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Cottian Alps

The Cottian Alps (Alpes Cottiennes ; Alpi Cozie ) are a mountain range in the southwestern part of the Alps. They form the border between France (Hautes-Alpes and Savoie) and Italy (Piedmont). The Fréjus Road Tunnel and Fréjus Rail Tunnel between Modane and Susa are important transportation arteries between France (Lyon, Grenoble) and Italy (Turin).

Etymology
The name Cottian comes from Marcus Julius Cottius, a king of the tribes inhabiting that mountainous region in the 1st century BC. Under his father Donnus, these tribes had previously opposed but later made peace with Julius Caesar. Cottius was succeeded by his son Gaius Julius Donnus II (reigned 3 BC-4 AD), and his grandson Marcus Julius Cottius II (reigned 5-63 AD), who was granted the title of king by the emperor Claudius. On his death, Nero annexed his kingdom as the province of Alpes Cottiae.

History
For a long part of the Middle Ages the Cottian Alps were divided between the Duchy of Savoy, which controlled their northern part and the easternmost slopes, and the Dauphiné, which at the time was independent from France. The Dauphins also held, in addition to the southwestern slopes of the range (Briançon and Queyras, now on the French side), the upper part of some of the valleys that were tributaries of the Po River (Valle di Susa, Chisone valley, Varaita Valley). The Alpine territory of Dauphiné, known as Escartons, used to have a limited autonomy and elected its own parliament. This semi-autonomous status lasted also after the annexation of the Dauphiné to France (1349), and was only abolished in 1713 due to the Treaty of Utrecht, which assigned to the House of Savoy all the mountainous area on the eastern side of the Cottian Alps.

After the treaty annexing Nice and Savoy to France, signed in Turin in March 1860 (Treaty of Turin), the north-western slopes of the range became part of the French republic.

Two eastern valleys of the Cottian Alps (Pellice and Germanasca) have been for centuries a kind of sanctuary for the Waldensians, a Christian movement that was persecuted as heretical from the 12th century onwards by the catholic church.

Geography
Administratively the range is divided between the Italian province of Cuneo and the Metropolitan City of Turin (the eastern slopes), and the French departments of Savoie, Hautes-Alpes, and Alpes-de-Haute-Provence (the western slopes).

The Cottian Alps are drained by the rivers Durance and Arc and their tributaries on the French side; and by the Dora Riparia and other tributaries of the Po on the Italian side.

Borders
The borders of the Cottian Alps are (clockwise):
 * the Maddalena Pass to the south, which connects the Cottian Alps with the Maritime Alps;
 * the Ubayette Valley, the Ubaye Valley, the Serre-Ponçon Lake, the high Durance Valley, and the Guisane Valley to the southwest;
 * the Col du Galibier to the west, which connects the Cottian Alps with the Dauphiné Alps;
 * the Valloirette Valley, the Maurienne Valley, and the Chardoux Creek to the northwest;
 * the Mont Cenis Pass to the north, which connects the Cottian Alps with the Graian Alps;
 * Mont Cenis Lake, the Cenischia Valley, the Dora Riparia Valley, the Po Plain, and the Varaita Valley to the east.

Peaks
The chief peaks of the Cottian Alps are:

Passes
The chief passes of the Cottian Alps are:

Maps

 * Italian official cartography (Istituto Geografico Militare – IGM); on-line version: www.pcn.minambiente.it
 * French official cartography (Institut Géographique National – IGN); on-line version: www.geoportail.fr

title: Cottian Alps


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Pennine Alps

The Pennine Alps (Alpes Pennines, Walliser Alpen, Alpi Pennine, Alpes Poeninae), sometimes referred to as the Valais Alps (which are just the Northern Swiss part of the Pennine Alps), are a mountain range in the western part of the Alps. They are located in Italy (the Aosta Valley and Piedmont) and Switzerland (Valais).

The Pennine Alps are amongst the three highest major subranges of the Alps, together with the Bernese Alps and the Graian Alps that include the Mont Blanc massif.

Geography
The Italian side is drained by the rivers Dora Baltea, Sesia and Toce, tributaries of the Po. The Swiss side is drained by the Rhône.

The Great St Bernard Tunnel, under the Great St Bernard Pass, leads from Martigny, Switzerland to Aosta.

Morphology
The main chain (watershed between the Mediterranean Sea and the Adriatic Sea) runs from west to east on the border between Italy (south) and Switzerland (north). From Mont Vélan, the first high summit east of St Bernard Pass, the chain rarely goes below 3000 metres and contains many four-thousanders such as Matterhorn or Monte Rosa. The valleys are quite similar on both side of the border, being generally oriented perpendicular to the main chain and descending progressively into the Rhône Valley on the north and the Aosta Valley on the south. Unlike many other mountain ranges, the higher peaks are often located outside the main chain and found themselves between the northern valleys (Grand Combin, Weisshorn, Mischabel, Weissmies).

Peaks
The chief peaks of the Pennine Alps are:

Glaciers
Main glaciers:

 * Gorner Glacier
 * Corbassière Glacier
 * Findel Glacier
 * Zmutt Glacier
 * Zinal Glacier
 * Otemma Glacier
 * Allalin Glacier
 * Ferpècle Glacier
 * Fee Glacier
 * Mont Miné Glacier
 * Ried Glacier
 * Turtmann Glacier
 * Moiry Glacier
 * Arolla Glacier
 * Moming Glacier
 * Cheilon Glacier
 * Rossbode Glacier

Passes
The chief passes of the Pennine Alps are:

Nature conservation
Some regional nature parks, like the Parco Naturale Alta Valsesia (6,511 ha - Piedmont, IT), the Riserva Naturale Mont Mars (390 ha - Aosta Valley, IT) and the Regional park of Binn valley (15,891 ha - Valais, CH), have been established on both sides of the main water divide.

Maps

 * Swiss official cartography (Swiss Federal Office of Topography - Swisstopo); on-line version: map.geo.admin.ch
 * Italian official cartography (Istituto Geografico Militare - IGM); on-line version: www.pcn.minambiente.it

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/

title: Pennine Alps


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Bernese Alps

The Bernese Alps (Berner Alpen, Alpes bernoises, Alpi bernesi) are a mountain range of the Alps, located in western Switzerland. Although the name suggests that they are located in the Berner Oberland region of the canton of Bern, portions of the Bernese Alps are in the adjacent cantons of Valais, Fribourg and Vaud, the latter being usually named Fribourg Alps and Vaud Alps respectively. The highest mountain in the range, the Finsteraarhorn, is also the highest point in the canton of Bern.

The Rhône valley separates them from the Chablais Alps in the west and from the Pennine Alps in the south; the upper Rhône valley separates them from the Lepontine Alps to the southeast; the Grimsel Pass and the Aare valley separates them from the Uri Alps in the east, and from the Emmental Alps in the north; their northwestern edge is not well defined, describing a line roughly from Lake Geneva to Lake Thun. The Bernese Alps are drained by the river Aare and its tributary the Saane in the north, the Rhône in the south, and the Reuss in the east.

The Bernese Alps are amongst the three highest major subranges of the Alps, together with the Pennine Alps and the Mont Blanc massif.

Geography
One of the most prominent Alpine ranges, the Bernese Alps extend from the gorge of Saint-Maurice, through which the Rhône finds its way to Lake Geneva, to the Grimsel Pass or, depending on the definition, to the river Reuss (thus including the Uri Alps). The principal ridge, a chain that runs 100 km from west (Dent de Morcles) to east (Sidelhorn), whose highest peak is the Finsteraarhorn, forms the watershed between the cantons of Bern and Valais. Except for the westernmost part, it is also the watershed between the Rhine (North Sea) and the Rhône (Mediterranean Sea). This chain is not centered inside the range but lies close (10 to 15 km) to the Rhône on the south. This makes a large difference between the south, where the lateral short valleys descend abruptly into the deep trench forming the valley of the Rhône and the north, where the Bernese Alps extends through a great part of the canton of Bern (Bernese Oberland), throwing out branches to the west into the adjoining cantons of Vaud and Fribourg. There the mountains progressively become lower and disappear into the hilly Swiss Plateau. The Bernese Alps have a large influence on the climate of Switzerland: while their north side is very exposed to weather, their south side is protected from it. As a consequence, agriculture consists essentially of dairy farming and cattle breeding on the northern foothills, while on the sunnier southern foothills (Rhone Valley) it also consists of vineyards.

Gemmi Pass is the most central of the major passes through the main chain. It also marks the separation between two distinct sections of the Bernese Alps: the chain west of Gemmi Pass, consisting mainly of foothills with a few large glacier-covered mountains (notably Dent de Morcles, Grand Muveran, Diablerets, Wildhorn and Wildstrubel) around 3000 m, and the chain east of Gemmi Pass, consisting mainly of summits around 4000 m on several subranges, with large valley glaciers between them. The latter section, contrary to the former, has very few foothills and is the most glaciated part of the Alps.

A characteristic in the orography of the Bernese Alps is, that whereas the western portion of that chain consists of a single series of summits with comparatively short projecting buttresses, the higher group presents a series of longitudinal ridges parallel to the axis of the main chain, and separated from each other by deep valleys that form the channels of great glaciers. Thus the Tschingel Glacier and the Kander Glacier, separate the portion of the main range lying between the Gemmi Pass and the Mittaghorn from the equally high parallel range of the Doldenhorn and Blümlisalp on its northern side. To the south, the same portion of the main range is divided from the still higher parallel range whose summits are the Aletschhorn and the Bietschhorn by the Lötschental and the Lötschenlücke. To this again succeeds the deep trench through which the lower part of the Aletsch Glacier flows down to the Rhône, enclosed by the minor ridge that culminates at the Eggishorn.

It is in the central and eastern portions of the range only that crystalline rocks make their appearance; the western part is composed almost exclusively of sedimentary deposits, and the secondary ridges extending through Bern and the adjoining cantons are formed of jurassic, cretaceous, or eocene strata.

Exploration
The beauty of the scenery and the facilities offered to travellers by the general extension of mountain railways make the northern side of the range, the Bernese Oberland, one of the portions of the Alps most visited by tourists. Since strangers first began to visit the Alps, the names of Grindelwald, Lauterbrunnen, and Interlaken have become famous. But unlike many other Alpine regions, which have been left to be explored by strangers, this region has been long visited by Swiss travellers and men of science. Among them were the brother Meyer of Aarau and Franz Joseph Hugi. They have explored most of the mountain ranges not very difficult to access, and have climbed most of the higher summits. In 1841, Louis Agassiz, with several scientific friends, established a temporary station on the Unteraar Glacier, and, along with scientific observations on the glaciers, started a series of expeditions. Several mountains in the area are named after Agassiz and the other explorers. The works of Desor and Gottlieb Studer have been followed by several other publications that bear testimony to Swiss mountaineering activity. Notwithstanding the activity of their predecessors, the members of the English Alpine Club have found scope for further exploits, amongst which may be reckoned the first ascents of the Aletschhorn and the Schreckhorn, and the still more arduous enterprise of crossing the range bypasses, such as the Jungfraujoch and Eigerjoch, which are considered among the most difficult in the Alps.

Jungfrau-Aletsch area
The Jungfrau-Aletsch area is located in the eastern Bernese Alps in the most glaciated region of the Alps. It was inscribed as a UNESCO World Heritage Site (Swiss Alps Jungfrau-Aletsch) in 2001 and further expanded in 2007. Its name comes from the Aletsch Glacier and the two summits of the Jungfrau and Bietschhorn, which constitute some of the most impressive features of the site. The actual site (after the extension) includes other large glacier valleys such as the Fiescher Glacier and the Aar Glaciers.

List of peaks
The chief peaks of the Bernese Alps are:

Glaciers
Main glaciers:

 * Aletsch Glacier
 * Fiescher Glacier
 * Unteraar Glacier
 * Lower Grindelwald Glacier
 * Oberaletsch Glacier
 * Mittelaletsch Glacier
 * Gauli Glacier
 * Lang Glacier
 * Upper Grindelwald Glacier
 * Kander Glacier
 * Tschingel Glacier
 * Rosenlaui Glacier
 * Plaine Morte Glacier
 * Wildstrubel Glacier
 * Tsanfleuron Glacier
 * Diablerets Glacier

List of mountains lakes

 * Grimselsee
 * Oberaarsee
 * Lac de Tseuzier
 * Daubensee
 * Lac de Sénin
 * Oschinensee

List of passes
The chief passes of the Bernese Alps are:

title: Bernese Alps


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Graian Alps

The Graian Alps (Alpes grées ; Alpi Graie ) are a mountain range in the western part of the Alps.

Etymology
The name Graie comes from the Graioceli Celtic tribe, which dwelled in the area surrounding the Mont Cenis pass and the Viù valley. Other sources claim that the name comes from the Celtic "Graig" meaning rock/stone, literally the Rocky Mountains

Geography
The Graian Alps are located in France (Auvergne-Rhône-Alpes), Italy (Piedmont and the Aosta Valley), and Switzerland (western Valais).

The French side of the Graian Alps is drained by the river Isère (Tarentaise valley) and its tributary Arc (Maurienne valley), and by the Arve. The Italian side is drained by the rivers Dora Riparia, Dora Baltea, Orco and Stura di Lanzo, tributaries of the Po.

The Graian Alps can also be divided into the following four groups:

 * the Mont Blanc group (north of the Little St Bernard Pass), including the Beaufortain Massif
 * the Central group (the watershed between the Little St Bernard Pass and the Col du Mont Cenis)
 * the Western or French group,
 * and the Eastern or Italian group, including the Gran Paradiso Massif.

Peaks
The main peaks of the Graian Alps are:

Passes
The main passes of the Graian Alps are shown in the table below. The group in which the pass is located is indicated with "MB" for Mont Blanc group, "C" for Central group, "E" for Eastern group, and "W" for Western group.

Nature conservation
The western group contains the Vanoise National Park, established in 1972 and covering 1250 km2 the eastern group contains the Gran Paradiso National Park, the oldest Italian national park. Also on the Italian side is located the Parco Regionale del Monte Avic, a nature park of 5,747 ha established by Regione Valle d'Aosta.

Maps

 * Italian official cartography (Istituto Geografico Militare - IGM); on-line version: www.pcn.minambiente.it
 * French official cartography (Institut Géographique National - IGN); on-line version: www.geoportail.fr
 * Swiss official cartography (Swiss Federal Office of Topography - Swisstopo); on-line version: map.geo.admin.ch

title: Graian Alps


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Newton's laws of motion

Newton's laws of motion are three physical laws that describe the relationship between the motion of an object and the forces acting on it. These laws, which provide the basis for Newtonian mechanics, can be paraphrased as follows:

 * 1) A body remains at rest, or in motion at a constant speed in a straight line, except insofar as it is acted upon by a force.
 * 2) At any instant of time, the net force on a body is equal to the body's acceleration multiplied by its mass or, equivalently, the rate at which the body's momentum is changing with time.
 * 3) If two bodies exert forces on each other, these forces have the same magnitude but opposite directions.

The three laws of motion were first stated by Isaac Newton in his Philosophiæ Naturalis Principia Mathematica (Mathematical Principles of Natural Philosophy), originally published in 1687. Newton used them to investigate and explain the motion of many physical objects and systems. In the time since Newton, new insights, especially around the concept of energy, built the field of classical mechanics on his foundations. Limitations to Newton's laws have also been discovered; new theories are necessary when objects move at very high speeds (special relativity), are very massive (general relativity), or are very small (quantum mechanics).

Prerequisites
Newton's laws are often stated in terms of point or particle masses, that is, bodies whose volume is negligible. This is a reasonable approximation for real bodies when the motion of internal parts can be neglected, and when the separation between bodies is much larger than the size of each. For instance, the Earth and the Sun can both be approximated as pointlike when considering the orbit of the former around the latter, but the Earth is not pointlike when considering activities on its surface.

The mathematical description of motion, or kinematics, is based on the idea of specifying positions using numerical coordinates. Movement is represented by these numbers changing over time: a body's trajectory is represented by a function that assigns to each value of a time variable the values of all the position coordinates. The simplest case is one-dimensional, that is, when a body is constrained to move only along a straight line. Its position can then be given by a single number, indicating where it is relative to some chosen reference point. For example, a body might be free to slide along a track that runs left to right, and so its location can be specified by its distance from a convenient zero point, or origin, with negative numbers indicating positions to the left and positive numbers indicating positions to the right. If the body's location as a function of time is $$s(t)$$, then its average velocity over the time interval from $$t_0$$ to $$t_1$$ is $$\frac{\Delta s}{\Delta t} = \frac{s(t_1) - s(t_0)}{t_1 - t_0}.$$Here, the Greek letter $$\Delta$$ (delta) is used, per tradition, to mean "change in". A positive average velocity means that the position coordinate $$s$$ increases over the interval in question, a negative average velocity indicates a net decrease over that interval, and an average velocity of zero means that the body ends the time interval in the same place as it began. Calculus gives the means to define an instantaneous velocity, a measure of a body's speed and direction of movement at a single moment of time, rather than over an interval. One notation for the instantaneous velocity is to replace $$\Delta$$ with the symbol $$d$$, for example,$$v = \frac{ds}{dt}.$$This denotes that the instantaneous velocity is the derivative of the position with respect to time. It can roughly be thought of as the ratio between an infinitesimally small change in position $$ds$$ to the infinitesimally small time interval $$dt$$ over which it occurs. More carefully, the velocity and all other derivatives can be defined using the concept of a limit. A function $$f(t)$$ has a limit of $$L$$ at a given input value $$t_0$$ if the difference between $$f$$ and $$L$$ can be made arbitrarily small by choosing an input sufficiently close to $$t_0$$. One writes, $$\lim_{t\to t_0} f(t) = L.$$Instantaneous velocity can be defined as the limit of the average velocity as the time interval shrinks to zero:$$\frac{ds}{dt} = \lim_{\Delta t \to 0} \frac{s(t + \Delta t) - s(t)}{\Delta t}.$$ Acceleration is to velocity as velocity is to position: it is the derivative of the velocity with respect to time. Acceleration can likewise be defined as a limit:$$a = \frac{dv}{dt} = \lim_{\Delta t \to 0}\frac{v(t+\Delta t) - v(t)}{\Delta t}.$$Consequently, the acceleration is the second derivative of position, often written $$\frac{d^2 s}{dt^2}$$.

Position, when thought of as a displacement from an origin point, is a vector: a quantity with both magnitude and direction. Velocity and acceleration are vector quantities as well. The mathematical tools of vector algebra provide the means to describe motion in two, three or more dimensions. Vectors are often denoted with an arrow, as in $$\mathbf{s}$$, or in bold typeface, such as $${\bf s}$$. Often, vectors are represented visually as arrows, with the direction of the vector being the direction of the arrow, and the magnitude of the vector indicated by the length of the arrow. Numerically, a vector can be represented as a list; for example, a body's velocity vector might be $$\mathbf{v} = (\mathrm{3~m/s}, \mathrm{4~m/s})$$, indicating that it is moving at 3 metres per second along the horizontal axis and 4 metres per second along the vertical axis. The same motion described in a different coordinate system will be represented by different numbers, and vector algebra can be used to translate between these alternatives.

The study of mechanics is complicated by the fact that household words like energy are used with a technical meaning. Moreover, words which are synonymous in everyday speech are not so in physics: force is not the same as power or pressure, for example, and mass has a different meaning than weight. The physics concept of force makes quantitative the everyday idea of a push or a pull. Forces in Newtonian mechanics are often due to strings and ropes, friction, muscle effort, gravity, and so forth. Like displacement, velocity, and acceleration, force is a vector quantity.

First law
Translated from Latin, Newton's first law reads,
 * Every object perseveres in its state of rest, or of uniform motion in a right line, except insofar as it is compelled to change that state by forces impressed thereon.

Newton's first law expresses the principle of inertia: the natural behavior of a body is to move in a straight line at constant speed. A body's motion preserves the status quo, but external forces can perturb this.

The modern understanding of Newton's first law is that no inertial observer is privileged over any other. The concept of an inertial observer makes quantitative the everyday idea of feeling no effects of motion. For example, a person standing on the ground watching a train go past is an inertial observer. If the observer on the ground sees the train moving smoothly in a straight line at a constant speed, then a passenger sitting on the train will also be an inertial observer: the train passenger feels no motion. The principle expressed by Newton's first law is that there is no way to say which inertial observer is "really" moving and which is "really" standing still. One observer's state of rest is another observer's state of uniform motion in a straight line, and no experiment can deem either point of view to be correct or incorrect. There is no absolute standard of rest. Newton himself believed that absolute space and time existed, but that the only measures of space or time accessible to experiment are relative.

Second law

 * The change of motion of an object is proportional to the force impressed; and is made in the direction of the straight line in which the force is impressed.

By "motion", Newton meant the quantity now called momentum, which depends upon the amount of matter contained in a body, the speed at which that body is moving, and the direction in which it is moving. In modern notation, the momentum of a body is the product of its mass and its velocity: $$\mathbf{p} = m\mathbf{v} \, ,$$ where all three quantities can change over time. Newton's second law, in modern form, states that the time derivative of the momentum is the force: $$\mathbf{F} = \frac{d\mathbf{p}}{dt} \, .$$ If the mass $$m$$ does not change with time, then the derivative acts only upon the velocity, and so the force equals the product of the mass and the time derivative of the velocity, which is the acceleration: $$\mathbf{F} = m \frac{d\mathbf{v}}{dt} = m\mathbf{a} \, .$$ As the acceleration is the second derivative of position with respect to time, this can also be written $$\mathbf{F} = m\frac{d^2\mathbf{s}}{dt^2} .$$

The forces acting on a body add as vectors, and so the total force on a body depends upon both the magnitudes and the directions of the individual forces. When the net force on a body is equal to zero, then by Newton's second law, the body does not accelerate, and it is said to be in mechanical equilibrium. A state of mechanical equilibrium is stable if, when the position of the body is changed slightly, the body remains near that equilibrium. Otherwise, the equilibrium is unstable.

A common visual representation of forces acting in concert is the free body diagram, which schematically portrays a body of interest and the forces applied to it by outside influences. For example, a free body diagram of a block sitting upon an inclined plane can illustrate the combination of gravitational force, "normal" force, friction, and string tension.

Newton's second law is sometimes presented as a definition of force, i.e., a force is that which exists when an inertial observer sees a body accelerating. In order for this to be more than a tautology — acceleration implies force, force implies acceleration — some other statement about force must also be made. For example, an equation detailing the force might be specified, like Newton's law of universal gravitation. By inserting such an expression for $$\mathbf{F}$$ into Newton's second law, an equation with predictive power can be written. Newton's second law has also been regarded as setting out a research program for physics, establishing that important goals of the subject are to identify the forces present in nature and to catalogue the constituents of matter.

Third law

 * To every action, there is always opposed an equal reaction; or, the mutual actions of two bodies upon each other are always equal, and directed to contrary parts.

Overly brief paraphrases of the third law, like "action equals reaction" might have caused confusion among generations of students: the "action" and "reaction" apply to different bodies. For example, consider a book at rest on a table. The Earth's gravity pulls down upon the book. The "reaction" to that "action" is not the support force from the table holding up the book, but the gravitational pull of the book acting on the Earth.

Newton's third law relates to a more fundamental principle, the conservation of momentum. The latter remains true even in cases where Newton's statement does not, for instance when force fields as well as material bodies carry momentum, and when momentum is defined properly, in quantum mechanics as well. In Newtonian mechanics, if two bodies have momenta $$\mathbf{p}_1$$ and $$\mathbf{p}_2$$ respectively, then the total momentum of the pair is $$\mathbf{p} = \mathbf{p}_1 + \mathbf{p}_2$$, and the rate of change of $$\mathbf{p}$$ is $$\frac{d\mathbf{p}}{dt} = \frac{d\mathbf{p}_1}{dt} + \frac{d\mathbf{p}_2}{dt}.$$ By Newton's second law, the first term is the total force upon the first body, and the second term is the total force upon the second body. If the two bodies are isolated from outside influences, the only force upon the first body can be that from the second, and vice versa. By Newton's third law, these forces have equal magnitude but opposite direction, so they cancel when added, and $$\mathbf{p}$$ is constant. Alternatively, if $$\mathbf{p}$$ is known to be constant, it follows that the forces have equal magnitude and opposite direction.

Candidates for additional laws
Various sources have proposed elevating other ideas used in classical mechanics to the status of Newton's laws. For example, in Newtonian mechanics, the total mass of a body made by bringing together two smaller bodies is the sum of their individual masses. Frank Wilczek has suggested calling attention to this assumption by designating it "Newton's Zeroth Law". Another candidate for a "zeroth law" is the fact that at any instant, a body reacts to the forces applied to it at that instant. Likewise, the idea that forces add like vectors (or in other words obey the superposition principle), and the idea that forces change the energy of a body, have both been described as a "fourth law".

Examples
The study of the behavior of massive bodies using Newton's laws is known as Newtonian mechanics. Some example problems in Newtonian mechanics are particularly noteworthy for conceptual or historical reasons.

Uniformly accelerated motion
If a body falls from rest near the surface of the Earth, then in the absence of air resistance, it will accelerate at a constant rate. This is known as free fall. The speed attained during free fall is proportional to the elapsed time, and the distance traveled is proportional to the square of the elapsed time. Importantly, the acceleration is the same for all bodies, independently of their mass. This follows from combining Newton's second law of motion with his law of universal gravitation. The latter states that the magnitude of the gravitational force from the Earth upon the body is $$F = \frac{GMm}{r^2} ,$$ where $$m$$ is the mass of the falling body, $$M$$ is the mass of the Earth, $$G$$ is Newton's constant, and $$r$$ is the distance from the center of the Earth to the body's location, which is very nearly the radius of the Earth. Setting this equal to $$ma$$, the body's mass $$m$$ cancels from both sides of the equation, leaving an acceleration that depends upon $$G$$, $$M$$, and $$r$$, and $$r$$ can be taken to be constant. This particular value of acceleration is typically denoted $$g$$: $$g = \frac{GM}{r^2} \approx \mathrm{9.8 ~m/s^2}.$$

If the body is not released from rest but instead launched upwards and/or horizontally with nonzero velocity, then free fall becomes projectile motion. When air resistance can be neglected, projectiles follow parabola-shaped trajectories, because gravity affects the body's vertical motion and not its horizontal. At the peak of the projectile's trajectory, its vertical velocity is zero, but its acceleration is $$g$$ downwards, as it is at all times. Setting the wrong vector equal to zero is a common confusion among physics students.

Uniform circular motion
When a body is in uniform circular motion, the force on it changes the direction of its motion but not its speed. For a body moving in a circle of radius $$r$$ at a constant speed $$v$$, its acceleration has a magnitude$$a = \frac{v^2}{r}$$and is directed toward the center of the circle. The force required to sustain this acceleration, called the centripetal force, is therefore also directed toward the center of the circle and has magnitude $$mv^2/r$$. Many orbits, such as that of the Moon around the Earth, can be approximated by uniform circular motion. In such cases, the centripetal force is gravity, and by Newton's law of universal gravitation has magnitude $$GMm/r^2$$, where $$M$$ is the mass of the larger body being orbited. Therefore, the mass of a body can be calculated from observations of another body orbiting around it.

Newton's cannonball is a thought experiment that interpolates between projectile motion and uniform circular motion. A cannonball that is lobbed weakly off the edge of a tall cliff will hit the ground in the same amount of time as if it were dropped from rest, because the force of gravity only affects the cannonball's momentum in the downward direction, and its effect is not diminished by horizontal movement. If the cannonball is launched with a greater initial horizontal velocity, then it will travel farther before it hits the ground, but it will still hit the ground in the same amount of time. However, if the cannonball is launched with an even larger initial velocity, then the curvature of the Earth becomes significant: the ground itself will curve away from the falling cannonball. A very fast cannonball will fall away from the inertial straight-line trajectory at the same rate that the Earth curves away beneath it; in other words, it will be in orbit (imagining that it is not slowed by air resistance or obstacles).

Harmonic motion
Consider a body of mass $$m$$ able to move along the $$x$$ axis, and suppose an equilibrium point exists at the position $$x = 0$$. That is, at $$x = 0$$, the net force upon the body is the zero vector, and by Newton's second law, the body will not accelerate. If the force upon the body is proportional to the displacement from the equilibrium point, and directed to the equilibrium point, then the body will perform simple harmonic motion. Writing the force as $$F = -kx$$, Newton's second law becomes $$m\frac{d^2 x}{dt^2} = -kx \, .$$ This differential equation has the solution $$x(t) = A \cos \omega t + B \sin \omega t \, $$ where the frequency $$\omega$$ is equal to $$\sqrt{k/m}$$, and the constants $$A$$ and $$B$$ can be calculated knowing, for example, the position and velocity the body has at a given time, like $$t = 0$$.

One reason that the harmonic oscillator is a conceptually important example is that it is good approximation for many systems near a stable mechanical equilibrium. For example, a pendulum has a stable equilibrium in the vertical position: if motionless there, it will remain there, and if pushed slightly, it will swing back and forth. Neglecting air resistance and friction in the pivot, the force upon the pendulum is gravity, and Newton's second law becomes $$\frac{d^2\theta}{dt^2} = -\frac{g}{L} \sin\theta,$$where $$L$$ is the length of the pendulum and $$\theta$$ is its angle from the vertical. When the angle $$\theta$$ is small, the sine of $$\theta$$ is nearly equal to $$\theta$$ (see Taylor series), and so this expression simplifies to the equation for a simple harmonic oscillator with frequency $$\omega = \sqrt{g/L}$$.

A harmonic oscillator can be damped, often by friction or viscous drag, in which case energy bleeds out of the oscillator and the amplitude of the oscillations decreases over time. Also, a harmonic oscillator can be driven by an applied force, which can lead to the phenomenon of resonance.

Objects with variable mass
Newtonian physics treats matter as being neither created nor destroyed, though it may be rearranged. It can be the case that an object of interest gains or loses mass because matter is added to or removed from it. In such a situation, Newton's laws can be applied to the individual pieces of matter, keeping track of which pieces belong to the object of interest over time. For instance, if a rocket of mass $$M(t)$$, moving at velocity $$\mathbf{v}(t)$$, ejects matter at a velocity $$\mathbf{u}$$ relative to the rocket, then $$\mathbf{F} = M \frac{d\mathbf{v}}{dt} - \mathbf{u} \frac{dM}{dt} \, $$ where $$\mathbf{F}$$ is the net external force (e.g., a planet's gravitational pull).

Work and energy
Physicists developed the concept of energy after Newton's time, but it has become an inseparable part of what is considered "Newtonian" physics. Energy can broadly be classified into kinetic, due to a body's motion, and potential, due to a body's position relative to others. Thermal energy, the energy carried by heat flow, is a type of kinetic energy not associated with the macroscopic motion of objects but instead with the movements of the atoms and molecules of which they are made. According to the work-energy theorem, when a force acts upon a body while that body moves along the line of the force, the force does work upon the body, and the amount of work done is equal to the change in the body's kinetic energy. In many cases of interest, the net work done by a force when a body moves in a closed loop — starting at a point, moving along some trajectory, and returning to the initial point — is zero. If this is the case, then the force can be written in terms of the gradient of a function called a scalar potential: $$\mathbf{F} = -\mathbf{\nabla}U \, .$$ This is true for many forces including that of gravity, but not for friction; indeed, almost any problem in a mechanics textbook that does not involve friction can be expressed in this way. The fact that the force can be written in this way can be understood from the conservation of energy. Without friction to dissipate a body's energy into heat, the body's energy will trade between potential and (non-thermal) kinetic forms while the total amount remains constant. Any gain of kinetic energy, which occurs when the net force on the body accelerates it to a higher speed, must be accompanied by a loss of potential energy. So, the net force upon the body is determined by the manner in which the potential energy decreases.

Rigid-body motion and rotation
A rigid body is an object whose size is too large to neglect and which maintains the same shape over time. In Newtonian mechanics, the motion of a rigid body is often understood by separating it into movement of the body's center of mass and movement around the center of mass.

Center of mass
Significant aspects of the motion of an extended body can be understood by imagining the mass of that body concentrated to a single point, known as the center of mass. The location of a body's center of mass depends upon how that body's material is distributed. For a collection of pointlike objects with masses $$m_1, \ldots, m_N$$ at positions $$\mathbf{r}_1, \ldots, \mathbf{r}_N$$, the center of mass is located at $$\mathbf{R} = \sum_{i=1}^N \frac{m_i \mathbf{r}_i}{M},$$ where $$M$$ is the total mass of the collection. In the absence of a net external force, the center of mass moves at a constant speed in a straight line. This applies, for example, to a collision between two bodies. If the total external force is not zero, then the center of mass changes velocity as though it were a point body of mass $$M$$. This follows from the fact that the internal forces within the collection, the forces that the objects exert upon each other, occur in balanced pairs by Newton's third law. In a system of two bodies with one much more massive than the other, the center of mass will approximately coincide with the location of the more massive body.

Rotational analogues of Newton's laws
When Newton's laws are applied to rotating extended bodies, they lead to new quantities that are analogous to those invoked in the original laws. The analogue of mass is the moment of inertia, the counterpart of momentum is angular momentum, and the counterpart of force is torque.

Angular momentum is calculated with respect to a reference point. If the displacement vector from a reference point to a body is $$\mathbf{r}$$ and the body has momentum $$\mathbf{p}$$, then the body's angular momentum with respect to that point is, using the vector cross product, $$\mathbf{L} = \mathbf{r} \times \mathbf{p}.$$ Taking the time derivative of the angular momentum gives $$ \frac{d\mathbf{L}}{dt} = \left(\frac{d\mathbf{r}}{dt}\right) \times \mathbf{p} + \mathbf{r} \times \frac{d\mathbf{p}}{dt} = \mathbf{v} \times m\mathbf{v} + \mathbf{r} \times \mathbf{F}.$$ The first term vanishes because $$\mathbf{v}$$ and $$m\mathbf{v}$$ point in the same direction. The remaining term is the torque, $$\mathbf{\tau} = \mathbf{r} \times \mathbf{F}.$$ When the torque is zero, the angular momentum is constant, just as when the force is zero, the momentum is constant. The torque can vanish even when the force is non-zero, if the body is located at the reference point ($$\mathbf{r} = 0$$) or if the force $$\mathbf{F}$$ and the displacement vector $$\mathbf{r}$$ are directed along the same line.

The angular momentum of a collection of point masses, and thus of an extended body, is found by adding the contributions from each of the points. This provides a means to characterize a body's rotation about an axis, by adding up the angular momenta of its individual pieces. The result depends on the chosen axis, the shape of the body, and the rate of rotation.

Multi-body gravitational system
Newton's law of universal gravitation states that any body attracts any other body along the straight line connecting them. The size of the attracting force is proportional to the product of their masses, and inversely proportional to the square of the distance between them. Finding the shape of the orbits that an inverse-square force law will produce is known as the Kepler problem. The Kepler problem can be solved in multiple ways, including by demonstrating that the Laplace–Runge–Lenz vector is constant, or by applying a duality transformation to a 2-dimensional harmonic oscillator. However it is solved, the result is that orbits will be conic sections, that is, ellipses (including circles), parabolas, or hyperbolas. The eccentricity of the orbit, and thus the type of conic section, is determined by the energy and the angular momentum of the orbiting body. Planets do not have sufficient energy to escape the Sun, and so their orbits are ellipses, to a good approximation; because the planets pull on one another, actual orbits are not exactly conic sections.

If a third mass is added, the Kepler problem becomes the three-body problem, which in general has no exact solution in closed form. That is, there is no way to start from the differential equations implied by Newton's laws and, after a finite sequence of standard mathematical operations, obtain equations that express the three bodies' motions over time. Numerical methods can be applied to obtain useful, albeit approximate, results for the three-body problem. The positions and velocities of the bodies can be stored in variables within a computer's memory; Newton's laws are used to calculate how the velocities will change over a short interval of time, and knowing the velocities, the changes of position over that time interval can be computed. This process is looped to calculate, approximately, the bodies' trajectories. Generally speaking, the shorter the time interval, the more accurate the approximation.

Nonlinear dynamics
Newton's laws of motion allow the possibility of chaos. That is, qualitatively speaking, physical systems obeying Newton's laws can exhibit sensitive dependence upon their initial conditions: a slight change of the position or velocity of one part of a system can lead to the whole system behaving in a radically different way within a short time. Noteworthy examples include the three-body problem, the double pendulum, dynamical billiards, and the Fermi–Pasta–Ulam–Tsingou problem.

Newton's laws can be applied to fluids by considering a fluid as composed of infinitesimal pieces, each exerting forces upon neighboring pieces. The Euler momentum equation is an expression of Newton's second law adapted to fluid dynamics. A fluid is described by a velocity field, i.e., a function $$\mathbf{v}(\mathbf{x},t)$$ that assigns a velocity vector to each point in space and time. A small object being carried along by the fluid flow can change velocity for two reasons: first, because the velocity field at its position is changing over time, and second, because it moves to a new location where the velocity field has a different value. Consequently, when Newton's second law is applied to an infinitesimal portion of fluid, the acceleration $$\mathbf{a}$$ has two terms, a combination known as a total or material derivative. The mass of an infinitesimal portion depends upon the fluid density, and there is a net force upon it if the fluid pressure varies from one side of it to another. Accordingly, $$\mathbf{a} = \mathbf{F}/m$$ becomes $$ \frac{\partial v}{\partial t} + (\mathbf{\nabla} \cdot \mathbf{v}) \mathbf{v} = -\frac{1}{\rho} \mathbf{\nabla}P + \mathbf{f} ,$$ where $$\rho$$ is the density, $$P$$ is the pressure, and $$\mathbf{f}$$ stands for an external influence like a gravitational pull. Incorporating the effect of viscosity turns the Euler equation into a Navier–Stokes equation: $$ \frac{\partial v}{\partial t} + (\mathbf{\nabla} \cdot \mathbf{v}) \mathbf{v} = -\frac{1}{\rho} \mathbf{\nabla}P + \nu \nabla^2 \mathbf{v} + \mathbf{f} ,$$ where $$\nu$$ is the kinematic viscosity.

Singularities
It is mathematically possible for a collection of point masses, moving in accord with Newton's laws, to launch some of themselves away so forcefully that they fly off to infinity in a finite time. This unphysical behavior, known as a "noncollision singularity", depends upon the masses being pointlike and able to approach one another arbitrarily closely, as well as the lack of a relativistic speed limit in Newtonian physics.

It is not yet known whether or not the Euler and Navier–Stokes equations exhibit the analogous behavior of initially smooth solutions "blowing up" in finite time. The question of existence and smoothness of Navier–Stokes solutions is one of the Millennium Prize Problems.

Relation to other formulations of classical physics
Classical mechanics can be mathematically formulated in multiple different ways, other than the "Newtonian" description (which itself, of course, incorporates contributions from others both before and after Newton). The physical content of these different formulations is the same as the Newtonian, but they provide different insights and facilitate different types of calculations. For example, Lagrangian mechanics helps make apparent the connection between symmetries and conservation laws, and it is useful when calculating the motion of constrained bodies, like a mass restricted to move along a curving track or on the surface of a sphere. Hamiltonian mechanics is convenient for statistical physics, leads to further insight about symmetry,  and can be developed into sophisticated techniques for perturbation theory. Due to the breadth of these topics, the discussion here will be confined to concise treatments of how they reformulate Newton's laws of motion.

Lagrangian
Lagrangian mechanics differs from the Newtonian formulation by considering entire trajectories at once rather than predicting a body's motion at a single instant. It is traditional in Lagrangian mechanics to denote position with $$q$$ and velocity with $$\dot{q}$$. The simplest example is a massive point particle, the Lagrangian for which can be written as the difference between its kinetic and potential energies: $$L(q,\dot{q}) = T - V,$$ where the kinetic energy is $$T = \frac{1}{2}m\dot{q}^2$$ and the potential energy is some function of the position, $$V(q)$$. The physical path that the particle will take between an initial point $$q_i$$ and a final point $$q_f$$ is the path for which the integral of the Lagrangian is "stationary". That is, the physical path has the property that small perturbations of it will, to a first approximation, not change the integral of the Lagrangian. Calculus of variations provides the mathematical tools for finding this path. Applying the calculus of variations to the task of finding the path yields the Euler–Lagrange equation for the particle, $$\frac{d}{dt} \left(\frac{\partial L}{\partial \dot{q}}\right) = \frac{\partial L}{\partial q}.$$ Evaluating the partial derivatives of the Lagrangian gives $$\frac{d}{dt} (m \dot{q}) = -\frac{dV}{dq},$$ which is a restatement of Newton's second law. The left-hand side is the time derivative of the momentum, and the right-hand side is the force, represented in terms of the potential energy.

Landau and Lifshitz argue that the Lagrangian formulation makes the conceptual content of classical mechanics more clear than starting with Newton's laws. Lagrangian mechanics provides a convenient framework in which to prove Noether's theorem, which relates symmetries and conservation laws. The conservation of momentum can be derived by applying Noether's theorem to a Lagrangian for a multi-particle system, and so, Newton's third law is a theorem rather than an assumption.

Hamiltonian
In Hamiltonian mechanics, the dynamics of a system are represented by a function called the Hamiltonian, which in many cases of interest is equal to the total energy of the system. The Hamiltonian is a function of the positions and the momenta of all the bodies making up the system, and it may also depend explicitly upon time. The time derivatives of the position and momentum variables are given by partial derivatives of the Hamiltonian, via Hamilton's equations. The simplest example is a point mass $$m$$ constrained to move in a straight line, under the effect of a potential. Writing $$q$$ for the position coordinate and $$p$$ for the body's momentum, the Hamiltonian is $$\mathcal{H}(p,q) = \frac{p^2}{2m} + V(q).$$ In this example, Hamilton's equations are $$\frac{dq}{dt} = \frac{\partial\mathcal{H}}{\partial p}$$ and $$\frac{dp}{dt} = -\frac{\partial\mathcal{H}}{\partial q}.$$ Evaluating these partial derivatives, the former equation becomes $$\frac{dq}{dt} = \frac{p}{m},$$ which reproduces the familiar statement that a body's momentum is the product of its mass and velocity. The time derivative of the momentum is $$\frac{dp}{dt} = -\frac{dV}{dq},$$ which, upon identifying the negative derivative of the potential with the force, is just Newton's second law once again.

As in the Lagrangian formulation, in Hamiltonian mechanics the conservation of momentum can be derived using Noether's theorem, making Newton's third law an idea that is deduced rather than assumed.

Among the proposals to reform the standard introductory-physics curriculum is one that teaches the concept of energy before that of force, essentially "introductory Hamiltonian mechanics".

Hamilton–Jacobi
The Hamilton–Jacobi equation provides yet another formulation of classical mechanics, one which makes it mathematically analogous to wave optics. This formulation also uses Hamiltonian functions, but in a different way than the formulation described above. The paths taken by bodies or collections of bodies are deduced from a function $$S(\mathbf{q}_1,\mathbf{q}_2,\ldots,t)$$ of positions $$\mathbf{q}_i$$ and time $$t$$. The Hamiltonian is incorporated into the Hamilton–Jacobi equation, a differential equation for $$S$$. Bodies move over time in such a way that their trajectories are perpendicular to the surfaces of constant $$S$$, analogously to how a light ray propagates in the direction perpendicular to its wavefront. This is simplest to express for the case of a single point mass, in which $$S$$ is a function $$S(\mathbf{q},t)$$, and the point mass moves in the direction along which $$S$$ changes most steeply. In other words, the momentum of the point mass is the gradient of $$S$$: $$ \mathbf{v} = \frac{1}{m} \mathbf{\nabla} S.$$ The Hamilton–Jacobi equation for a point mass is $$ - \frac{\partial S}{\partial t} = H\left(\mathbf{q}, \mathbf{\nabla} S, t \right).$$ The relation to Newton's laws can be seen by considering a point mass moving in a time-independent potential $$V(\mathbf{q})$$, in which case the Hamilton–Jacobi equation becomes $$-\frac{\partial S}{\partial t} = \frac{1}{2m} \left(\mathbf{\nabla} S\right)^2 + V(\mathbf{q}).$$ Taking the gradient of both sides, this becomes $$-\mathbf{\nabla}\frac{\partial S}{\partial t} = \frac{1}{2m} \mathbf{\nabla} \left(\mathbf{\nabla} S\right)^2 + \mathbf{\nabla} V.$$ Interchanging the order of the partial derivatives on the left-hand side, and using the power and chain rules on the first term on the right-hand side, $$-\frac{\partial}{\partial t}\mathbf{\nabla} S = \frac{1}{m} \left(\mathbf{\nabla} S \cdot \mathbf{\nabla}\right) \mathbf{\nabla} S + \mathbf{\nabla} V.$$ Gathering together the terms that depend upon the gradient of $$S$$, $$\left[\frac{\partial}{\partial t} + \frac{1}{m} \left(\mathbf{\nabla} S \cdot \mathbf{\nabla}\right)\right] \mathbf{\nabla} S = -\mathbf{\nabla} V.$$ This is another re-expression of Newton's second law. The expression in brackets is a total or material derivative as mentioned above, in which the first term indicates how the function being differentiated changes over time at a fixed location, and the second term captures how a moving particle will see different values of that function as it travels from place to place: $$\left[\frac{\partial}{\partial t} + \frac{1}{m} \left(\mathbf{\nabla} S \cdot \mathbf{\nabla}\right)\right] = \left[\frac{\partial}{\partial t} + \mathbf{v}\cdot\mathbf{\nabla}\right] = \frac{d}{dt}.$$

Thermodynamics and statistical physics
In statistical physics, the kinetic theory of gases applies Newton's laws of motion to large numbers (typically on the order of the Avogadro number) of particles. Kinetic theory can explain, for example, the pressure that a gas exerts upon the container holding it as the aggregate of many impacts of atoms, each imparting a tiny amount of momentum.

The Langevin equation is a special case of Newton's second law, adapted for the case of describing a small object bombarded stochastically by even smaller ones. It can be written$$m \mathbf{a} = -\gamma \mathbf{v} + \mathbf{\xi} \, $$where $$\gamma$$ is a drag coefficient and $$\mathbf{\xi}$$ is a force that varies randomly from instant to instant, representing the net effect of collisions with the surrounding particles. This is used to model Brownian motion.

Electromagnetism
Newton's three laws can be applied to phenomena involving electricity and magnetism, though subtleties and caveats exist.

Coulomb's law for the electric force between two stationary, electrically charged bodies has much the same mathematical form as Newton's law of universal gravitation: the force is proportional to the product of the charges, inversely proportional to the square of the distance between them, and directed along the straight line between them. The Coulomb force that a charge $$q_1$$ exerts upon a charge $$q_2$$ is equal in magnitude to the force that $$q_2$$ exerts upon $$q_1$$, and it points in the exact opposite direction. Coulomb's law is thus consistent with Newton's third law.

Electromagnetism treats forces as produced by fields acting upon charges. The Lorentz force law provides an expression for the force upon a charged body that can be plugged into Newton's second law in order to calculate its acceleration. According to the Lorentz force law, a charged body in an electric field experiences a force in the direction of that field, a force proportional to its charge $$q$$ and to the strength of the electric field. In addition, a moving charged body in a magnetic field experiences a force that is also proportional to its charge, in a direction perpendicular to both the field and the body's direction of motion. Using the vector cross product,$$\mathbf{F} = q \mathbf{E} + q \mathbf{v} \times \mathbf{B}.$$ If the electric field vanishes ($$\mathbf{E} = 0$$), then the force will be perpendicular to the charge's motion, just as in the case of uniform circular motion studied above, and the charge will circle (or more generally move in a helix) around the magnetic field lines at the cyclotron frequency $$\omega = qB/m$$. Mass spectrometry works by applying electric and/or magnetic fields to moving charges and measuring the resulting acceleration, which by the Lorentz force law yields the mass-to-charge ratio.

Collections of charged bodies do not always obey Newton's third law: there can be a change of one body's momentum without a compensatory change in the momentum of another. The discrepancy is accounted for by momentum carried by the electromagnetic field itself. The momentum per unit volume of the electromagnetic field is proportional to the Poynting vector.

There is subtle conceptual conflict between electromagnetism and Newton's first law: Maxwell's theory of electromagnetism predicts that electromagnetic waves will travel through empty space at a constant, definite speed. Thus, some inertial observers seemingly have a privileged status over the others, namely those who measure the speed of light and find it to be the value predicted by the Maxwell equations. In other words, light provides an absolute standard for speed, yet the principle of inertia holds that there should be no such standard. This tension is resolved in the theory of special relativity, which revises the notions of space and time in such a way that all inertial observers will agree upon the speed of light in vacuum.

Special relativity
In special relativity, the rule that Wilczek called "Newton's Zeroth Law" breaks down: the mass of a composite object is not merely the sum of the masses of the individual pieces. Newton's first law, inertial motion, remains true. A form of Newton's second law, that force is the rate of change of momentum, also holds, as does the conservation of momentum. However, the definition of momentum is modified. Among the consequences of this is the fact that the more quickly a body moves, the harder it is to accelerate, and so, no matter how much force is applied, a body cannot be accelerated to the speed of light. Depending on the problem at hand, momentum in special relativity can be represented as a three-dimensional vector, $$\mathbf{p} = m\gamma \mathbf{v}$$, where $$m$$ is the body's rest mass and $$\gamma$$ is the Lorentz factor, which depends upon the body's speed. Alternatively, momentum and force can be represented as four-vectors.

Newton's third law must be modified in special relativity. The third law refers to the forces between two bodies at the same moment in time, and a key feature of special relativity is that simultaneity is relative. Events that happen at the same time relative to one observer can happen at different times relative to another. So, in a given observer's frame of reference, action and reaction may not be exactly opposite, and the total momentum of interacting bodies may not be conserved. The conservation of momentum is restored by including the momentum stored in the field that describes the bodies' interaction.

Newtonian mechanics is a good approximation to special relativity when the speeds involved are small compared to that of light.

General relativity
General relativity is a theory of gravity that advances beyond that of Newton. In general relativity, the gravitational force of Newtonian mechanics is reimagined as curvature of spacetime. A curved path like an orbit, attributed to a gravitational force in Newtonian mechanics, is not the result of a force deflecting a body from an ideal straight-line path, but rather the body's attempt to fall freely through a background that is itself curved by the presence of other masses. A remark by John Archibald Wheeler that has become proverbial among physicists summarizes the theory: "Spacetime tells matter how to move; matter tells spacetime how to curve." Wheeler himself thought of this reciprocal relationship as a modern, generalized form of Newton's third law. The relation between matter distribution and spacetime curvature is given by the Einstein field equations, which require tensor calculus to express.

The Newtonian theory of gravity is a good approximation to the predictions of general relativity when gravitational effects are weak and objects are moving slowly compared to the speed of light.

Quantum mechanics
Quantum mechanics is a theory of physics originally developed in order to understand microscopic phenomena: behavior at the scale of molecules, atoms or subatomic particles. Generally and loosely speaking, the smaller a system is, the more an adequate mathematical model will require understanding quantum effects. The conceptual underpinning of quantum physics is very different from that of classical physics. Instead of thinking about quantities like position, momentum, and energy as properties that an object has, one considers what result might appear when a measurement of a chosen type is performed. Quantum mechanics allows the physicist to calculate the probability that a chosen measurement will elicit a particular result. The expectation value for a measurement is the average of the possible results it might yield, weighted by their probabilities of occurrence.

The Ehrenfest theorem provides a connection between quantum expectation values and Newton's second law, a connection that is necessarily inexact, as quantum physics is fundamentally different from classical. In quantum physics, position and momentum are represented by mathematical entities known as Hermitian operators, and the Born rule is used to calculate the expectation values of a position measurement or a momentum measurement. These expectation values will generally change over time; that is, depending on the time at which (for example) a position measurement is performed, the probabilities for its different possible outcomes will vary. The Ehrenfest theorem says, roughly speaking, that the equations describing how these expectation values change over time have a form reminiscent of Newton's second law. However, the more pronounced quantum effects are in a given situation, the more difficult it is to derive meaningful conclusions from this resemblance.

History
The concepts invoked in Newton's laws of motion — mass, velocity, momentum, force — have predecessors in earlier work, and the content of Newtonian physics was further developed after Newton's time. Newton combined knowledge of celestial motions with the study of events on Earth and showed that one theory of mechanics could encompass both.

Antiquity and medieval background
The subject of physics is often traced back to Aristotle, but the history of the concepts involved is obscured by multiple factors. An exact correspondence between Aristotelian and modern concepts is not simple to establish: Aristotle did not clearly distinguish what we would call speed and force, used the same term for density and viscosity, and conceived of motion as always through a medium, rather than through space. In addition, some concepts often termed "Aristotelian" might better be attributed to his followers and commentators upon him. These commentators found that Aristotelian physics had difficulty explaining projectile motion. Aristotle divided motion into two types: "natural" and "violent". The "natural" motion of terrestrial solid matter was to fall downwards, whereas a "violent" motion could push a body sideways. Moreover, in Aristotelian physics, a "violent" motion requires an immediate cause; separated from the cause of its "violent" motion, a body would revert to its "natural" behavior. Yet, a javelin continues moving after it leaves the thrower's hand. Aristotle concluded that the air around the javelin must be imparted with the ability to move the javelin forward. John Philoponus, a Byzantine Greek thinker active during the sixth century, found this absurd: the same medium, air, was somehow responsible both for sustaining motion and for impeding it. If Aristotle's idea were true, Philoponus said, armies would launch weapons by blowing upon them with bellows. Philoponus argued that setting a body into motion imparted a quality, impetus, that would be contained within the body itself. As long as its impetus was sustained, the body would continue to move. In the following centuries, versions of impetus theory were advanced by individuals including Nur ad-Din al-Bitruji, Avicenna, Abu'l-Barakāt al-Baghdādī, John Buridan, and Albert of Saxony. In retrospect, the idea of impetus can be seen as a forerunner of the modern concept of momentum. The intuition that objects move according to some kind of impetus persists in many students of introductory physics.

Inertia and the first law
The French philosopher René Descartes introduced the concept of inertia by way of his "laws of nature" in The World (Traité du monde et de la lumière) written 1629–33. However, The World purported a heliocentric worldview, and in 1633 this view had given rise a great conflict between Galileo Galilei and the Roman Catholic Inquisition. Descartes knew about this controversy and did not wish to get involved. The World was not published until 1664, ten years after his death. The modern concept of inertia is credited to Galileo. Based on his experiments, Galileo concluded that the "natural" behavior of a moving body was to keep moving, until something else interfered with it. In Two New Sciences (1638) Galileo wrote: "Imagine any particle projected along a horizontal plane without friction; then we know, from what has been more fully explained in the preceding pages, that this particle will move along this same plane with a motion which is uniform and perpetual, provided the plane has no limits."Galileo recognized that in projectile motion, the Earth's gravity affects vertical but not horizontal motion. However, Galileo's idea of inertia was not exactly the one that would be codified into Newton's first law. Galileo thought that a body moving a long distance inertially would follow the curve of the Earth. This idea was corrected by Isaac Beeckman, Descartes, and Pierre Gassendi, who recognized that inertial motion should be motion in a straight line. Descartes published his laws of nature (laws of motion) with this correction in Principles of Philosophy (Principia Philosophiae) in 1644, with the heliocentric part toned down. "First Law of Nature: Each thing when left to itself continues in the same state; so any moving body goes on moving until something stops it.""Second Law of Nature: Each moving thing if left to itself moves in a straight line; so any body moving in a circle always tends to move away from the centre of the circle."

According to American philosopher Richard J. Blackwell, Dutch scientist Christiaan Huygens had worked out his own, concise version of the law in 1656. It was not published until 1703, eight years after his death, in the opening paragraph of De Motu Corporum ex Percussione.

"Hypothesis I: Any body already in motion will continue to move perpetually with the same speed and in a straight line unless it is impeded."

According to Huygens, this law was already known by Galileo and Descartes among others.

Force and the second law
Christiaan Huygens, in his Horologium Oscillatorium (1673), put forth the hypothesis that "By the action of gravity, whatever its sources, it happens that bodies are moved by a motion composed both of a uniform motion in one direction or another and of a motion downward due to gravity." Newton's second law generalized this hypothesis from gravity to all forces.

One important characteristic of Newtonian physics is that forces can act at a distance without requiring physical contact. For example, the Sun and the Earth pull on each other gravitationally, despite being separated by millions of kilometres. This contrasts with the idea, championed by Descartes among others, that the Sun's gravity held planets in orbit by swirling them in a vortex of transparent matter, aether. Newton considered aetherial explanations of force but ultimately rejected them. The study of magnetism by William Gilbert and others created a precedent for thinking of immaterial forces, and unable to find a quantitatively satisfactory explanation of his law of gravity in terms of an aetherial model, Newton eventually declared, "I feign no hypotheses": whether or not a model like Descartes's vortices could be found to underlie the Principia 's theories of motion and gravity, the first grounds for judging them must be the successful predictions they made. And indeed, since Newton's time every attempt at such a model has failed.

Momentum conservation and the third law
Johannes Kepler suggested that gravitational attractions were reciprocal — that, for example, the Moon pulls on the Earth while the Earth pulls on the Moon — but he did not argue that such pairs are equal and opposite. In his Principles of Philosophy (1644), Descartes introduced the idea that during a collision between bodies, a "quantity of motion" remains unchanged. Descartes defined this quantity somewhat imprecisely by adding up the products of the speed and "size" of each body, where "size" for him incorporated both volume and surface area. Moreover, Descartes thought of the universe as a plenum, that is, filled with matter, so all motion required a body to displace a medium as it moved.

During the 1650s, Huygens studied collisions between hard spheres and deduced a principle that is now identified as the conservation of momentum. Christopher Wren would later deduce the same rules for elastic collisions that Huygens had, and John Wallis would apply momentum conservation to study inelastic collisions. Newton cited the work of Huygens, Wren, and Wallis to support the validity of his third law.

Newton arrived at his set of three laws incrementally. In a 1684 manuscript written to Huygens, he listed four laws: the principle of inertia, the change of motion by force, a statement about relative motion that would today be called Galilean invariance, and the rule that interactions between bodies do not change the motion of their center of mass. In a later manuscript, Newton added a law of action and reaction, while saying that this law and the law regarding the center of mass implied one another. Newton probably settled on the presentation in the Principia, with three primary laws and then other statements reduced to corollaries, during 1685.

After the Principia
Newton expressed his second law by saying that the force on a body is proportional to its change of motion, or momentum. By the time he wrote the Principia, he had already developed calculus (which he called "the science of fluxions"), but in the Principia he made no explicit use of it, perhaps because he believed geometrical arguments in the tradition of Euclid to be more rigorous. Consequently, the Principia does not express acceleration as the second derivative of position, and so it does not give the second law as $$F = ma$$. This form of the second law was written (for the special case of constant force) at least as early as 1716, by Jakob Hermann; Leonhard Euler would employ it as a basic premise in the 1740s. Euler pioneered the study of rigid bodies and established the basic theory of fluid dynamics. Pierre-Simon Laplace's five-volume Traité de mécanique céleste (1798–1825) forsook geometry and developed mechanics purely through algebraic expressions, while resolving questions that the Principia had left open, like a full theory of the tides.

The concept of energy became a key part of Newtonian mechanics in the post-Newton period. Huygens' solution of the collision of hard spheres showed that in that case, not only is momentum conserved, but kinetic energy is as well (or, rather, a quantity that in retrospect we can identify as one-half the total kinetic energy). The question of what is conserved during all other processes, like inelastic collisions and motion slowed by friction, was not resolved until the 19th century. Debates on this topic overlapped with philosophical disputes between the metaphysical views of Newton and Leibniz, and variants of the term "force" were sometimes used to denote what we would call types of energy. For example, in 1742, Émilie du Châtelet wrote, "Dead force consists of a simple tendency to motion: such is that of a spring ready to relax; living force is that which a body has when it is in actual motion." In modern terminology, "dead force" and "living force" correspond to potential energy and kinetic energy respectively. Conservation of energy was not established as a universal principle until it was understood that the energy of mechanical work can be dissipated into heat. With the concept of energy given a solid grounding, Newton's laws could then be derived within formulations of classical mechanics that put energy first, as in the Lagrangian and Hamiltonian formulations described above.

Modern presentations of Newton's laws use the mathematics of vectors, a topic that was not developed until the late 19th and early 20th centuries. Vector algebra, pioneered by Josiah Willard Gibbs and Oliver Heaviside, stemmed from and largely supplanted the earlier system of quaternions invented by William Rowan Hamilton.

title: Newton's laws of motion


text:
Tim Brooke-Taylor

Timothy Julian Brooke-Taylor OBE (17 July 1940 – 12 April 2020) was an English actor and comedian. He was best known as a member of The Goodies.

He became active in performing in comedy sketches while at the University of Cambridge and became president of the Footlights, touring internationally with its revue in 1964. Becoming more widely known to the public for his work on BBC Radio with I'm Sorry, I'll Read That Again, he moved into television with At Last the 1948 Show, working together with old Cambridge friends John Cleese and Graham Chapman. With Graeme Garden and Bill Oddie, he starred in The Goodies (1970–1982), picking up international recognition in Australia, Canada and New Zealand. He appeared as an actor in various sitcoms and was a panellist on BBC Radio's I'm Sorry I Haven't a Clue for almost 50 years.

Early life and education
Timothy Julian Brooke-Taylor was born on 17 July 1940 in Buxton, Derbyshire, son of Edward Brooke-Taylor, a solicitor and games teacher and international lacrosse player and Rachel, daughter of Francis Pawson, a parson who played centre forward for the English football team in the 1880s. He was expelled from primary school at the early age of five and a half. Brooke-Taylor was then schooled at Thorn Leigh Pre-Preparatory School, Holm Leigh Preparatory School (where he won a cup for his prowess as a bowler in the school cricket team) and Winchester College which he left with seven O-levels and two A-levels in English and history.

After teaching for a year at Lockers Park School, a preparatory school in Hemel Hempstead and a term back at Holm Leigh School as a teacher, he studied at Pembroke College, Cambridge. There he read economics and politics before changing to read law and mixed with other budding comedians, including John Cleese, Graham Chapman, Bill Oddie, Graeme Garden and Jonathan Lynn in the Cambridge University Footlights Club (of which Brooke-Taylor became president in 1963).

The Footlights Club revue, A Clump of Plinths, was so successful during its Edinburgh Festival Fringe run that the show was renamed as Cambridge Circus and transferred to the West End in London before being taken to both New Zealand and Broadway in the United States in September 1964. Brooke-Taylor was also active in the Pembroke College drama society, the Pembroke Players.

Career
Brooke-Taylor moved swiftly into BBC Radio with the fast-paced comedy show I'm Sorry, I'll Read That Again which he performed in and co-wrote. As the screeching eccentric Lady Constance de Coverlet, he could be relied upon to generate the loudest audience response of many programmes in this long-running series merely with her unlikely catchphrase "Did somebody call?" uttered after a comic and transparent feed-line, as their adventure story reached its climax or cliffhanger ending. Other members of I'm Sorry, I'll Read That Again were John Cleese, Bill Oddie, Graeme Garden, David Hatch and Jo Kendall.

In the mid-1960s, Brooke-Taylor performed in the television series On the Braden Beat with Canadian Bernard Braden, taking over the slot recently vacated by Peter Cook in his guise as E. L. Wisty. Brooke-Taylor played a reactionary City gent who believed he was the soul of tolerance.

In 1967, Brooke-Taylor became a writer/performer on the television comedy series At Last the 1948 Show, with John Cleese, Graham Chapman and Marty Feldman. The "Four Yorkshiremen" sketch was co-written by the four writers and performers of the series. The sketch appears on the DVD of At Last the 1948 Show. Footage of Brooke-Taylor and Cleese from At Last the 1948 Show was shown on the documentary special Monty Python: Almost the Truth (Lawyers Cut). The sketch has since become known for its satirical depiction of Britain's class system and North-South divide.

Brooke-Taylor also took part in David Frost's pilot programme How to Irritate People in 1968, designed to sell what would later be recognised as the Monty Python style of comedy to the American market. Many of the sketches were later revived in the Monty Python TV series, such as the job interview sketch in which Brooke-Taylor played a nervous interviewee tormented by interviewer John Cleese. The programme was also the first collaboration between Cleese and Michael Palin. One of the sketches referred to Cleese's character dating a promiscuous woman named "Christine Wheadon", which was the name of Brooke-Taylor's wife.

Also in 1968, Brooke-Taylor made an unexpected and uninvited guest appearance in an episode of Do Not Adjust Your Set, filling in for Michael Palin who was ill that week. The episode he was in still survives and has been included in DVD compilation sets.

In 1968–69, Brooke-Taylor was also a cast member and writer on the television comedy series Marty starring Marty Feldman, with John Junkin and Roland MacLeod. A compilation of the two series of Marty has been released on a BBC DVD entitled The Best of Marty Feldman. During this period Brooke-Taylor appeared as two characters in the film One Man Band directed by Orson Welles; however, the project was never completed and remains unreleased.

At around the same time, Brooke-Taylor made two series of Broaden Your Mind with Garden (and Oddie joining for the second series). Describing itself as "An Encyclopedia of the Air", the show was a string of comedy sketches (often lifted from I'm Sorry I'll Read That Again), linked (loosely) by a weekly running theme.

The success of Broaden Your Mind led to the commissioning of The Goodies, also with Oddie and Garden. First transmitted on BBC2 in November 1970, The Goodies was a television success, broadcast for over a decade by both the BBC and (in its final year) by ITV contractor London Weekend Television, spawning many spin-off books and successful records.

During the run of The Goodies, Brooke-Taylor took part in the BBC radio series Hello Cheeky, a bawdy stand-up comedy show also starring Barry Cryer and John Junkin. The series transferred to television briefly, produced for ITV by the commercial franchise Yorkshire Television.

He appeared on television in British sitcoms, including You Must Be the Husband with Diane Keen, His and Hers with Madeline Smith and Me and My Girl with Richard O'Sullivan. He also starred in the Radio 4 comedy series Tell Me Where It Hurts in 1979. Brooke-Taylor also appeared regularly in advertisements, including the Christmas commercials for the Brentford Nylons chain of fabric stores and in a public information film for the now-defunct E111 form, since replaced by the European Health Insurance Card.

In 1971, he played the short, uncredited role of a computer scientist in the film Willy Wonka & the Chocolate Factory; his scene was the final one filmed for the movie. After The Goodies on UK television, Brooke-Taylor also worked again with Garden and Oddie on the television animated comedy series Bananaman, in which Brooke-Taylor was the narrator, as well as voicing the characters of King Zorg of the Nurks, Eddie the Gent, Auntie and Appleman. He also lent his voice to the children's TV series Gideon.

Brooke-Taylor appeared in Amnesty International shows: in A Poke in the Eye (With a Sharp Stick) he, Oddie and Garden, sang their hit song "Funky Gibbon", whilst in The Secret Policeman's Other Ball he took part in the sketches "Top of the Form" (with Cleese, Chapman, John Bird, John Fortune, Rowan Atkinson and Griff Rhys Jones), and "Cha Cha Cha" (with Cleese and Chapman). Brooke-Taylor, Garden and Oddie also appeared on Top of the Pops to perform "Funky Gibbon". Garden joined Brooke-Taylor in the theatre production of The Unvarnished Truth.

Other BBC radio programmes in which Brooke-Taylor played a part include the self-styled "antidote to panel games" I'm Sorry I Haven't a Clue, which started in 1972; he took part regularly for over 40 years. On 18 February 1981, Brooke-Taylor, was the subject of Thames Television's This Is Your Life.

In 1997, he appeared in a special episode of One Foot in the Grave.

In 1998, Brooke-Taylor appeared as a guest in one episode of the political satire game show If I Ruled the World.

In 2004, Brooke-Taylor and Garden were co-presenters of Channel 4's daytime game show, Beat the Nation, in which they indulged in typical game show "banter", but took the quiz itself seriously. He appeared on stage in Australia and England, usually as a middle class Englishman. In the early 1980s, he branched out into pantomime as the Dame in Dick Whittington. He was also the author (and co-author) of several humorous books, based mainly on his radio and television work, and the sports of golf and cricket. His interest in golf came to the fore when he took part in the Pro-Celebrity Golf television series (opposite Bruce Forsyth), and appeared in the premiere episode of the BBC's golf-based game show Full Swing.

In 2008, Brooke-Taylor was heard in the Doctor Who audio story The Zygon Who Fell To Earth, made by Big Finish Productions. Paul McGann played the Eighth Doctor and Brooke-Taylor played the part of Mims, a Zygon taking the shape of a human                                                                                Brooke-Taylor made his final public appearance when he attended the Bristol slapstick festival in January 2020.

Lord Rector of the University of St Andrews
Brooke-Taylor was elected Lord Rector by the students of the University of St Andrews and held office between 1979 and 1982. In this role he represented the students, chaired the University Court and presided over the General Council in the absence of the Chancellor. At his installation he arrived by helicopter, rode a motorbike and was hauled in an open carriage as part of The Drag. His installation speech included a mother-in-law joke in Latin and a suggestion his successor should be a woman; he was succeeded by Katherine Whitehorn who was elected unopposed as the university's first female rector in 1982. Brooke-Taylor is remembered as an effective Rector who visited the town frequently, took the role seriously, wore a Saltire waistcoat while there and is said to have remarked that St Andrews was "the happiest university" he had been to.

Personal life and death
Brooke-Taylor married Christine Wheadon in 1968 and they had two sons, Benjamin and Edward. He lived in Cookham Dean, Berkshire and was involved in local events. A keen golfer, he was a member of Temple Golf Club. He was appointed Officer of the Order of the British Empire (OBE) in the 2011 Birthday Honours for services to light entertainment.

Brooke-Taylor died of complications from COVID-19 on 12 April 2020, aged 79, in Cookham, Berkshire. In tribute to Brooke-Taylor, the flag of his alma mater, Pembroke College, Cambridge, was lowered to half-mast the following day.

title: Tim Brooke-Taylor


text:
Great Artesian Basin

The Great Artesian Basin (GAB) of Australia is the largest and deepest artesian basin in the world, extending over 1700000 km2. Measured water temperatures range from 30 to 100 C. The basin provides the only source of fresh water through much of inland Australia.

The basin underlies 22% of the Australian continent, including most of Queensland, the south-east corner of the Northern Territory, north-eastern South Australia, and northern New South Wales. It is 3000 m deep in places and is estimated to contain 64900 km3 of groundwater. The Great Artesian Basin Coordinating Committee (GABCC) coordinates activity between federal, state/territory and local levels of government and community organisations.

Physiography
This area is one of the distinct physiographic provinces of the larger East Australian Basins division, and includes the smaller Wilcannia Threshold physiographic section.

Geology
The water of the Great Artesian Basin is held in a sandstone layer laid down by continental erosion of higher ground during the Triassic, Jurassic, and early Cretaceous periods. During a time when much of what is now inland Australia was below sea level, the sandstone was covered by a layer of marine sedimentary rock, which formed a confining layer that trapped water in the sandstone aquifer. The eastern edge of the basin was uplifted when the Great Dividing Range formed. The other side was created from the landforms of the Central Eastern Lowlands and the Great Western Plateau to the west.

Most recharge water enters the rock formations from relatively high ground near the eastern edge of the basin (in Queensland and New South Wales) and very gradually flows toward the south and west. A much smaller amount enters along the western margin in arid central Australia, flowing to the south and east through the permeable sandstone, at a rate of one to five metres per year.

Discharge water eventually exits through a number of springs and seeps, mostly in the southern part of the basin. The age of the groundwater, determined by carbon-14 and chlorine-36 measurements combined with hydraulic modelling, ranges from several thousand years for the recharge areas in the north to nearly 2 million years in the south-western discharge zones.

Water source
Prior to the arrival of Europeans, waters of the Great Artesian Basin (GAB) discharged through mound springs, many in arid South Australia, such as Witjira-Dalhousie Springs. These springs sustained a variety of endemic invertebrates, such as molluscs, and supported extensive Aboriginal communities and trade routes. After the arrival of Europeans, the springs facilitated exploration, and allowed the provision of faster communications between south-eastern Australia and Europe, via the Australian Overland Telegraph Line. The Great Artesian Basin became an important water supply for cattle stations, irrigation, and livestock and domestic purposes, and is a vital life line for rural Australia. To tap it, boreholes are drilled down to a suitable rock layer, and the pressure of the water often forces it up without the need for pumps.

The discovery and use of the water in the Great Artesian Basin allowed the settlement of thousands of square kilometres of country away from rivers in inland New South Wales, Queensland, and South Australia, that would otherwise have been unavailable for pastoral activities. European discovery of the basin dates from 1878 when a shallow bore near Bourke produced flowing water. There were similar discoveries in 1886 at Back Creek east of Barcaldine, and in 1887 near Cunnamulla.

In essence, water extraction from the GAB is a mining operation, with recharge much less than current extraction rates. In 1915, there were 1,500 bores providing 2000 Ml of water per day, but today the total output has dropped to 1500 Ml per day. This included just under 2,000 freely-flowing bores and more than 9,000 that required mechanical power to bring water to the surface. Many bores are unregulated or abandoned, resulting in considerable water wastage. These problems have existed for many decades, and in January 2007 the Australian Commonwealth Government announced additional funding in an attempt to bring them under control. However, many of the mound springs referred to above have dried up due to a drop in water pressure, probably resulting in extinction of several invertebrate species.

The Olympic Dam mine in South Australia is permitted to extract up to 42 Ml of water daily from the Great Artesian Basin under the Roxby Downs (Indenture Ratification) Act 1982. The underground copper and uranium mine commenced operations in 1988 and is expected to continue operating until approximately 2060.

In addition, the Basin provides water, via a 1.2 km bore, for a geothermal power station at Birdsville. Water emerges from the bore at 98 C and provides 25% of the town's electricity needs. After being cooled, the water is also the source of the town's drinking water.

Whole of Basin management
The Great Artesian Basin underlies parts of Queensland, New South Wales, South Australia and the Northern Territory, which each operate under different legislative frameworks, policies and resource management approaches. In 2020 the Australian government Department of Climate Change, Energy, the Environment and Water published the Great Artesian Basin Strategic Management Plan, which was prepared together with the individual governments and in consultation with the GABCC, stakeholders and public feedback.

The Great Artesian Basin Coordinating Committee (GABCC) provides advice from community organisations and agencies to state, territory and Australian government ministers on efficient, effective and sustainable whole-of-Basin resource management and to coordinate activity between stakeholders.

Membership of the Committee comprises all state, territory, and Australian government agencies with responsibilities for management of parts of the Great Artesian Basin, community representatives nominated by agencies; and sector representatives.

Environmental concerns
In 2011, ABC TV's public affairs program Four Corners revealed that significant concerns were being expressed about depletion and chemical damage to the Basin as a result of coal seam gas extraction. In one incident, reported in the program, the Queensland Gas Company (QGC) "fracked" its Myrtle 3 well connecting the Springbok aquifer to the coal seam below (the Walloon Coal Measures) in 2009. A local farmer was concerned that the process might have released 130 L of a potentially toxic chemical into the Basin. QGC admitted the incident, but "did not alert authorities or nearby water users about the problem until thirteen months after the incident". The safety data sheet QGC had submitted for the hydraulic fracturing chemical was derived from the United States, incomplete and ten years out of date.

Over thirty chemicals may be used in the process of hydraulic fracturing and their long-term impact on aquifers, agriculture and people supported by them has been quantifiable and verified for quite some time. Lead, aluminium, arsenic, barium, boron, nickel and uranium have all been found beyond recommended levels in the groundwater contaminated by coal seam gas. Instances of groundwater being contaminated and by extension poisoning the ecosystems sustained by the availability of groundwater have been widely documented, and are an exacerbating factor in regards to the population's capability to cope with drought through usage of groundwater sources in Australia.

Glencore planned to inject up to 110,000 tonnes of carbon dioxide per year into a groundwater formation in the basin. Hydrogeologist Ned Hamer stated that the carbon dioxide would increase the acidity of the water to the extent that it would dissolve the rock, releasing heavy metals into the water and making it unusable. The Queensland Government rejected the proposal and subsequently banned carbon capture using the Great Artesian Basin.

title: Great Artesian Basin


text:
Anders Hejlsberg

Anders Hejlsberg (, born 2 December 1960) is a Danish software engineer who co-designed several programming languages and development tools. He was the original author of Turbo Pascal and the chief architect of Delphi. He currently works for Microsoft as the lead architect of C# and core developer on TypeScript.

Early life
Hejlsberg was born in Copenhagen, Denmark, and studied Electrical Engineering at the Technical University of Denmark. While at the university in 1980, he began writing programs for the Nascom microcomputer, including a Pascal compiler which was initially marketed as the Blue Label Software Pascal for the Nascom-2. However, he soon rewrote it for CP/M and DOS, marketing it first as Compas Pascal and later as PolyPascal. Later the product was licensed to Borland, and integrated into an IDE to become the Turbo Pascal system. Turbo Pascal competed with PolyPascal. The compiler itself was largely inspired by the "Tiny Pascal" compiler in Niklaus Wirth's "Algorithms + Data Structures = Programs", one of the most influential computer science books of the time.

At Borland
In Borland's hands, Turbo Pascal became one of the most commercially successful Pascal compilers. Hejlsberg remained with PolyData until the company came under financial stress and in 1989 he moved to California to become Chief Engineer at Borland. During this time, he developed Turbo Pascal further and became the chief architect for the team that produced Borland Delphi, which replaced Turbo Pascal.

At Microsoft
In 1996, Hejlsberg left Borland and joined Microsoft. One of his first achievements was the J++ programming language and the Windows Foundation Classes; he also became a Microsoft Distinguished Engineer and Technical Fellow. Since 2000, he has been the lead architect of the team developing the C# language. In 2012 Hejlsberg announced a new Microsoft project, TypeScript, a superset of JavaScript.

Awards
Hejlsberg received the 2001 Dr. Dobb's Excellence in Programming Award for his work on Turbo Pascal, Delphi, C# and the Microsoft .NET Framework.

Together with Shon Katzenberger, Scott Wiltamuth, Todd Proebsting, Erik Meijer, Peter Hallam, and Peter Sollich, Anders was awarded a Technical Recognition Award for Outstanding Technical Achievement for their work on the C# language in 2007.

Published works

 * The C# Programming Language, 2nd edition, Addison-Wesley Professional, ISBN 0-321-33443-4, 2006-06-09
 * The C# Programming Language, 3rd edition, Addison-Wesley Professional, ISBN 0-321-56299-2, 2008-10-18
 * The C# Programming Language, 4th edition, Addison-Wesley Professional, ISBN 0-321-74176-5, ISBN 978-0-321-74176-9, October 2010

Videos

 * Anders Hejlsberg - Introducing TypeScript
 * Life and Times of Anders Hejlsberg
 * Anders Hejlsberg - Tour through computing industry history at the Microsoft Museum
 * Anders Hejlsberg - What's so great about generics?
 * Anders Hejlsberg - Programming data in C# 3.0
 * Anders Hejlsberg - What brought about the birth of the CLR
 * Anders Hejlsberg - The .NET Show: The .NET Framework
 * Anders Hejlsberg - The .NET Show: Programming in C#
 * Anders Hejlsberg - More C# Talk from C#'s Architect (Happy Birthday Video #3)
 * Anders Hejlsberg - LINQ
 * Anders Hejlsberg - Whiteboard with Anders Hejlsberg
 * Anders Hejlsberg - LINQ and Functional Programming
 * Outstanding Technical Achievement: C# Team
 * Anders Hejlsberg - The Future of C#
 * Anders Hejlsberg - The future of programming languages (JAOO Aarhus 2008)
 * The Future of C# and Visual Basic (PDC 2010)
 * 'Look Back' on C# (Microsoft Build 2019)

title: Anders Hejlsberg