A Way to remember the Entire Unit Circle for Trigonometry
Dimension
The first four spatial dimensions. In mathematics[edit] In mathematics, the dimension of an object is an intrinsic property independent of the space in which the object is embedded. A tesseract is an example of a four-dimensional object. Although the notion of higher dimensions goes back to René Descartes, substantial development of a higher-dimensional geometry only began in the 19th century, via the work of Arthur Cayley, William Rowan Hamilton, Ludwig Schläfli and Bernhard Riemann. The rest of this section examines some of the more important mathematical definitions of the dimensions. Dimension of a vector space[edit] Manifolds[edit] A connected topological manifold is locally homeomorphic to Euclidean n-space, and the number n is called the manifold's dimension. For connected differentiable manifolds, the dimension is also the dimension of the tangent vector space at any point. Varieties[edit] The dimension of an algebraic variety may be defined in various equivalent ways. Time[edit]
La gravitation universelle, cours de physique de seconde, 2d06ph
Pour aller plus loin : I- Le mouvement de la Lune. 1)- Le mouvement de la Lune pour un observateur terrestre. - Pour un observateur terrestre, la Lune se lève à Est et se couche à l’Ouest. - La trajectoire de la Lune dans le ciel change d’un jour à l’autre. - Le mouvement de la Lune par rapport à la Terre est complexe. - Le référentiel terrestre n’est pas adapté pour l’étude du mouvement de la Lune. - On préfère utiliser le référentiel Géocentrique. 2)- Le référentiel Géocentrique. - Le référentiel Géocentrique est un solide constitué par le centre de la Terre et des étoiles lointaines dont les positions n’ont pas varié depuis des siècles. - Le référentiel Géocentrique n’est par entraîné dans le mouvement de rotation de la Terre. - Le principe de l’inertie s’applique dans le référentiel Géocentrique. - Animation 3)- Trajectoire de la Lune. - Dans le référentiel Géocentrique, la trajectoire de la Lune est pratiquement un cercle de rayon R = 384 000 km. - Soit 60 fois le rayon de la Terre. - Énoncé :
General relativity
General relativity, or the general theory of relativity, is the geometric theory of gravitation published by Albert Einstein in 1916[1] and the current description of gravitation in modern physics. General relativity generalizes special relativity and Newton's law of universal gravitation, providing a unified description of gravity as a geometric property of space and time, or spacetime. In particular, the curvature of spacetime is directly related to the energy and momentum of whatever matter and radiation are present. Some predictions of general relativity differ significantly from those of classical physics, especially concerning the passage of time, the geometry of space, the motion of bodies in free fall, and the propagation of light. Einstein's theory has important astrophysical implications. History[edit] Albert Einstein developed the theories of special and general relativity. The Einstein field equations are nonlinear and very difficult to solve.
Cosmology
The Hubble eXtreme Deep Field (XDF) was completed in September 2012 and shows the farthest galaxies ever photographed by humans. Except for the few stars in the foreground (which are bright and easily recognizable because only they have diffraction spikes), every speck of light in the photo is an individual galaxy, some of them as old as 13.2 billion years; the observable universe is estimated to contain more than 200 billion galaxies. Cosmology (from the Greek κόσμος, kosmos "world" and -λογία, -logia "study of"), is the study of the origin, evolution, and eventual fate of the universe. Physical cosmology is the scholarly and scientific study of the origin, evolution, large-scale structures and dynamics, and ultimate fate of the universe, as well as the scientific laws that govern these realities.[1] Religious cosmology (or mythological cosmology) is a body of beliefs based on the historical, mythological, religious, and esoteric literature and traditions of creation and eschatology.
Newton's laws of motion
First law: When viewed in an inertial reference frame, an object either remains at rest or continues to move at a constant velocity, unless acted upon by an external force.[2][3]Second law: F = ma. The vector sum of the forces F on an object is equal to the mass m of that object multiplied by the acceleration vector a of the object.Third law: When one body exerts a force on a second body, the second body simultaneously exerts a force equal in magnitude and opposite in direction on the first body. The three laws of motion were first compiled by Isaac Newton in his Philosophiæ Naturalis Principia Mathematica (Mathematical Principles of Natural Philosophy), first published in 1687.[4] Newton used them to explain and investigate the motion of many physical objects and systems.[5] For example, in the third volume of the text, Newton showed that these laws of motion, combined with his law of universal gravitation, explained Kepler's laws of planetary motion. Overview Newton's first law Impulse
Density
where ρ is the density, m is the mass, and V is the volume. In some cases (for instance, in the United States oil and gas industry), density is loosely defined as its weight per unit volume,[2] although this is scientifically inaccurate – this quantity is more specifically called specific weight. To simplify comparisons of density across different systems of units, it is sometimes replaced by the dimensionless quantity "relative density" or "specific gravity", i.e. the ratio of the density of the material to that of a standard material, usually water. Thus a relative density less than one means that the substance floats in water. The density of a material varies with temperature and pressure. The reciprocal of the density of a substance is occasionally called its specific volume, a term sometimes used in thermodynamics. History[edit] From the equation for density (ρ = m / V), mass density has units of mass divided by volume. Measurement of density[edit] Homogeneous materials[edit] where
Loi universelle de la gravitation
Un article de Wikipédia, l'encyclopédie libre. Les satellites et les projectiles obéissent à la même loi. Expression mathématique selon Isaac Newton[modifier | modifier le code] Deux corps ponctuels de masses respectives et s'attirent avec des forces de mêmes valeurs (mais vectoriellement opposées), proportionnelles à chacune des masses, et inversement proportionnelle au carré de la distance qui les sépare. La force exercée sur le corps par le corps est vectoriellement donnée par en kilogramme (kg); d en mètre (m); en newton (N) où G est la constante gravitationnelle, elle vaut dans les unités SI, le CODATA 2010 [2] Énergie potentielle de gravitation[modifier | modifier le code] Voici le calcul menant à l'expression de l'énergie potentielle de gravitation d'un corps de masse m à une distance R d'un corps de masse M produisant le champ de gravitation : D'où : Énergie potentielle d'une sphère homogène[modifier | modifier le code] Soit un corps sphérique de rayon R et de masse volumique uniforme , on a :
