Explanation.

In "On Floating Bodies", Archimedes suggested that (c. 250 BCE):  Archimedes' principle allows the buoyancy of any floating object partially or fully immersed in a fluid to be calculated. The downward force on the object is simply its weight. The upward, or buoyant, force on the object is that stated by Archimedes' principle, above. Thus, the net force on the object is the difference between the magnitudes of the buoyant force and its weight. If this net force is positive, the object rises; if negative, the object sinks; and if zero, the object is neutrally buoyant—that is, it remains in place without either rising or sinking. In simple words, Archimedes' principle states that, when a body is partially or completely immersed in a fluid, it experiences an apparent loss in weight that is equal to the weight of the fluid displaced by the immersed part of the body(s).

Formula.

Consider a cuboid immersed in a fluid, with one (hence two: top and bottom) of its sides orthogonal to the direction of gravity (assumed constant across the cube's stretch). The fluid will exert a normal force on each face, but only the normal forces on top and bottom will contribute to buoyancy. The pressure difference between the bottom and the top face is directly proportional to the height (difference in depth of submersion). Multiplying the pressure difference by the area of a face gives a net force on the cuboid – the buoyancy, equaling in size the weight of the fluid displaced by the cuboid. By summing up sufficiently many arbitrarily small cuboids this reasoning may be extended to irregular shapes, and so, whatever the shape of the submerged body, the buoyant force is equal to the weight of the displaced fluid.  The weight of the displaced fluid is directly proportional to the volume of the displaced fluid (if the surrounding fluid is of uniform density). The weight of the object in the fluid is reduced, because of the force acting on it, which is called upthrust. In simple terms, the principle states that the buoyant force (F) on an object is equal to the weight of the fluid displaced by the object, or the density (ρ) of the fluid multiplied by the submerged volume (V) times the gravity (g)  We can express this relation in the equation: where formula_3 (F in the figure) denotes the buoyant force applied onto the submerged object, formula_4 denotes the density of the fluid, formula_5 represents the volume of the displaced fluid and formula_6 is the acceleration due to gravity. Thus, among completely submerged objects with equal masses, objects with greater volume have greater buoyancy. Suppose a rock's weight is measured as 10 newtons when suspended by a string in a vacuum with gravity acting on it. Suppose that, when the rock is lowered into the water, it displaces water of weight 3 newtons. The force it then exerts on the string from which it hangs would be 10 newtons minus the 3 newtons of buoyant force: 10 − 3 = 7 newtons. Buoyancy reduces the apparent weight of objects that have sunk completely to the sea-floor. It is generally easier to lift an object through the water than it is to pull it out of the water.  For a fully submerged object, Archimedes' principle can be reformulated as follows:  then inserted into the quotient of weights, which has been expanded by the mutual volume  yields the formula below. The density of the immersed object relative to the density of the fluid can easily be calculated without measuring any volume is  Example: If you drop wood into water, buoyancy will keep it afloat.  Example: A helium balloon in a moving car. When increasing speed or driving in a curve, the air moves in the opposite direction to the car's acceleration. However, due to buoyancy, the balloon is pushed "out of the way" by the air and will drift in the same direction as the car's acceleration.  When an object is immersed in a liquid, the liquid exerts an upward force, which is known as the buoyant force, that is proportional to the weight of the displaced liquid. The sum force acting on the object, then, is equal to the difference between the weight of the object ('down' force) and the weight of displaced liquid ('up' force). Equilibrium, or neutral buoyancy, is achieved when these two weights (and thus forces) are equal.

Forces and equilibrium.

The equation to calculate the pressure inside a fluid in equilibrium is:  where f is the force density exerted by some outer field on the fluid, and "σ" is the Cauchy stress tensor. In this case the stress tensor is proportional to the identity tensor:  Here "δ" is the Kronecker delta. Using this the above equation becomes:  Assuming the outer force field is conservative, that is it can be written as the negative gradient of some scalar valued function:  Then:  Therefore, the shape of the open surface of a fluid equals the equipotential plane of the applied outer conservative force field. Let the "z"-axis point downward. In this case the field is gravity, so Φ = −"ρgz" where "g" is the gravitational acceleration, "ρ" is the mass density of the fluid. Taking the pressure as zero at the surface, where "z" is zero, the constant will be zero, so the pressure inside the fluid, when it is subject to gravity, is  So pressure increases with depth below the surface of a liquid, as "z" denotes the distance from the surface of the liquid into it. Any object with a non-zero vertical depth will have different pressures on its top and bottom, with the pressure on the bottom being greater. This difference in pressure causes the upward buoyancy force.  The buoyancy force exerted on a body can now be calculated easily, since the internal pressure of the fluid is known. The force exerted on the body can be calculated by integrating the stress tensor over the surface of the body which is in contact with the fluid:  The surface integral can be transformed into a volume integral with the help of the Gauss theorem:  where "V" is the measure of the volume in contact with the fluid, that is the volume of the submerged part of the body, since the fluid doesn't exert force on the part of the body which is outside of it.  The magnitude of buoyancy force may be appreciated a bit more from the following argument. Consider any object of arbitrary shape and volume "V" surrounded by a liquid. The force the liquid exerts on an object within the liquid is equal to the weight of the liquid with a volume equal to that of the object. This force is applied in a direction opposite to gravitational force, that is of magnitude:  where "ρ" is the density of the fluid, "V" is the volume of the displaced body of liquid, and "g" is the gravitational acceleration at the location in question.  If this volume of liquid is replaced by a solid body of exactly the same shape, the force the liquid exerts on it must be exactly the same as above. In other words, the "buoyancy force" on a submerged body is directed in the opposite direction to gravity and is equal in magnitude to  The net force on the object must be zero if it is to be a situation of fluid statics such that Archimedes principle is applicable, and is thus the sum of the buoyancy force and the object's weight  If the buoyancy of an (unrestrained and unpowered) object exceeds its weight, it tends to rise. An object whose weight exceeds its buoyancy tends to sink. Calculation of the upwards force on a submerged object during its accelerating period cannot be done by the Archimedes principle alone; it is necessary to consider dynamics of an object involving buoyancy. Once it fully sinks to the floor of the fluid or rises to the surface and settles, Archimedes principle can be applied alone. For a floating object, only the submerged volume displaces water. For a sunken object, the entire volume displaces water, and there will be an additional force of reaction from the solid floor.  In order for Archimedes' principle to be used alone, the object in question must be in equilibrium (the sum of the forces on the object must be zero), therefore;  and therefore  showing that the depth to which a floating object will sink, and the volume of fluid it will displace, is independent of the gravitational field regardless of geographic location.  It can be the case that forces other than just buoyancy and gravity come into play. This is the case if the object is restrained or if the object sinks to the solid floor. An object which tends to float requires a tension restraint force T in order to remain fully submerged. An object which tends to sink will eventually have a normal force of constraint N exerted upon it by the solid floor. The constraint force can be tension in a spring scale measuring its weight in the fluid, and is how apparent weight is defined.  If the object would otherwise float, the tension to restrain it fully submerged is:  When a sinking object settles on the solid floor, it experiences a normal force of:  Another possible formula for calculating buoyancy of an object is by finding the apparent weight of that particular object in the air (calculated in Newtons), and apparent weight of that object in the water (in Newtons). To find the force of buoyancy acting on the object when in air, using this particular information, this formula applies:  The final result would be measured in Newtons.  Air's density is very small compared to most solids and liquids. For this reason, the weight of an object in air is approximately the same as its true weight in a vacuum. The buoyancy of air is neglected for most objects during a measurement in air because the error is usually insignificant (typically less than 0.1% except for objects of very low average density such as a balloon or light foam).

Simplified model.

A simplified explanation for the integration of the pressure over the contact area may be stated as follows:  Consider a cube immersed in a fluid with the upper surface horizontal.  The sides are identical in area, and have the same depth distribution, therefore they also have the same pressure distribution, and consequently the same total force resulting from hydrostatic pressure, exerted perpendicular to the plane of the surface of each side.  There are two pairs of opposing sides, therefore the resultant horizontal forces balance in both orthogonal directions, and the resultant force is zero.  The upward force on the cube is the pressure on the bottom surface integrated over its area. The surface is at constant depth, so the pressure is constant. Therefore, the integral of the pressure over the area of the horizontal bottom surface of the cube is the hydrostatic pressure at that depth multiplied by the area of the bottom surface.  Similarly, the downward force on the cube is the pressure on the top surface integrated over its area. The surface is at constant depth, so the pressure is constant. Therefore, the integral of the pressure over the area of the horizontal top surface of the cube is the hydrostatic pressure at that depth multiplied by the area of the top surface.  As this is a cube, the top and bottom surfaces are identical in shape and area, and the pressure difference between the top and bottom of the cube is directly proportional to the depth difference, and the resultant force difference is exactly equal to the weight of the fluid that would occupy the volume of the cube in its absence.  This means that the resultant upward force on the cube is equal to the weight of the fluid that would fit into the volume of the cube, and the downward force on the cube is its weight, in the absence of external forces.  This analogy is valid for variations in the size of the cube.  If two cubes are placed alongside each other with a face of each in contact, the pressures and resultant forces on the sides or parts thereof in contact are balanced and may be disregarded, as the contact surfaces are equal in shape, size and pressure distribution, therefore the buoyancy of two cubes in contact is the sum of the buoyancies of each cube. This analogy can be extended to an arbitrary number of cubes.  An object of any shape can be approximated as a group of cubes in contact with each other, and as the size of the cube is decreased, the precision of the approximation increases. The limiting case for infinitely small cubes is the exact equivalence.  Angled surfaces do not nullify the analogy as the resultant force can be split into orthogonal components and each dealt with in the same way.

Refinements.

Archimedes' principle does not consider the surface tension (capillarity) acting on the body. Moreover, Archimedes' principle has been found to break down in complex fluids.  There is an exception to Archimedes' principle known as the bottom (or side) case. This occurs when a side of the object is touching the bottom (or side) of the vessel it is submerged in, and no liquid seeps in along that side. In this case, the net force has been found to be different from Archimedes' principle, owing to the fact that since no fluid seeps in on that side, the symmetry of pressure is broken.

Principle of flotation.

Archimedes' principle shows the buoyant force and displacement of fluid. However, the concept of Archimedes' principle can be applied when considering why objects float. Proposition 5 of Archimedes' treatise "On Floating Bodies" states that In other words, for an object floating on a liquid surface (like a boat) or floating submerged in a fluid (like a submarine in water or dirigible in air) the weight of the displaced liquid equals the weight of the object. Thus, only in the special case of floating does the buoyant force acting on an object equal the objects weight. Consider a 1-ton block of solid iron. As iron is nearly eight times as dense as water, it displaces only 1/8 ton of water when submerged, which is not enough to keep it afloat. Suppose the same iron block is reshaped into a bowl. It still weighs 1 ton, but when it is put in water, it displaces a greater volume of water than when it was a block. The deeper the iron bowl is immersed, the more water it displaces, and the greater the buoyant force acting on it. When the buoyant force equals 1 ton, it will sink no farther.  When any boat displaces a weight of water equal to its own weight, it floats. This is often called the "principle of flotation": A floating object displaces a weight of fluid equal to its own weight. Every ship, submarine, and dirigible must be designed to displace a weight of fluid at least equal to its own weight. A 10,000-ton ship's hull must be built wide enough, long enough and deep enough to displace 10,000 tons of water and still have some hull above the water to prevent it from sinking. It needs extra hull to fight waves that would otherwise fill it and, by increasing its mass, cause it to submerge. The same is true for vessels in air: a dirigible that weighs 100 tons needs to displace 100 tons of air. If it displaces more, it rises; if it displaces less, it falls. If the dirigible displaces exactly its weight, it hovers at a constant altitude.  While they are related to it, the principle of flotation and the concept that a submerged object displaces a volume of fluid equal to its own volume are "not" Archimedes' principle. Archimedes' principle, as stated above, equates the "buoyant force" to the weight of the fluid displaced.  One common point of confusion regarding Archimedes' principle is the meaning of displaced volume. Common demonstrations involve measuring the rise in water level when an object floats on the surface in order to calculate the displaced water. This measurement approach fails with a buoyant submerged object because the rise in the water level is directly related to the volume of the object and not the mass (except if the effective density of the object equals exactly the fluid density).

Eureka.

Archimedes reportedly exclaimed "Eureka" after he realized how to detect whether a crown is made of impure gold. While he did not use Archimedes' principle in the widespread tale and only used displaced water for measuring the volume of the crown, there is an alternative approach using the principle: Balance the crown and pure gold on a scale in the air and then put the scale into water. According to Archimedes' principle, if the density of the crown differs from the density of pure gold, the scale will get out of balance under water.

Archimedes' principle states that the upward buoyant force that is exerted on a body immersed in a fluid, whether fully or partially submerged, is equal to the weight of the fluid that the body displaces. Archimedes' principle is a law of physics fundamental to fluid mechanics. It was formulated by Archimedes of Syracuse.

Archimédův zákon je fyzikální poučka z hydrostatiky, která říká: "Těleso ponořené do tekutiny, která je v klidu, je nadlehčováno silou rovnající se tíze tekutiny stejného objemu, jako je ponořená část tělesa."


History.

In the Western world prior to the 16th century, it was generally assumed that the speed of a falling body would be proportional to its weight—that is, a 10 kg object was expected to fall ten times faster than an otherwise identical 1 kg object through the same medium. The ancient Greek philosopher Aristotle (384–322 BC) discussed falling objects in "Physics" (Book VII), one of the oldest books on mechanics (see Aristotelian physics).  In 12th-century Iraq, Abu'l-Barakāt al-Baghdādī gave an explanation for the gravitational acceleration of falling bodies. He proposed an explanation of the acceleration of falling bodies by the accumulation of successive increments of power with successive increments of velocity. According to Shlomo Pines, al-Baghdādī's theory of motion was "the oldest negation of Aristotle's fundamental dynamic law [namely, that a constant force produces a uniform motion], [and is thus an] anticipation in a vague fashion of the fundamental law of classical mechanics [namely, that a force applied continuously produces acceleration]." In the 14th century, Jean Buridan and Albert of Saxony referred to Abu'l-Barakat in explaining that the acceleration of a falling body is a result of its increasing impetus.  According to a tale that may be apocryphal, in 1589–92 Galileo dropped two objects of unequal mass from the Leaning Tower of Pisa. Given the speed at which such a fall would occur, it is doubtful that Galileo could have extracted much information from this experiment. Most of his observations of falling bodies were really of bodies rolling down ramps. This slowed things down enough to the point where he was able to measure the time intervals with water clocks and his own pulse (stopwatches having not yet been invented). He repeated this "a full hundred times" until he had achieved "an accuracy such that the deviation between two observations never exceeded one-tenth of a pulse beat." In 1589–92, Galileo wrote "De Motu Antiquiora", an unpublished manuscript on the motion of falling bodies.

Examples.

Examples of objects in free fall include: Technically, an object is in free fall even when moving upwards or instantaneously at rest at the top of its motion. If gravity is the only influence acting, then the acceleration is always downward and has the same magnitude for all bodies, commonly denoted formula_1.  Since all objects fall at the same rate in the absence of other forces, objects and people will experience weightlessness in these situations.  Examples of objects not in free fall:  The example of a falling skydiver who has not yet deployed a parachute is not considered free fall from a physics perspective, since he experiences a drag force that equals his weight once he has achieved terminal velocity (see below). Near the surface of the Earth, an object in free fall in a vacuum will accelerate at approximately 9.8 m/s, independent of its mass. With air resistance acting on an object that has been dropped, the object will eventually reach a terminal velocity, which is around 53 m/s (195 km/h or 122 mph) for a human skydiver. The terminal velocity depends on many factors including mass, drag coefficient, and relative surface area and will only be achieved if the fall is from sufficient altitude. A typical skydiver in a spread-eagle position will reach terminal velocity after about 12 seconds, during which time he will have fallen around 450 m (1,500 ft).  Free fall was demonstrated on the moon by astronaut David Scott on August 2, 1971. He simultaneously released a hammer and a feather from the same height above the moon's surface. The hammer and the feather both fell at the same rate and hit the ground at the same time. This demonstrated Galileo's discovery that, in the absence of air resistance, all objects experience the same acceleration due to gravity. On the Moon, however, the gravitational acceleration is approximately 1.63 m/s, or only about ⁄ that on Earth.

Free fall in Newtonian mechanics.

Uniform gravitational field without air resistance.

This is the "textbook" case of the vertical motion of an object falling a small distance close to the surface of a planet. It is a good approximation in air as long as the force of gravity on the object is much greater than the force of air resistance, or equivalently the object's velocity is always much less than the terminal velocity (see below).  where

Uniform gravitational field with air resistance.

This case, which applies to skydivers, parachutists or any body of mass, formula_10, and cross-sectional area, formula_11, with Reynolds number well above the critical Reynolds number, so that the air resistance is proportional to the square of the fall velocity, formula_12, has an equation of motion where formula_14 is the air density and formula_15 is the drag coefficient, assumed to be constant although in general it will depend on the Reynolds number.  Assuming an object falling from rest and no change in air density with altitude, the solution is:  where the terminal speed is given by  The object's speed versus time can be integrated over time to find the vertical position as a function of time:  Using the figure of 56 m/s for the terminal velocity of a human, one finds that after 10 seconds he will have fallen 348 metres and attained 94% of terminal velocity, and after 12 seconds he will have fallen 455 metres and will have attained 97% of terminal velocity. However, when the air density cannot be assumed to be constant, such as for objects falling from high altitude, the equation of motion becomes much more difficult to solve analytically and a numerical simulation of the motion is usually necessary. The figure shows the forces acting on meteoroids falling through the Earth's upper atmosphere. HALO jumps, including Joe Kittinger's and Felix Baumgartner's record jumps also belong in this category.

Inverse-square law gravitational field.

It can be said that two objects in space orbiting each other in the absence of other forces are in free fall around each other, e.g. that the Moon or an artificial satellite "falls around" the Earth, or a planet "falls around" the Sun. Assuming spherical objects means that the equation of motion is governed by Newton's Law of Universal Gravitation, with solutions to the gravitational two-body problem being elliptic orbits obeying Kepler's laws of planetary motion. This connection between falling objects close to the Earth and orbiting objects is best illustrated by the thought experiment, Newton's cannonball.  The motion of two objects moving radially towards each other with no angular momentum can be considered a special case of an elliptical orbit of eccentricity (radial elliptic trajectory). This allows one to compute the free-fall time for two point objects on a radial path. The solution of this equation of motion yields time as a function of separation:  where  Substituting "y "= 0 we get the free-fall time.  The separation as a function of time is given by the inverse of the equation. The inverse is represented exactly by the analytic power series:  Evaluating this yields: where  formula_22

Free fall in general relativity.

In general relativity, an object in free fall is subject to no force and is an inertial body moving along a geodesic. Far away from any sources of space-time curvature, where spacetime is flat, the Newtonian theory of free fall agrees with general relativity. Otherwise the two disagree; e.g., only general relativity can account for the precession of orbits, the orbital decay or inspiral of compact binaries due to gravitational waves, and the relativity of direction (geodetic precession and frame dragging).  The experimental observation that all objects in free fall accelerate at the same rate, as noted by Galileo and then embodied in Newton's theory as the equality of gravitational and inertial masses, and later confirmed to high accuracy by modern forms of the Eötvös experiment, is the basis of the equivalence principle, from which basis Einstein's theory of general relativity initially took off.

In Newtonian physics, free fall is any motion of a body where gravity is the only force acting upon it. In the context of general relativity, where gravitation is reduced to a space-time curvature, a body in free fall has no force acting on it.

Volný pád je pohyb tělesa o hmotnosti formula_1 v tíhovém poli, při kterém počáteční rychlost tělesa je "nulová" a kromě tíhové síly na těleso nepůsobí "žádná" další síla, popř. jsou další síly "zanedbatelné" (tzn. "odpor prostředí se zanedbává").


History.

Etymology.

The word "acoustic" is derived from the Greek word ἀκουστικός ("akoustikos"), meaning "of or for hearing, ready to hear"and that from ἀκουστός ("akoustos"), "heard, audible", which in turn derives from the verb ἀκούω("akouo"), "I hear".  The Latin synonym is "sonic", after which the term sonics used to be a synonym for acoustics and later a branch of acoustics. Frequencies above and below the audible range are called "ultrasonic" and "infrasonic", respectively.

Early research in acoustics.

In the 6th century BC, the ancient Greek philosopher Pythagoras wanted to know why some combinations of musical sounds seemed more beautiful than others, and he found answers in terms of numerical ratios representing the harmonic overtone series on a string. He is reputed to have observed that when the lengths of vibrating strings are expressible as ratios of integers (e.g. 2 to 3, 3 to 4), the tones produced will be harmonious, and the smaller the integers the more harmonious the sounds. For example, a string of a certain length would sound particularly harmonious with a string of twice the length (other factors being equal). In modern parlance, if a string sounds the note C when plucked, a string twice as long will sound a C an octave lower. In one system of musical tuning, the tones in between are then given by 16:9 for D, 8:5 for E, 3:2 for F, 4:3 for G, 6:5 for A, and 16:15 for B, in ascending order.  Aristotle (384–322 BC) understood that sound consisted of compressions and rarefactions of air which "falls upon and strikes the air which is next to it...", a very good expression of the nature of wave motion.  In about 20 BC, the Roman architect and engineer Vitruvius wrote a treatise on the acoustic properties of theaters including discussion of interference, echoes, and reverberation—the beginnings of architectural acoustics. In Book V of his "De architectura" ("The Ten Books of Architecture") Vitruvius describes sound as a wave comparable to a water wave extended to three dimensions, which, when interrupted by obstructions, would flow back and break up following waves. He described the ascending seats in ancient theaters as designed to prevent this deterioration of sound and also recommended bronze vessels of appropriate sizes be placed in theaters to resonate with the fourth, fifth and so on, up to the double octave, in order to resonate with the more desirable, harmonious notes.  During the Islamic golden age, Abū Rayhān al-Bīrūnī (973-1048) is believed to postulated that the speed of sound was much slower than the speed of light.  The physical understanding of acoustical processes advanced rapidly during and after the Scientific Revolution. Mainly Galileo Galilei (1564–1642) but also Marin Mersenne (1588–1648), independently, discovered the complete laws of vibrating strings (completing what Pythagoras and Pythagoreans had started 2000 years earlier). Galileo wrote "Waves are produced by the vibrations of a sonorous body, which spread through the air, bringing to the tympanum of the ear a stimulus which the mind interprets as sound", a remarkable statement that points to the beginnings of physiological and psychological acoustics. Experimental measurements of the speed of sound in air were carried out successfully between 1630 and 1680 by a number of investigators, prominently Mersenne. Meanwhile, Newton (1642–1727) derived the relationship for wave velocity in solids, a cornerstone of physical acoustics (Principia, 1687).

Age of Enlightenment and onward.

Substantial progress in acoustics, resting on firmer mathematical and physical concepts, was made during the eighteenth century by Euler (1707–1783), Lagrange (1736–1813), and d'Alembert (1717–1783). During this era, continuum physics, or field theory, began to receive a definite mathematical structure. The wave equation emerged in a number of contexts, including the propagation of sound in air.  In the nineteenth century the major figures of mathematical acoustics were Helmholtz in Germany, who consolidated the field of physiological acoustics, and Lord Rayleigh in England, who combined the previous knowledge with his own copious contributions to the field in his monumental work "The Theory of Sound" (1877). Also in the 19th century, Wheatstone, Ohm, and Henry developed the analogy between electricity and acoustics.  The twentieth century saw a burgeoning of technological applications of the large body of scientific knowledge that was by then in place. The first such application was Sabine's groundbreaking work in architectural acoustics, and many others followed. Underwater acoustics was used for detecting submarines in the first World War. Sound recording and the telephone played important roles in a global transformation of society. Sound measurement and analysis reached new levels of accuracy and sophistication through the use of electronics and computing. The ultrasonic frequency range enabled wholly new kinds of application in medicine and industry. New kinds of transducers (generators and receivers of acoustic energy) were invented and put to use.

Fundamental concepts of acoustics.

Definition.

Acoustics is defined by ANSI/ASA S1.1-2013 as "(a) Science of sound, including its production, transmission, and effects, including biological and psychological effects. (b) Those qualities of a room that, together, determine its character with respect to auditory effects."  The study of acoustics revolves around the generation, propagation and reception of mechanical waves and vibrations.  The steps shown in the above diagram can be found in any acoustical event or process. There are many kinds of cause, both natural and volitional. There are many kinds of transduction process that convert energy from some other form into sonic energy, producing a sound wave. There is one fundamental equation that describes sound wave propagation, the acoustic wave equation, but the phenomena that emerge from it are varied and often complex. The wave carries energy throughout the propagating medium. Eventually this energy is transduced again into other forms, in ways that again may be natural and/or volitionally contrived. The final effect may be purely physical or it may reach far into the biological or volitional domains. The five basic steps are found equally well whether we are talking about an earthquake, a submarine using sonar to locate its foe, or a band playing in a rock concert.  The central stage in the acoustical process is wave propagation. This falls within the domain of physical acoustics. In fluids, sound propagates primarily as a pressure wave. In solids, mechanical waves can take many forms including longitudinal waves, transverse waves and surface waves.  Acoustics looks first at the pressure levels and frequencies in the sound wave and how the wave interacts with the environment. This interaction can be described as either a diffraction, interference or a reflection or a mix of the three. If several media are present, a refraction can also occur. Transduction processes are also of special importance to acoustics.

Wave propagation: pressure levels.

In fluids such as air and water, sound waves propagate as disturbances in the ambient pressure level. While this disturbance is usually small, it is still noticeable to the human ear. The smallest sound that a person can hear, known as the threshold of hearing, is nine orders of magnitude smaller than the ambient pressure. The loudness of these disturbances is related to the sound pressure level (SPL) which is measured on a logarithmic scale in decibels.

Wave propagation: frequency.

Physicists and acoustic engineers tend to discuss sound pressure levels in terms of frequencies, partly because this is how our ears interpret sound. What we experience as "higher pitched" or "lower pitched" sounds are pressure vibrations having a higher or lower number of cycles per second. In a common technique of acoustic measurement, acoustic signals are sampled in time, and then presented in more meaningful forms such as octave bands or time frequency plots. Both of these popular methods are used to analyze sound and better understand the acoustic phenomenon.  The entire spectrum can be divided into three sections: audio, ultrasonic, and infrasonic. The audio range falls between 20 Hz and 20,000 Hz. This range is important because its frequencies can be detected by the human ear. This range has a number of applications, including speech communication and music. The ultrasonic range refers to the very high frequencies: 20,000 Hz and higher. This range has shorter wavelengths which allow better resolution in imaging technologies. Medical applications such as ultrasonography and elastography rely on the ultrasonic frequency range. On the other end of the spectrum, the lowest frequencies are known as the infrasonic range. These frequencies can be used to study geological phenomena such as earthquakes.  Analytic instruments such as the spectrum analyzer facilitate visualization and measurement of acoustic signals and their properties. The spectrogram produced by such an instrument is a graphical display of the time varying pressure level and frequency profiles which give a specific acoustic signal its defining character.

Transduction in acoustics.

A transducer is a device for converting one form of energy into another. In an electroacoustic context, this means converting sound energy into electrical energy (or vice versa). Electroacoustic transducers include loudspeakers, microphones, particle velocity sensors, hydrophones and sonar projectors. These devices convert a sound wave to or from an electric signal. The most widely used transduction principles are electromagnetism, electrostatics and piezoelectricity.  The transducers in most common loudspeakers (e.g. woofers and tweeters), are electromagnetic devices that generate waves using a suspended diaphragm driven by an electromagnetic voice coil, sending off pressure waves. Electret microphones and condenser microphones employ electrostatics—as the sound wave strikes the microphone's diaphragm, it moves and induces a voltage change. The ultrasonic systems used in medical ultrasonography employ piezoelectric transducers. These are made from special ceramics in which mechanical vibrations and electrical fields are interlinked through a property of the material itself.

Acoustician.

An acoustician is an expert in the science of sound.

Education.

There are many types of acoustician, but they usually have a Bachelor's degree or higher qualification. Some possess a degree in acoustics, while others enter the discipline via studies in fields such as physics or engineering. Much work in acoustics requires a good grounding in Mathematics and science. Many acoustic scientists work in research and development. Some conduct basic research to advance our knowledge of the perception (e.g. hearing, psychoacoustics or neurophysiology) of speech, music and noise. Other acoustic scientists advance understanding of how sound is affected as it moves through environments, e.g. Underwater acoustics, Architectural acoustics or Structural acoustics. Other areas of work are listed under subdisciplines below. Acoustic scientists work in government, university and private industry laboratories. Many go on to work in Acoustical Engineering. Some positions, such as Faculty (academic staff) require a Doctor of Philosophy.

Subdisciplines.

These subdisciplines are a slightly modified list from the PACS (Physics and Astronomy Classification Scheme) coding used by the Acoustical Society of America.

Archaeoacoustics.

Archaeoacoustics, also known as the archaeology of sound, is one of the only ways to experience the past with senses other than our eyes. Archaeoacoustics is studied by testing the acoustic properties of prehistoric sites, including caves. Iegor Rezkinoff, a sound archaeologist, studies the acoustic properties of caves through natural sounds like humming and whistling. Archaeological theories of acoustics are focused around ritualistic purposes as well as a way of echolocation in the caves. In archaeology, acoustic sounds and rituals directly correlate as specific sounds were meant to bring ritual participants closer to a spiritual awakening. Parallels can also be drawn between cave wall paintings and the acoustic properties of the cave; they are both dynamic. Because archaeoacoustics is a fairly new archaeological subject, acoustic sound is still being tested in these prehistoric sites today.

Aeroacoustics.

Aeroacoustics is the study of noise generated by air movement, for instance via turbulence, and the movement of sound through the fluid air. This knowledge is applied in acoustical engineering to study how to quieten aircraft. Aeroacoustics is important for understanding how wind musical instruments work.

Acoustic signal processing.

Acoustic signal processing is the electronic manipulation of acoustic signals. Applications include: active noise control; design for hearing aids or cochlear implants; echo cancellation; music information retrieval, and perceptual coding (e.g. MP3 or Opus).

Architectural acoustics.

Architectural acoustics (also known as building acoustics) involves the scientific understanding of how to achieve good sound within a building. It typically involves the study of speech intelligibility, speech privacy, music quality, and vibration reduction in the built environment.

Bioacoustics.

Bioacoustics is the scientific study of the hearing and calls of animal calls, as well as how animals are affected by the acoustic and sounds of their habitat.

Electroacoustics.

This subdiscipline is concerned with the recording, manipulation and reproduction of audio using electronics. This might include products such as mobile phones, large scale public address systems or virtual reality systems in research laboratories.

Environmental noise and soundscapes.

Environmental acoustics is concerned with noise and vibration caused by railways, road traffic, aircraft, industrial equipment and recreational activities. The main aim of these studies is to reduce levels of environmental noise and vibration. Research work now also has a focus on the positive use of sound in urban environments: soundscapes and tranquility.

Musical acoustics.

Musical acoustics is the study of the physics of acoustic instruments; the audio signal processing used in electronic music; the computer analysis of music and composition, and the perception and cognitive neuroscience of music.

Psychoacoustics.

Many studies have been conducted to identify the relationship between acoustics and cognition, or more commonly known as psychoacoustics, in which what one hears is a combination of perception and biological aspects. The information intercepted by the passage of sound waves through the ear is understood and interpreted through the brain, emphasizing the connection between the mind and acoustics. Psychological changes have been seen as brain waves slow down or speed up as a result of varying auditory stimulus which can in turn affect the way one thinks, feels, or even behaves. This correlation can be viewed in normal, everyday situations in which listening to an upbeat or uptempo song can cause one's foot to start tapping or a slower song can leave one feeling calm and serene. In a deeper biological look at the phenomenon of psychoacoustics, it was discovered that the central nervous system is activated by basic acoustical characteristics of music. By observing how the central nervous system, which includes the brain and spine, is influenced by acoustics, the pathway in which acoustic affects the mind, and essentially the body, is evident.

Speech.

Acousticians study the production, processing and perception of speech. Speech recognition and Speech synthesis are two important areas of speech processing using computers. The subject also overlaps with the disciplines of physics, physiology, psychology, and linguistics.

Ultrasonics.

Ultrasonics deals with sounds at frequencies too high to be heard by humans. Specialisms include medical ultrasonics (including medical ultrasonography), sonochemistry, material characterisation and underwater acoustics (Sonar).

Underwater acoustics.

Underwater acoustics is the scientific study of natural and man-made sounds underwater. Applications include sonar to locate submarines, underwater communication by whales, climate change monitoring by measuring sea temperatures acoustically, sonic weapons, and marine bioacoustics.

Vibration and dynamics.

This is the study of how mechanical systems vibrate and interact with their surroundings. Applications might include: ground vibrations from railways; vibration isolation to reduce vibration in operating theatres; studying how vibration can damage health (vibration white finger); vibration control to protect a building from earthquakes, or measuring how structure-borne sound moves through buildings.

Acoustics is a branch of physics that deals with the study of mechanical waves in gases, liquids, and solids including topics such as vibration, sound, ultrasound and infrasound. A scientist who works in the field of acoustics is an acoustician while someone working in the field of acoustics technology may be called an acoustical engineer. The application of acoustics is present in almost all aspects of modern society with the most obvious being the audio and noise control industries.

Akustika je rozsáhlý vědní obor, zabývající se vznikem zvukového vlnění, jeho šířením, vnímáním zvuku sluchem a přenosu prostorem až po vnímání lidskými smysly. Má celou řadu poddisciplín, např. hudební akustika zkoumá fyzikální základy hudby, hudebních nástrojů a prostorů, stavební akustika zvukové jevy a souvislosti v uzavřeném prostoru, budovách a stavbách, prostorová akustika šíření zvuku v obecném prostoru, fyziologická akustika vznikem zvuku v hlasovém orgánu člověka a jeho vnímáním v uchu, psychoakustika vnímání zvuku v mozku atd. Akustika patří mezi nejstarší obory fyziky. Akustika se dále dělí podle oblasti zájmu. Slovo AKUSTIKA pochází z řec. akoustikós, což znamená ""týkající se slyšení"", od akoúo znamenající ""slyším"."


Plot.

Discharged Czechoslovak lieutenant Viktor Chotovický (Petr Čepek) returns to his homeland after spending much of the war in Aberdeen, Scotland employed at a RAF desk job. He has been appointed the trustee of an empty manor formerly occupied by the German family of a notorious Nazi war-criminal imprisoned by the Czechoslovak authorities. Viktor meets the Nazi's beautiful daughter Adelheid Heidenmann (Emma Černá), who is forced to work as a cleaning lady at her own mansion. Her brother is an SS officer who allegedly disappeared in the Eastern Front. Viktor makes Adelheid his captive maid, and soon falls in love with her. His heart is torn between feelings of desire and his national identity and sympathies. Adelheid also slowly becomes sympathetic towards Viktor, but at the same time silently hopes for the return of her brother Hansgeorg. When he does Viktor narrowly escapes death. Viktor refuses to testify against Adelheid because he is alone and has nobody else. However, Adelheid commits suicide in her cell, Viktor walks off into the snow-covered countryside and is last seen wandering towards a mine field.

Production.

As in other novels by Körner, the story is set in Sudetenland in Northern Moravia. The movie was shot in Lužec castle located close the town of Vroutek (German: "Rudig") in western Bohemia and in the villages close to Liberec in Northern Bohemia.  The soundtrack, adapted by Zdeněk Liška is based on existing music by Bach and Strauss, which complements the atmosphere of the film. The film was produced by Film Studio Barrandov Czechoslovakia in 1969.

Reception.

The film has received very positive reviews after its release in 1969. Many critics called it Vláčil's second best film (after "Marketa Lazarová"). The film wasn't taken pleasantly by authorities and it received limited release and propagation which resulted in a small attendance in cinemas.

Adelheid is a 1970 Czechoslovak drama film directed by František Vláčil, based on a 1967 novel of the same name by Czech writer Vladimír Körner. The story is about the complicated relationship between Czech man Viktor and German woman Adelheid, and about relationships between Czechs and Germans in postwar Czechoslovakia in general.

Adelheid je český film režiséra Františka Vláčila, natočený v roce 1969 podle stejnojmenné novely Vladimíra Körnera. Děj se odehrává v Sudetech krátce po skončení druhé světové války. Do vesnice je jako správce znárodněného majetku přidělen bývalý voják ze západní fronty (Petr Čepek), je ubytován ve vile po místním aktivním nacistovi, kde se setkává s jeho dcerou (Emma Černá). Ve filmu se stýkají traumata obou hlavních postav, způsobená prožitými událostmi. Atmosféru filmu úspěšně doplňuje a spoluvytváří sborová hudba ve stylu germánské majestátní hudby Richarda Wagnera od skladatelů Bacha a Strausse mladšího. Film byl natáčen v Kryštofově Údolí u Liberce a na zámečku v Lužci u Lubence na Podbořansku.


History.

Astronomy is an ancient science, long separated from the study of terrestrial physics. In the Aristotelian worldview, bodies in the sky appeared to be unchanging spheres whose only motion was uniform motion in a circle, while the earthly world was the realm which underwent growth and decay and in which natural motion was in a straight line and ended when the moving object reached its destination. Consequently, it was held that the celestial region was made of a fundamentally different kind of matter from that found in the terrestrial sphere; either Fire as maintained by Plato, or Aether as maintained by Aristotle. During the 17th century, natural philosophers such as Galileo, Descartes, and Newton began to maintain that the celestial and terrestrial regions were made of similar kinds of material and were subject to the same natural laws. Their challenge was that the tools had not yet been invented with which to prove these assertions.  For much of the nineteenth century, astronomical research was focused on the routine work of measuring the positions and computing the motions of astronomical objects. A new astronomy, soon to be called astrophysics, began to emerge when William Hyde Wollaston and Joseph von Fraunhofer independently discovered that, when decomposing the light from the Sun, a multitude of dark lines (regions where there was less or no light) were observed in the spectrum. By 1860 the physicist, Gustav Kirchhoff, and the chemist, Robert Bunsen, had demonstrated that the dark lines in the solar spectrum corresponded to bright lines in the spectra of known gases, specific lines corresponding to unique chemical elements. Kirchhoff deduced that the dark lines in the solar spectrum are caused by absorption by chemical elements in the Solar atmosphere. In this way it was proved that the chemical elements found in the Sun and stars were also found on Earth.  Among those who extended the study of solar and stellar spectra was Norman Lockyer, who in 1868 detected radiant, as well as dark, lines in solar spectra. Working with chemist Edward Frankland to investigate the spectra of elements at various temperatures and pressures, he could not associate a yellow line in the solar spectrum with any known elements. He thus claimed the line represented a new element, which was called helium, after the Greek Helios, the Sun personified.  In 1885, Edward C. Pickering undertook an ambitious program of stellar spectral classification at Harvard College Observatory, in which a team of woman computers, notably Williamina Fleming, Antonia Maury, and Annie Jump Cannon, classified the spectra recorded on photographic plates. By 1890, a catalog of over 10,000 stars had been prepared that grouped them into thirteen spectral types. Following Pickering's vision, by 1924 Cannon expanded the catalog to nine volumes and over a quarter of a million stars, developing the Harvard Classification Scheme which was accepted for worldwide use in 1922.  In 1895, George Ellery Hale and James E. Keeler, along with a group of ten associate editors from Europe and the United States, established "The Astrophysical Journal: An International Review of Spectroscopy and Astronomical Physics". It was intended that the journal would fill the gap between journals in astronomy and physics, providing a venue for publication of articles on astronomical applications of the spectroscope; on laboratory research closely allied to astronomical physics, including wavelength determinations of metallic and gaseous spectra and experiments on radiation and absorption; on theories of the Sun, Moon, planets, comets, meteors, and nebulae; and on instrumentation for telescopes and laboratories.  Around 1920, following the discovery of the Hertzsprung–Russell diagram still used as the basis for classifying stars and their evolution, Arthur Eddington anticipated the discovery and mechanism of nuclear fusion processes in stars, in his paper "The Internal Constitution of the Stars". At that time, the source of stellar energy was a complete mystery; Eddington correctly speculated that the source was fusion of hydrogen into helium, liberating enormous energy according to Einstein's equation "E = mc". This was a particularly remarkable development since at that time fusion and thermonuclear energy, and even that stars are largely composed of hydrogen (see metallicity), had not yet been discovered.  In 1925 Cecilia Helena Payne (later Cecilia Payne-Gaposchkin) wrote an influential doctoral dissertation at Radcliffe College, in which she applied ionization theory to stellar atmospheres to relate the spectral classes to the temperature of stars. Most significantly, she discovered that hydrogen and helium were the principal components of stars. Despite Eddington's suggestion, this discovery was so unexpected that her dissertation readers convinced her to modify the conclusion before publication. However, later research confirmed her discovery.  By the end of the 20th century, studies of astronomical spectra had expanded to cover wavelengths extending from radio waves through optical, x-ray, and gamma wavelengths. In the 21st century it further expanded to include observations based on gravitational waves.

Observational astrophysics.

Observational astronomy is a division of the astronomical science that is concerned with recording and interpreting data, in contrast with theoretical astrophysics, which is mainly concerned with finding out the measurable implications of physical models. It is the practice of observing celestial objects by using telescopes and other astronomical apparatus.  The majority of astrophysical observations are made using the electromagnetic spectrum.  Other than electromagnetic radiation, few things may be observed from the Earth that originate from great distances. A few gravitational wave observatories have been constructed, but gravitational waves are extremely difficult to detect. Neutrino observatories have also been built, primarily to study our Sun. Cosmic rays consisting of very high energy particles can be observed hitting the Earth's atmosphere.  Observations can also vary in their time scale. Most optical observations take minutes to hours, so phenomena that change faster than this cannot readily be observed. However, historical data on some objects is available, spanning centuries or millennia. On the other hand, radio observations may look at events on a millisecond timescale (millisecond pulsars) or combine years of data (pulsar deceleration studies). The information obtained from these different timescales is very different.  The study of our very own Sun has a special place in observational astrophysics. Due to the tremendous distance of all other stars, the Sun can be observed in a kind of detail unparalleled by any other star. Our understanding of our own Sun serves as a guide to our understanding of other stars.  The topic of how stars change, or stellar evolution, is often modeled by placing the varieties of star types in their respective positions on the Hertzsprung–Russell diagram, which can be viewed as representing the state of a stellar object, from birth to destruction.

Theoretical astrophysics.

Theoretical astrophysicists use a wide variety of tools which include analytical models (for example, polytropes to approximate the behaviors of a star) and computational numerical simulations. Each has some advantages. Analytical models of a process are generally better for giving insight into the heart of what is going on. Numerical models can reveal the existence of phenomena and effects that would otherwise not be seen.  Theorists in astrophysics endeavor to create theoretical models and figure out the observational consequences of those models. This helps allow observers to look for data that can refute a model or help in choosing between several alternate or conflicting models.  Theorists also try to generate or modify models to take into account new data. In the case of an inconsistency, the general tendency is to try to make minimal modifications to the model to fit the data. In some cases, a large amount of inconsistent data over time may lead to total abandonment of a model.  Topics studied by theoretical astrophysicists include stellar dynamics and evolution; galaxy formation and evolution; magnetohydrodynamics; large-scale structure of matter in the universe; origin of cosmic rays; general relativity and physical cosmology, including string cosmology and astroparticle physics. Astrophysical relativity serves as a tool to gauge the properties of large scale structures for which gravitation plays a significant role in physical phenomena investigated and as the basis for black hole ("astro")physics and the study of gravitational waves.  Some widely accepted and studied theories and models in astrophysics, now included in the Lambda-CDM model, are the Big Bang, cosmic inflation, dark matter, dark energy and fundamental theories of physics. Wormholes are examples of hypotheses which are yet to be proven (or disproven).

Popularization.

The roots of astrophysics can be found in the seventeenth century emergence of a unified physics, in which the same laws applied to the celestial and terrestrial realms. There were scientists who were qualified in both physics and astronomy who laid the firm foundation for the current science of astrophysics. In modern times, students continue to be drawn to astrophysics due to its popularization by the Royal Astronomical Society and notable educators such as prominent professors Lawrence Krauss, Subrahmanyan Chandrasekhar, Stephen Hawking, Hubert Reeves, Carl Sagan, Neil deGrasse Tyson and Patrick Moore. The efforts of the early, late, and present scientists continue to attract young people to study the history and science of astrophysics.

Astrophysics is the branch of astronomy that employs the principles of physics and chemistry "to ascertain the nature of the astronomical objects, rather than their positions or motions in space". Among the objects studied are the Sun, other stars, galaxies, extrasolar planets, the interstellar medium and the cosmic microwave background. Emissions from these objects are examined across all parts of the electromagnetic spectrum, and the properties examined include luminosity, density, temperature, and chemical composition. Because astrophysics is a very broad subject, "astrophysicists" apply concepts and methods from many disciplines of physics, including classical mechanics, electromagnetism, statistical mechanics, thermodynamics, quantum mechanics, relativity, nuclear and particle physics, and atomic and molecular physics.

Astrofyzika (dříve též "kosmická fyzika") je vědní obor ležící na rozhraní fyziky a astronomie. Zabývá se fyzikou vesmíru, včetně fyzikálních vlastností (svítivost, hustota, teplota, chemické složení) astronomických objektů jako jsou hvězdy, galaxie a mezihvězdná hmota, jakož i jejich vzájemné působení.


Physical characteristics.

Internal structure.

Mercury appears to have a solid silicate crust and mantle overlying a solid, iron sulfide outer core layer, a deeper liquid core layer, and a solid inner core.  Mercury is one of four terrestrial planets in the Solar System, and is a rocky body like Earth. It is the smallest planet in the Solar System, with an equatorial radius of. Mercury is also smaller—albeit more massive—than the largest natural satellites in the Solar System, Ganymede and Titan. Mercury consists of approximately 70% metallic and 30% silicate material. Mercury's density is the second highest in the Solar System at 5.427 g/cm, only

Surface geology.

Mercury's surface is similar in appearance to that of the Moon, showing extensive mare-like plains and heavy cratering, indicating that it has been geologically inactive for billions of years. Because knowledge of Mercury's geology had been based only on the 1975 flyby and terrestrial observations, it is the least understood of the terrestrial planets. As data from "MESSENGER" orbiter are processed, this knowledge will increase. For example, an unusual crater with radiating troughs has been discovered that scientists called "the spider". It was later named Apollodorus.  Albedo features are areas of markedly different reflectivity, as seen by telescopic observation. Mercury has dorsa (also called "wrinkle-ridges"), Moon-like highlands, montes (mountains), planitiae (plains), rupes (escarpments), and valles (valleys).  Names for features on Mercury come from a variety of sources. Names coming from people are limited to the deceased. Craters are named for artists, musicians, painters, and

Impact basins and craters.

Craters on Mercury range in diameter from small bowl-shaped cavities to multi-ringed impact basins hundreds of kilometers across. They appear in all states of degradation, from relatively fresh rayed craters to highly degraded crater remnants. Mercurian craters differ subtly from lunar craters in that the area blanketed by their ejecta is much smaller, a consequence of Mercury's stronger surface gravity. According to IAU rules, each new crater must be named after an artist that was famous for more than fifty years, and dead for more than three years, before the date the crater is named.  The largest known crater is, with a diameter of 1,550 km. The impact that created the Caloris Basin was so powerful

Plains.

There are two geologically distinct plains regions on Mercury. Gently rolling, hilly plains in the regions between craters are Mercury's oldest visible surfaces, predating the heavily cratered terrain. These inter-crater plains appear to have obliterated many earlier craters, and show a general paucity of smaller craters below about 30 km in diameter.  Smooth plains are widespread flat areas that fill depressions of various sizes and bear a strong resemblance to the lunar maria. Notably, they fill

Compressional features.

One unusual feature of Mercury's surface is the numerous compression folds, or rupes, that crisscross the plains. As Mercury's interior cooled, it contracted and its surface began to deform, creating wrinkle ridges and lobate scarps associated with thrust faults. The scarps can reach lengths of 1000 km and heights of 3 km. These compressional features can be seen on top of other

Volcanology.

Images obtained by "MESSENGER" have revealed evidence for pyroclastic flows on Mercury from low-profile shield volcanoes. "MESSENGER" data has helped identify 51 pyroclastic deposits on the surface, where 90% of them are found within impact craters. A study of the degradation state of the impact craters that host pyroclastic deposits suggests that pyroclastic activity occurred on Mercury over a prolonged interval.  A "rimless depression" inside the southwest rim of the Caloris Basin consists of at least nine overlapping volcanic vents, each individually up to 8 km in diameter. It is thus a "compound volcano". The vent floors are at a least 1 km below their brinks and they bear a closer resemblance to volcanic craters sculpted by explosive eruptions or modified by collapse into void spaces created by magma withdrawal back down into a conduit. Scientists could not quantify the age of the volcanic complex system, but reported that it could be of the order of a billion years.

Surface conditions and exosphere.

The surface temperature of Mercury ranges from at the most extreme places: 0°N, 0°W, or 180°W. It never rises above 180 K at the poles, due to the absence of an atmosphere and a steep temperature gradient between the equator and the poles. The subsolar point reaches about 700 K during perihelion (0°W or 180°W), but only 550 K at aphelion (90° or 270°W). On the dark side of the planet, temperatures average 110 K. The intensity of sunlight on Mercury's surface ranges between 4.59 and 10.61 times the solar constant (1,370 W·m).  Although the daylight temperature

Magnetic field and magnetosphere.

Despite its small size and slow 59-day-long rotation, Mercury has a significant, and apparently global, magnetic field. According to measurements taken by, it is about 1.1% the strength of Earth's. The magnetic-field strength at Mercury's equator is about. Like that of Earth, Mercury's magnetic field is dipolar. Unlike Earth's, Mercury's poles are nearly aligned with the planet's spin axis. Measurements from both the and "MESSENGER" space probes have indicated that the strength and shape of the magnetic field are stable.  It is likely that this magnetic field is generated by a dynamo effect, in a manner similar to the magnetic field of Earth. This dynamo effect would result from the circulation of the planet's iron-rich liquid core. Particularly strong tidal effects caused by the planet's high orbital eccentricity would serve to keep the core in the liquid state necessary

Orbit, rotation, and longitude.

Mercury has the most eccentric orbit of all the planets; its eccentricity is 0.21 with its distance from the Sun ranging from. It takes 87.969 Earth days to complete an orbit. The diagram illustrates the effects of the eccentricity, showing Mercury's orbit overlaid with a circular orbit having the same semi-major axis. Mercury's higher velocity when it is near perihelion is clear from the greater distance it covers in each 5-day interval. In the diagram the varying distance of Mercury to the Sun is represented by the size of the planet, which is inversely proportional to Mercury's distance from the Sun. This varying distance to the Sun leads to Mercury's surface being flexed by tidal bulges raised by the Sun that are about 17 times stronger than the Moon's on Earth. Combined with a 3:2 spin–orbit resonance of the planet's rotation around its axis, it also results in complex variations of the surface temperature. The resonance makes a single solar day on Mercury last exactly two Mercury years, or about 176 Earth days.  Mercury's orbit is inclined by 7 degrees to the plane of Earth's orbit (the ecliptic), as shown in the diagram on the right. As a result, transits of Mercury across the face of the Sun can only occur when the planet is crossing the plane of the ecliptic at the time it lies between Earth and the Sun, which is in May or November. This occurs about every seven years on average.  Mercury's axial tilt is almost zero, with the best measured value as low as 0.027 degrees. This is significantly smaller than that of Jupiter, which has the second smallest axial tilt of all planets at 3.1 degrees. This means that to an observer at Mercury's poles, the center of the Sun never rises more than 2.1 arcminutes above the horizon.  At certain points on Mercury's surface, an observer would be able to see the Sun peek up a little more than two-thirds of the way over the horizon, then reverse and set before rising again, all within the same Mercurian day. This is because approximately four Earth days before perihelion, Mercury's angular orbital velocity equals its angular rotational velocity so that the Sun's apparent motion ceases; closer to perihelion, Mercury's angular orbital velocity then exceeds the angular rotational velocity. Thus, to a hypothetical observer on Mercury, the Sun appears to move in a retrograde direction. Four Earth days after perihelion, the Sun's normal apparent motion resumes. A similar effect would have occurred if Mercury had been in synchronous rotation: the alternating gain and loss of rotation over revolution would have caused a libration of 23.65° in longitude.  For the same reason, there are two points on Mercury's equator, 180 degrees apart in longitude, at either of which, around perihelion in alternate Mercurian years (once a Mercurian day), the Sun passes overhead, then reverses its apparent motion and passes overhead again, then reverses a second time and passes overhead a third time, taking a total of about 16 Earth-days for this entire process. In the other alternate Mercurian years, the same thing happens at the other of these two points. The amplitude of the retrograde motion is small, so the overall effect is that, for two or three weeks, the Sun is almost stationary overhead, and is at its most brilliant because Mercury is at perihelion, its closest to the Sun. This prolonged exposure to the Sun at its brightest makes these two points the hottest places on Mercury. Maximum temperature occurs when the Sun is at an angle of about 25 degrees past noon due to diurnal temperature lag, at 0.4 Mercury days and 0.8 Mercury years past sunrise. Conversely, there are two other points on the equator, 90 degrees of longitude apart from the first ones, where the Sun passes overhead only when the planet is at aphelion in alternate years, when the apparent motion of the Sun in Mercury's sky is relatively rapid. These points, which are the ones on the equator where the apparent retrograde motion of the Sun happens when it is crossing the horizon as described in the preceding paragraph, receive much less solar heat than the first ones described above.  Mercury attains inferior conjunction (nearest approach to Earth) every 116 Earth days on average, but this interval can range from 105 days to 129 days due to the planet's eccentric orbit. Mercury can come as near as to Earth, and that is slowly declining: The next approach to within is in 2679, and to within in 4487, but it will not be closer to Earth than until 28,622. Its period of retrograde motion as seen from Earth can vary from 8 to 15 days on either side of inferior conjunction. This large range arises from the planet's high orbital eccentricity. On average, Mercury is the closest planet to the Earth, and it is the closest planet to each of the other planets in the Solar System.

Biological considerations.

Habitability.

There may be scientific support, based on studies reported in March 2020, for considering that parts

Observation.

Mercury's apparent magnitude is calculated to vary between −2.48 (brighter than Sirius) around superior conjunction and +7.25 (below the limit of naked-eye visibility) around inferior conjunction. The mean apparent magnitude is 0.23 while the standard deviation of 1.78 is the largest of any planet. The mean apparent magnitude at superior conjunction is −1.89 while that at inferior conjunction is +5.93. Observation of Mercury is complicated by its proximity to the Sun, as it is lost in the Sun's glare for much of the time. Mercury can be observed for only a brief period during either morning or evening twilight.  Mercury can, like several other planets and the brightest stars, be seen during a total solar eclipse.  Like the Moon and Venus, Mercury exhibits phases as seen from Earth. It is "new" at inferior conjunction and "full" at superior conjunction. The planet is rendered invisible from Earth on both of these occasions because of its being obscured by the Sun, except its new phase during a transit.  Mercury is technically brightest as seen from Earth when it is at a full phase. Although Mercury is farthest from Earth when it is full, the greater illuminated area that is visible and the opposition brightness surge more than compensates for the distance. The opposite is true for Venus, which appears brightest when it is a crescent, because it is much closer to Earth than when gibbous. Nonetheless, the brightest (full phase) appearance of Mercury is an essentially impossible time for practical observation, because of the extreme proximity of the Sun. Mercury is best observed at the first and last quarter, although they are phases of lesser brightness. The first and last quarter phases occur at greatest elongation east and west of the Sun, respectively. At both of these times

Observation history.

Ancient astronomers.

The earliest known recorded observations of Mercury are from the Mul.Apin tablets. These observations were most likely made by an Assyrian astronomer around the 14th century BC. The cuneiform name used to designate Mercury on the Mul.Apin tablets is transcribed as Udu.Idim.Gu\u.Ud ("the jumping planet"). Babylonian records of Mercury date back to the 1st millennium BC. The Babylonians called the planet Nabu after the messenger to the gods in their mythology.  The ancients knew Mercury by different names depending on whether it was an evening star or a morning star. By about 350 BC, the ancient Greeks had realized the two stars were one. They knew the planet as Στίλβων "Stilbōn", meaning "twinkling", and Ἑρμής "Hermēs", for its fleeting motion, a name that is retained in modern Greek (Ερμής "Ermis"). The Romans named the planet after the swift-footed Roman messenger god, Mercury (Latin "Mercurius"), which they equated with the Greek Hermes, because it moves across the sky faster than any other planet. The astronomical symbol for Mercury is a stylized version of Hermes' caduceus.  The Greco-Egyptian astronomer Ptolemy wrote about the possibility of planetary transits across the face of the Sun in his

Ground-based telescopic research.

The first telescopic observations of Mercury were made by Galileo in the early 17th century. Although he observed phases when he looked at Venus, his telescope was not powerful enough to see the phases of Mercury. In 1631, Pierre Gassendi made the first telescopic observations of the transit of a planet across the Sun when he saw a transit of Mercury predicted by Johannes Kepler. In 1639, Giovanni Zupi used a telescope to discover that the planet had orbital phases similar to Venus and the Moon. The observation demonstrated conclusively that Mercury orbited around the Sun.  A rare event in astronomy is the passage of one planet in front of another (occultation), as seen from Earth. Mercury and Venus occult each other every few centuries, and the event of May 28, 1737 is the only one historically observed, having been seen by John Bevis at the Royal Greenwich Observatory. The next occultation of Mercury by Venus will be on December 3, 2133.  The difficulties inherent in observing Mercury mean that it has been far less studied than the other planets. In 1800, Johann Schröter made observations of surface features, claiming to have observed mountains. Friedrich Bessel used Schröter's drawings to erroneously estimate the rotation period as 24 hours and an axial tilt of 70°. In the 1880s, Giovanni Schiaparelli mapped the planet more accurately, and suggested that Mercury's rotational period was 88 days, the same as its orbital period due to tidal locking. This phenomenon is known as synchronous rotation. The effort to map the surface of Mercury was continued by Eugenios Antoniadi, who published a book in 1934

Research with space probes.

Reaching Mercury from Earth poses significant technical challenges, because it orbits so much closer to the Sun than Earth. A Mercury-bound spacecraft launched from Earth must travel over into the Sun's gravitational potential well. Mercury has an orbital speed of, whereas Earth's orbital speed is. Therefore, the spacecraft must make a large change in velocity (delta-v) to enter a Hohmann transfer orbit that passes near Mercury, as compared to the delta-v required for other planetary missions.  The potential energy liberated by moving down the Sun's potential well becomes kinetic energy; requiring another large delta-v change to do anything other than rapidly pass by Mercury. To land safely or enter a stable orbit the spacecraft would rely entirely on rocket motors. Aerobraking is ruled out because Mercury has a negligible atmosphere. A trip to Mercury requires more rocket fuel than that required to escape the Solar System completely. As a result, only two space probes have visited it so far. A proposed alternative approach would use a solar sail to attain a Mercury-synchronous orbit around the Sun.

"Mariner 10".

The first spacecraft to visit Mercury was NASA's (1974–1975). The spacecraft used the gravity of Venus to adjust its orbital velocity so that it could approach Mercury, making it both the first spacecraft to use this gravitational "slingshot" effect and the first NASA mission to visit multiple planets. provided the first close-up images of Mercury's surface, which immediately showed its heavily cratered nature, and revealed many other types of geological features, such as the giant scarps that were later ascribed to the effect of the planet shrinking slightly as its iron core cools. Unfortunately, the same face of the planet was lit at each of close approaches. This made close observation of both sides of the

"MESSENGER".

A second NASA mission to Mercury, named "MESSENGER" (MErcury Surface, Space ENvironment, GEochemistry, and Ranging), was launched on August 3, 2004. It made a fly-by of Earth in August 2005, and of Venus in October 2006 and June 2007 to place it onto the correct trajectory to reach an orbit around Mercury. A first fly-by of Mercury occurred on January 14, 2008, a second on October 6, 2008, and a third on September 29, 2009. Most of the hemisphere not imaged by was mapped during these fly-bys. The probe successfully entered an elliptical orbit around the planet on March 18, 2011. The first orbital image of Mercury was obtained on March 29, 2011. The

"BepiColombo".

The European Space Agency and the Japanese Space Agency developed and launched a joint mission called "BepiColombo", which will orbit Mercury with two probes: one to map the planet and the other to study its magnetosphere. Launched on October 20, 2018, "BepiColombo" is expected to reach Mercury in 2025. It will release a magnetometer probe into an elliptical orbit, then chemical rockets will fire to deposit the mapper probe into a circular orbit. Both probes will operate for one terrestrial year. The mapper probe carries an array of spectrometers similar to those on "MESSENGER", and will study the planet at many different wavelengths including infrared, ultraviolet, X-ray and gamma ray.

Mercury is the smallest and innermost planet in the Solar System. Its orbit around the Sun takes 87.97 days, the shortest of all the planets in the Solar System. It is named after the Roman deity Mercury, the messenger of the gods.

Merkur je Slunci nejbližší a současně i nejmenší planetou sluneční soustavy, dosahuje pouze o 40 % větší velikosti než pozemský Měsíc a je menší než Jupiterův měsíc Ganymed a Saturnův Titan. Merkur nemá žádný měsíc. Jeho oběžná dráha je ze všech planet nejblíže ke Slunci a jeden oběh trvá pouze 87,969 dne. Dráha Merkuru má největší výstřednost dráhy ze všech planet sluneční soustavy a sama planeta má nejmenší – téměř nulový – sklon rotační osy. Během dvou oběhů kolem Slunce dojde ke třem otočením kolem rotační osy. Perihelium jeho dráhy se stáčí ke Slunci o 43 vteřin za století; fenomén, který ve 20. století vysvětlil Albert Einstein obecnou teorií relativity. Při pohledu ze Země dosahuje Merkur jasnosti mezi -2,0 až 5,5, takže je viditelný i pouhým okem, ale jelikož se nikdy nevzdaluje od Slunce dále než na 28,3° je většinu roku těžko pozorovatelný. Nejlepší podmínky tak nastávají při soumraku či úsvitu, než vyjde Slunce nad horizont.