen.
In the case of measuring the mass of single stars, near which there are no visible objects whose orbit can be used for calculations, astronomers make a compromise. Today it is read that the mass of one star is the same. Scientists are also helped by the relationship between mass and luminosity of a star, since both of these characteristics depend on the strength of nuclear reactions and the size of the star - direct indicators of mass.
Star mass value
The secret to the massiveness of stars lies not in quality, but in quantity. Our Sun, like most stars, is 98% composed of the two lightest elements in nature - hydrogen and helium. But at the same time, it contains 98% of the entire mass!
How can such light substances come together into huge burning balls? To do this you need to be free from large cosmic bodies space, a lot of material and an initial push - so that the first kilograms of helium and hydrogen begin to attract each other. In molecular clouds, where stars are born, nothing prevents hydrogen and helium from accumulating. There are so many of them that gravity begins to forcefully push together the nuclei of hydrogen atoms. This starts a thermonuclear reaction that turns hydrogen into helium.
It is logical that what more mass star, the greater its luminosity. Indeed, in a massive star there is much more hydrogen “fuel” for a thermonuclear reaction, and gravitational compression, activating the process - stronger. The proof is in the most massive star, R136a1, mentioned at the beginning of the article - being 256 times heavier, it shines 8.7 million times brighter than our star!
But massiveness also has back side: due to the intensity of the processes, hydrogen “burns” faster in thermo nuclear reactions inside . Therefore, massive stars do not live very long. cosmic scale- several hundred, or even tens of millions of years.
- Interesting fact: when the mass of a star is 30 times the mass of the Sun, it can live no more than 3 million years - regardless of how much more its mass is 30 times the Sun. This is due to the Eddington radiation limit being exceeded. The energy of the transcendental star becomes so powerful that it tears out the substance of the star in streams - and with what more massive star, the greater the mass loss becomes.
Above we looked at the main physical processes, related to the mass of the star. Now let’s try to figure out which stars can be “made” with their help.
Which now works at the International space station, read:
"...continued the preliminary collection of cargo for our Soyuz, including our personal quota of 1.5 kg, and packed our other personal belongings for return to Earth".
Thought about it. Ok, astronauts can take 1.5 kg of things with them from orbit. But how will they determine their mass in conditions of weightlessness (microgravity)?
Option 1 - accounting. All things on the spacecraft must be weighed in advance. It should be thoroughly known how much a pen cap, sock and flash drive weigh.
Option 2 - centrifugal. We unwind the object on a calibrated spring; from angular velocity, radius of rotation and deformation of the spring, we calculate its mass.
Option 3 - second Newtonian (F=ma). We push the body with a spring and measure its acceleration. Knowing the push force of the spring, we obtain the mass.
It turned out to be the fourth.
The dependence of the period of oscillation of the spring on the mass of the body attached to it is used.
Meter of body mass and small masses in zero gravity “IM-01M” (mass meter): 
"IM" was used at the Salyut and Mir stations. The massmeter's own weight was 11 kg, weighing took half a minute, during which the device high accuracy measured the period of oscillation of a platform with a load.
This is how Valentin Lebedev describes the procedure in his “Diary of a Cosmonaut” (1982):
“This is the first time we have to weigh ourselves in space. It is clear that ordinary scales cannot work here, since there is no weight. Our scales, unlike those on earth, are unusual; they work on a different principle and are an oscillating platform on springs.
Before weighing, I lower the platform, squeezing the springs, to the clamps, lie down on it, pressing tightly to the surface, and fix myself, grouping my body so that it does not dangle, wrapping my legs and arms around the profile support of the platform. I press the shutter. A slight push and I feel vibrations. Their frequency is displayed on the indicator in a digital code. I read its value, subtract the code for the vibration frequency of the platform, measured without a person, and use the table to determine my weight."
Orbital manned station "Almaz", mass meter number 5: 
A modernized version of this device is now on the International Space Station:
To be fair, option 1 (preliminary weighing of everything) is still used for general control, and option 3 (Newton’s second law) is used in the Space Linear Acceleration Mass Measurement Device weighing device (
The scale will show a more accurate weight if you stand still on the scale. When bending or squatting, the scale will show a decrease in weight. At the end of the bend or squat, the scale will show an increase in weight.
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Why a body suspended by a thread. swings until its center of gravity is located directly below the point of suspension?
If the center of gravity is not under the suspension point, then gravity creates a torque; if the center of gravity is under the suspension point, then the torque of gravity is zero.
Because the balls are identical, then the ball moving before the impact will stop, and the ball at rest before the impact will acquire its speed.
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Warm air rises. Why is it warmer in the lower layers of the troposphere?
Rising up atmospheric air expands and cools.
Why is the shadow of the feet on the ground less blurry than the shadow of the head?
This is explained by the fact that the shadows formed by different parts of an extended light source overlap each other, and the boundaries of these shadows do not coincide. The distances between the boundaries of shadows from different parts of the source will be smallest if the distance from the object to the surface on which the shadow is formed is relatively small.
In the water flowing from water tap, part of the dissolved air is released in the form of a huge number of small bubbles. At the boundaries of these bubbles, the light undergoes numerous reflections, which is why the water takes on a milky white light.
Such an engine will work, but its efficiency will be low, since most of the work done will go towards compressing the gas.
In nails, as a result of their magnetization, the poles of the same name are located nearby. The poles of the same name repel. At the points of suspension, friction prevents repulsion, and below, the ends of the nails, hanging freely, diverge, experiencing repulsive forces.
Why is the glass in ancient buildings that has survived to this day thicker at the bottom?
Glass is amorphous body. The atoms in it, like in a liquid, are not ordered and can move. Therefore, vertical glass flows slowly, and after a few centuries you can notice that the lower part of the glass becomes thicker.
What is the energy consumed by the refrigerator used for?
The electricity consumed by the refrigerator is used to heat the room.
Drop weight hot water, held by forces surface tension, it will be less. The surface tension coefficient of water decreases with increasing temperature.
You can use ice to make fire on a sunny day if you make a biconvex lens from ice. A biconvex lens has the property of collecting light falling on it. Sun rays to one point (in focus), thereby you can get at this point high temperature and ignite flammable material.
Why does the setting sun appear red to us?
A light wave travels a longer distance in the atmosphere from the setting sun than from the sun at its zenith. Light passing through the atmosphere is scattered by the air and the particles in it. Scattering occurs mainly of short-wave radiation.
A person can run faster than his shadow if the shadow is formed on a wall parallel to which the person is running and the light source is moving faster than a human in the same direction as m and man.
In which of the cases does the rope stretch more strongly - if a person pulls its ends with his hands in different directions, or if he pulls with both hands on one end, tying the other to the wall? Assume that in both cases each hand acts on the rope with the same force.
In the second case, the rope stretches more. If we assume that each hand acts on the rope with a force equal in magnitude to F, then in the first case the rope experiences a force F, and in the second case - 2F.
During a full moon, large dark spots on the Moon are visible at the top of its disk. Why are these spots located at the bottom on maps of the Moon?
The image of the Moon on the maps corresponds to its image obtained using a telescope.
How will the period of oscillation of a bucket of water suspended on a long cord change if water gradually flows out of a hole in its bottom?
For this system, a good approximation is the model mathematical pendulum, the period of oscillations of which depends on its length.
If the bucket is initially filled entirely, then when the water flows out, the oscillation period will initially increase. This is explained by the fact that the center of gravity of the “bucket-water” system will decrease, and as a result, the length of the pendulum will increase. Then the period will decrease due to an increase in the center of gravity of the bucket-water system. When all the water from the bucket is poured out, the oscillation period will become equal to the original one, because the original length of the pendulum will be restored.
The concept of Mass raises a lot of questions: Does the mass of bodies depend on their speed? Is the mass additive when combining bodies into a system (i.e. m12 = m1 + m2)? How to measure body mass in space?
Different physics teachers answer these questions differently, so it is not surprising that the first commandment young specialist When someone comes to work at a research institute, it becomes “forget everything you learned at school.” On this page I will introduce you to the point of view of specialists who come into contact with these issues in their scientific work. But let's first take a closer look at the physical meaning of the concept of mass.
I have already talked about the mathematical-geometric interpretation of mass as curvature geodetic lines four-dimensional space/time, but in his 1905 work Einstein gave mass and physical meaning, introducing the concept of rest energy into physics.
Today, when they talk about mass, physicists mean the coefficient determined by the formula:
m2=E2/c4-p2/c2 (1)
In all formulas, the following notations are used (unless otherwise specified):
Such a mass does not change when moving from one inertial reference frame to another inertial system. This is easy to verify if you use the Lorentz transformation for E and p, where v is the speed of one system relative to the other, and the vector v is directed along the x axis:
(2)
Thus, unlike E and p, which are components of a 4-dimensional vector, mass is a Lorentzian invariant.
Food for thought:
The Lorentz transformation underpins the entire world of Einstein's formulas. It goes back to a theory proposed by physicist Hendrik Anton Lorentz. The essence, in brief, comes down to the following: the longitudinal - in the direction of movement - dimensions of a fast moving body are reduced. Back in 1909, the famous Austrian physicist Paul Ehrenfest doubted this conclusion. Here is his objection: let's say that moving objects really are flattened. Okay, let's do the experiment with the disk. We will rotate it, gradually increasing the speed. The size of the disk, as Mr. Einstein says, will decrease; in addition, the disk will become distorted. When the rotation speed reaches the speed of light, the disk will simply disappear.
Einstein was shocked because Ehrenfest was right. The creator of the theory of relativity published a couple of his counterarguments on the pages of one of the special journals, and then helped his opponent get the position of professor of physics in the Netherlands, which he had long been striving for. Ehrenfest moved there in 1912. In turn, the discovery of Ehrenfest that we mentioned disappears from the pages of books about the partial theory of relativity: the so-called Ehrenfest paradox.
It was only in 1973 that Ehrenfest's speculative experiment was put into practice. Physicist Thomas E. Phipps photographed a disk spinning with enormous speed. These photographs (taken using flash) were supposed to serve as proof of Einstein's formulas. However, there was a mistake with this. The dimensions of the disk - contrary to theory - have not changed. "Longitudinal compression" heralded private theory relativity turned out to be the ultimate fiction. Phipps sent a report on his work to the editors of the popular journal Nature. She rejected it. In the end, the article was published on the pages of a certain special magazine published in a small circulation in Italy. However, no one ever reprinted it. There was no sensation. The article went unnoticed.
No less remarkable is the fate of experiments in which they tried to record time dilation during movement.
By the way, from relation (1) the famous Einstein expression for the rest energy E0=mc2 is obtained (if p=0). . And if we take the speed of light as the unit of speed, i.e. put c = 1, then the mass of the body is equal to its rest energy. And since energy is conserved, then mass is a conserved quantity that does not depend on speed. Here is the answer to
first question And it is the rest energy, “dormant” in massive bodies, that is partially released in chemical and especially nuclear reactions.
Now, let's look at the issue of additivity:
To move to another inertial reference system, one should apply Lorentz transformations to a body at rest in the original frame. In this case, a connection is immediately obtained between the energy and momentum of the body and its speed:
(3)
Note: Particles of light, photons, are massless. Therefore, from the above equations it follows that for a photon v = c.
Energy and momentum are additive. Total energy of two free bodies equal to the sum of their energies (E = E1 + E2), with momentum similarly. But if we substitute these amounts into formula (1) we see that
The total mass turns out to depend on the angle between the pulses p1 and p2.
It follows from this that the mass of a system of two photons, with energies E, is equal to 2E/c2 if they fly in opposite sides, and zero if they fly in one direction. Which is very unusual for a person encountering the theory of relativity for the first time, but it is a fact! Newtonian mechanics, where mass is additive, does not work at speeds comparable to the speed of light. The property of mass additivity follows from the formulas only in the limit when v< So, to implement the principle of relativity and constancy of the speed of light, Lorentz transformations are necessary, and from them it follows that the relationship between momentum and speed is given by formula (3), and not by Newton’s formula p = mv. A hundred years ago, through the inertia of thinking, they tried to transfer Newton’s formula into relativistic physics, and this is how the idea of relativistic mass arose, which grows with increasing energy and, consequently, with increasing speed. The formula m=E/c2, according to today's point of view, is an artifact, creating confusion in the minds: on the one hand, the photon is massless, and on the other, it has mass. Why does the E0 notation make sense? Because energy depends on the frame of reference, and the index zero in this case indicates that this is energy in the rest frame. Why is the notation m0 (rest mass) unreasonable? Because mass does not depend on the frame of reference. The assertion about the equivalence of energy and mass also contributes to the resulting confusion. Indeed, whenever there is mass, there is also energy corresponding to it: rest energy E0=mc2. However, when there is energy, there is not always mass. The mass of the photon is zero, and its energy is non-zero. The energies of particles in cosmic rays or in modern accelerators are many orders of magnitude higher than their masses (in units where c = 1). An outstanding role in the formation of modern relativistic language was played by R. Feynman, who in the 1950s created a relativistically invariant perturbation theory in quantum field theory in general and in quantum electrodynamics in particular. Conservation of the 4-vector energy - momentum is the basis of the famous technique of Feynman diagrams, or, as they are otherwise called, Feynman graphs. In all his scientific works, Feynman used the concept of mass given by formula (1). Physicists who began their acquaintance with the theory of relativity with the Field Theory of Landau and Lifshitz, or the scientific articles of Feynman, could no longer come up with the idea of calling the mass of a body the energy divided by c2, however, in the popular presentation (including the famous Feynman lectures on physics) this artifact remained. And this is a very sad fact, a partial explanation of which, it seems to me, must be sought in the fact that even the greatest physicists, moving from scientific to educational activities, try to adapt to the consciousness of a wide range of readers brought up on m=E/c2 It is in order to get rid of such “blunders” that it is necessary that a unified modern scientific terminology be adopted in the educational literature on the theory of relativity. The parallel use of modern and long-outdated symbols and terms is reminiscent of the Mars probe, which crashed in 1999 because one of the companies involved in its creation used inches, while the others used the metric system Today, physics has come close to the question of the nature of the mass of both truly elementary particles, such as leptons and quarks, and particles such as the proton and neutron, called hadrons. This question is closely related to the search for the so-called Higgs bosons and to the structure and evolution of the vacuum. And here the words about the nature of mass refer, of course, to the invariant mass m, defined in formula (1), and not to the relativistic mass, which simply represents the total energy of a free particle In the theory of relativity, mass is not a measure of inertia. (formula F-ma). The measure of inertia is the total energy of a body or system of bodies. Physicists do not attach any labels, especially those corresponding to Newton’s idea of mass, to particles. After all, physicists also consider massless particles to be particles. Considering what has just been said, it is not surprising that radiation transfers energy from one body to another, and therefore inertia And a short summary: Mass has the same value in all frames of reference, it is invariant regardless of how the particle moves The question "Does energy have rest mass?" doesn't make sense. It is not energy that has mass, but a body (particle) or a system of particles. The authors of textbooks who conclude from E0=mc2 that “energy has mass” are simply writing a meaningless phrase. It is possible to identify mass and energy only by violating logic, since mass is a relativistic scalar, and energy is a component of a 4-vector. In reasonable terminology, it can only sound: “Equivalence of rest energy and mass.” How to measure body mass in space? So we know that Mass is a fundamental physical quantity that determines the inertial and gravitational physical properties of a body. From the point of view of the theory of relativity, the mass of a body m characterizes its rest energy, which, according to Einstein’s relation: , where is the speed of light. In Newton's theory of gravity, mass serves as the source of the force of universal gravity, which attracts all bodies to each other. The force with which a body of mass attracts a body of mass is determined by Newton's law of gravity: The inertial properties of mass in non-relativistic (Newtonian) mechanics are determined by the relation. From the above, it is possible to obtain at least three ways to determine body mass in zero gravity. You can annihilate (convert all mass into energy) the body under study and measure the released energy - using Einstein's relation to get the answer. (Suitable for very small bodies - for example, this way you can find out the mass of an electron). But even a bad theorist should not propose such a solution. The annihilation of one kilogram of mass releases 2·1017 joules of heat in the form of hard gamma radiation Using a test body, measure the force of attraction acting on it from the object under study and, knowing the distance using Newton’s relation, find the mass (analogous to the Cavendish experiment). This is a complex experiment that requires sophisticated techniques and sensitive equipment, but today nothing is impossible in such a measurement of (active) gravitational mass of the order of a kilogram or more with quite decent accuracy. It’s just that this is a serious and subtle experience, which you must prepare before the launch of your ship. In earthly laboratories, Newton's law has been tested with excellent accuracy for relatively small masses in the distance range from one centimeter to about 10 meters. Affect the body with any known power(for example, attach a dynamometer to a body) and measure its acceleration, and use the ratio to find the mass of the body (Suitable for bodies of intermediate size). You can use the law of conservation of momentum. To do this, you need to have one body of known mass, and measure the velocities of the bodies before and after the interaction. The best way weighing the body - measuring/comparing it inert mass. And this is the method that is very often used in physical measurements(and not only in zero gravity). As you probably remember from personal experience and from a physics course, a weight attached to a spring oscillates with a very specific frequency: w = (k/m)1/2, where k is the stiffness of the spring, m is the mass of the weight. Thus, by measuring the oscillation frequency of a weight on a spring, its mass can be determined with the required accuracy. Moreover, it makes absolutely no difference whether there is weightlessness or not. In zero gravity, it is convenient to secure the holder for the measured mass between two springs, tensioned in opposite direction. (For fun, you can determine how the sensitivity of the scale depends on the pre-tension of the springs). IN real life Such scales are used to determine humidity and concentration of certain gases. A piezoelectric crystal is used as a spring, frequency natural vibrations which is determined by its rigidity and mass. A coating is applied to the crystal that selectively absorbs moisture (or certain gas or liquid molecules). The concentration of molecules captured by the coating is in a certain equilibrium with their concentration in the gas. Molecules captured by the coating slightly change the mass of the crystal and, accordingly, the frequency of its natural vibrations, which is determined electronic circuit(remember, I said that the crystal is piezoelectric)... Such “scales” are very sensitive and allow you to determine very small concentrations of water vapor or some other gases in the air. Yes, if you happen to be in zero gravity, then remember that the absence of weight does not mean the absence of mass, and in the event of an impact on the side of your spaceship bruises and bumps will be real Heirs (Article 1117). Requests to invalidate a will are subject to a general three-year statute of limitations (Article 196 of the Civil Code). Chapter III Problems legal regulation Institute of inheritance by will and development prospects. §1 Some novelties and problems of legal regulation of the institution of inheritance by will. Increased... Regularities, regardless of our knowledge about the nature of phenomena. Every effect has its cause. Like everything else in physics, the concept of determinism changed as physics and all natural sciences developed. In the 19th century, Newton's theory was finally formed and established. Significant contribution P.S. Laplace (1749 - 1827) contributed to its formation. He was the author of classic works on celestial mechanics and... With increasing duration space flights doctors raised the question of the need to monitor the weight of astronauts. A transition to another habitat certainly leads to a restructuring of the body, including a redistribution of fluid flows in it. In weightlessness, the blood flow changes - from the lower extremities, a significant part of it flows to chest and head. The process of dehydration of the body is stimulated and the person loses weight. However, the loss of even a fifth of water, which is 60-65%% in humans, is very dangerous for the body. Therefore, doctors needed a reliable device to constantly monitor the body weight of astronauts during flight and in preparation for returning to Earth. Conventional “earthly” scales determine not the mass, but the weight of the body - that is, the force of gravity with which it presses on the device. In zero gravity, such a principle is unacceptable - both a speck of dust and a container with cargo, when different weight, have equal - zero weight. When creating a weight meter in zero gravity, engineers had to use a different principle. The body mass meter in zero gravity is built according to the harmonic oscillator circuit. As is known, the period of free oscillations of a load on a spring depends on its mass. Thus, the oscillator system recalculates the oscillation period of a special platform with an astronaut or some object placed on it to mass. The body whose mass is to be measured is fixed on a spring in such a way that it can perform free vibrations along the axis of the spring. Period T (\displaystyle T) these fluctuations are associated with body weight M (\displaystyle M) ratio: where K is the spring elasticity coefficient. Thus, knowing K (\displaystyle K) and measuring T (\displaystyle T), can be found M (\displaystyle M). From the formula it is clear that the period of oscillation does not depend on either the amplitude or the acceleration of gravity. The “chair”-looking device consists of four parts: platforms for placing the astronaut (upper part), a base that is attached to the “floor” of the station (lower part), a rack and a mechanical middle part, as well as an electronic reading unit. Device size: 79.8 x 72 x 31.8 cm. Material: aluminum, rubber, organic glass. The weight of the device is about 11 kilograms. Top part device on which the astronaut lies with his chest consists of three parts. A rectangular sheet of plexiglass is attached to the upper platform. A chin rest for the astronaut extends from the end of the platform on a metal rod. The lower part of the device is a horseshoe-shaped base to which the mechanical part of the device and the reading measurement unit are attached. The mechanical part consists of a vertical cylindrical strut along which a second cylinder moves externally on bearings. On the outside of the movable cylinder there are two flywheels with stoppers to fix the movable system in the middle position. A shaped platform for the cosmonaut’s body, which determines its mass, is attached to the top end of the movable cylinder using two tubular brackets. Attached to the lower half of the movable cylinder are two handles with triggers at the ends, with the help of which the stoppers of the movable system are recessed into the handles. At the bottom of the outer cylinder there is a footrest for the astronaut, which has two rubber caps. A metal rod moves inside the cylindrical rack, embedded at one end in the upper platform; At the opposite end of the rod there is a plate, on both sides of which two springs are attached, which establish the moving system of the device in the middle position when in conditions of weightlessness. A magnetoelectric sensor is fixed at the bottom of the rack, which records the oscillation period of the moving system. The sensor automatically takes into account the duration of the oscillation period with an accuracy of a thousandth of a second. As shown above, the vibration frequency of the “chair” depends on the mass of the load. Thus, the astronaut just needs to swing a little on such a swing, and after a while the electronics will calculate and display the measurement result. To measure an astronaut's body weight, 30 seconds are enough. Subsequently, it turned out that the “cosmic scales” are much more accurate than the medical ones used in everyday life. This is the first time I have to weigh myself in space. It is clear that ordinary scales cannot work here, since there is no weight. Our scales, unlike those on earth, are unusual; they work on a different principle and are an oscillating platform on springs. Before weighing, I lower the platform, squeezing the springs, to the clamps, lie down on it, pressing tightly to the surface, and fix myself, grouping my body so that it does not dangle, wrapping my legs and arms around the profile support of the platform. I press the shutter. A slight push and I feel vibrations. Their frequency is displayed on the indicator in a digital code. I read its value, subtract the code for the vibration frequency of the platform, measured without a person, and use the table to determine my weight. It turned out to be 74 kg. A device for measuring the body weight of an astronaut was created no later than 1976 at the Leningrad special design and technology bureau "Biofizpribor" (SKTB "Biofizpribor")
or to be more precise.
, where is a vector
Operating principle of the mass meter
Device
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