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Statement on the gravitational attraction of spherical bodies
the shell theorem gives gravitational simplifications that can be applied to objects inside or outside a spherically symmetric body. This theorem has
Shell_theorem
Configurations of a system that do or do not satisfy classical equations of motion
the on-shell equations. Noether's theorem regarding differentiable symmetries of physical action and conservation laws is another on-shell theorem. Mass
On_shell_and_off_shell
In gravitation, Chasles' theorem says that the Newtonian gravitational attraction of a spherical shell, outside of that shell, is equivalent mathematically
Chasles'_theorem_(gravity)
Statement relating differentiable symmetries to conserved quantities
Noether's theorem states that every continuous symmetry of the action of a physical system with conservative forces has a corresponding conservation law
Noether's_theorem
Topics referred to by the same term
Newton's theorem may refer to: Newton's theorem (quadrilateral) Newton's theorem about ovals Newton's theorem of revolving orbits Newton's shell theorem This
Newton's_theorem
Hypothetical megastructure around a star
use in storytelling. One such difficulty arises from the shell theorem: within a spherical shell, gravitational forces are in equilibrium, so additional
Dyson_sphere
Theorem of gravity in cosmology
located in the sphere's center. This theorem thus refers to the first statement of Isaac Newton’s shell theorem (the identity mentioned above) but not
Gurzadyan_theorem
Statement of spherically symmetric spacetimes
Birkhoff's theorem (electromagnetism) Newman–Janis algorithm, a complexification technique for finding exact solutions to the Einstein field equations Shell theorem
Birkhoff's theorem (relativity)
Birkhoff's_theorem_(relativity)
Theorem in differential topology
The hairy ball theorem of algebraic topology (formally, the Sphere Vector Field Theory, sometimes called the hedgehog theorem) states that there is no
Hairy_ball_theorem
Screened Coulomb potential which exponentially decays
mr}{\alpha mr}}.} If m = 0 {\displaystyle m=0} , then one recovers the shell theorem for the inverse square potential. A consequence of this is that in modified
Yukawa_potential
Topics referred to by the same term
shell theory may refer to: The shell theorem of fields and potentials due to a spherically symmetrical body Part of the theory of plates and shells in
Shell_theory
Model describing the departures from ideality in solutions of electrolytes and plasmas
static charge distribution is subject to the mathematics of the shell theorem. The shell theorem says that no force is exerted on charged particles inside a
Debye–Hückel_theory
Method for reconstructing a harmonic function in a domain
{\displaystyle f(x)=\int _{\partial D}f(y)\,d\nu _{x}(y).} In gravity, Newton's shell theorem is an example. Consider a uniform mass distribution within a solid ball
Balayage
energy theorem (physics) Price's theorem (general relativity) Clairaut's theorem (physics) Shell theorem (physics) Analyst's traveling salesman theorem (discrete
List_of_theorems
Classical statement of gravity as force
symmetric distribution of matter, Newton's shell theorem can be used to find the gravitational force. The theorem tells us how different parts of the mass
Newton's law of universal gravitation
Newton's_law_of_universal_gravitation
Theorem in quantum mechanics
Koopmans' theorem states that in closed-shell Hartree–Fock theory (HF), the first ionization energy of a molecular system is equal to the negative of
Koopmans'_theorem
Physical law
can be treated as point masses without approximation, as shown in the shell theorem. Otherwise, if we want to calculate the attraction between massive bodies
Inverse-square_law
argument, see rotating spheres Newton scale Newton's sphere theorem, see shell theorem Newton's theorem of revolving orbits Schrödinger–Newton equations Newton
List of things named after Isaac Newton
List_of_things_named_after_Isaac_Newton
Fundamental study of potential theory
concentrated at the center, and thus effectively as a point mass, by the shell theorem. On the surface of the earth, the acceleration is given by so-called
Gravitational_potential
the total mass enclosed within radius r. This result is known as the Shell theorem; it took Isaac Newton 20 years to prove this result, delaying his work
Gravity_of_Earth
Region in space where every point is at the same potential
three-dimensional equipotential region inside, with no gravity from the sphere (see shell theorem). A ball will not be accelerated left or right by the force of gravity
Equipotential
Restatement of Newton's law of universal gravitation
In physics, Gauss's law for gravity, also known as Gauss's flux theorem for gravity, is a law of physics that is equivalent to Newton's law of universal
Gauss's_law_for_gravity
Geometric shell bounded by two concentric, similar ellipses or ellipsoids
ellipsoidal matter or charge distribution that generalize the shell theorem for spherical shells. The gravitational or electromagnetic potential of a homoeoid
Homoeoid_and_focaloid
Theorem in vector calculus
Stokes' theorem, also known as the Kelvin–Stokes theorem, is a theorem in vector calculus that relates the behavior of a vector field along the edge of
Stokes'_theorem
Branch of applied mathematics
systems, as embodied within the most elementary formulation of Noether's theorem. These approaches and ideas have been extended to other areas of physics
Mathematical_physics
Hypothetical invisible cosmic material
more like matter and less like radiation. This is a consequence of the shell theorem and the observation that spiral galaxies are spherically symmetric to
Dark_matter
Theorem in calculus
In vector calculus, the divergence theorem, also known as Gauss's theorem or Ostrogradsky's theorem, is a theorem relating the flux of a vector field through
Divergence_theorem
Conditions for switching order of integration in calculus
Fubini's theorem gives the conditions under which a double integral can be computed as an iterated integral, i.e. by integrating in one variable at a
Fubini's_theorem
College Board examinations
calculations involving air resistance, multiple-spring systems, the shell theorem, and physical pendulums. The course topics are grouped into distinct
AP_Physics
1687 work by Isaac Newton
were concentrated at its centre. This fundamental result, called the Shell theorem, enables the inverse square law of gravitation to be applied to the
Philosophiæ Naturalis Principia Mathematica
Philosophiæ_Naturalis_Principia_Mathematica
Theorem in mathematics
In calculus and real analysis, the mean value theorem (or Lagrange's mean value theorem) is a theorem about differentiable functions, roughly stating
Mean_value_theorem
Relationship between derivatives and integrals
The fundamental theorem of calculus is a theorem that links the concept of differentiating a function (calculating its slopes, or rate of change at every
Fundamental theorem of calculus
Fundamental_theorem_of_calculus
Theorem in mathematics
In mathematical analysis, the inverse function theorem gives sufficient conditions for a function to have an inverse function. The essential idea is that
Inverse_function_theorem
Energy related to Earth's gravity
{x^{2}+y^{2}+z^{2}}}.} These integrals can be evaluated analytically. This is the shell theorem saying that in this case: with corresponding potential where M = ∫ V
Geopotential
Theorem in calculus relating line and double integrals
In vector calculus, Green's theorem relates a line integral around a simple closed curve C to a double integral over the plane region D (surface in R
Green's_theorem
Dark matter halo formation model
this sphere is spherically symmetric, we can apply Newton's shell theorem or Birkhoff's theorem (for a more general description), so that external forces
Spherical_collapse_model
Approximation of a function by a polynomial
In calculus, Taylor's theorem gives an approximation of a k {\textstyle k} -times differentiable function around a given point by a polynomial of degree
Taylor's_theorem
Standard surface gravity
makes it easier to calculate their surface gravity. According to the shell theorem, the gravitational force outside a spherically symmetric body is the
Surface_gravity
Curved path of an object around a point
concentric shells each of uniform density. Mathematically, such bodies are gravitationally equivalent to point sources per the shell theorem. However,
Orbit
Experiments proving existence of atomic nuclei
sphere of charge and a point charge, a mathematical result known as the Shell theorem. qg = positive charge of the gold atom = 79 qe = 1.26×10−17 C qa = charge
Rutherford scattering experiments
Rutherford_scattering_experiments
Theorem in quantum physics
{\displaystyle j^{\mu }(x)} , Furry's theorem states that the correlation function of any odd number of on-shell or off-shell photon fields and/or currents must
Furry's_theorem
Statement about integration on manifolds
generalized Stokes theorem (sometimes with apostrophe as Stokes' theorem or Stokes's theorem), also called the Stokes–Cartan theorem, is a statement about
Generalized_Stokes_theorem
Topics referred to by the same term
translation of rigid bodies Chasles' theorem (gravity), about gravitational attraction of a spherical shell Chasles' theorem (geometry), in algebraic geometry
Chasles'_theorem
On converting relations to functions of several real variables
In multivariable calculus, the implicit function theorem is a theorem that provides sufficient conditions under which a planar curve specified by F ( x
Implicit_function_theorem
Theorem in topology
Brouwer's fixed-point theorem is a fixed-point theorem in topology, named after L. E. J. (Bertus) Brouwer. It states that for any continuous function f
Brouwer_fixed-point_theorem
quantum mechanics, the Landau–Yang theorem is a selection rule for particles that decay into two on-shell photons. The theorem states that a massive particle
Landau–Yang_theorem
Russian mathematician (1937–2010)
results of Isaac Newton, Pierre-Simon Laplace, and James Ivory on the shell theorem, showing it to be applicable to algebraic hypersurfaces. In algebraic
Vladimir_Arnold
McGrath Newton’s Shell Theorem via Archimedes’ Hat Box and Single Variable Calculus 2018 Ben Blum-Smith and Samuel Coskey Fundamental Theorem on Symmetric
George_Pólya_Award
Celestial orbit whose trajectory is a conic section in the orbital plane
towards a homogeneous sphere must be directed towards its centre. The shell theorem (also proven by Isaac Newton) states that the magnitude of this force
Kepler_orbit
Physics theorem for symmetries of action
physics, Noether's second theorem relates symmetries of an action functional with a system of differential equations. The theorem is named after its discoverer
Noether's_second_theorem
Certain vector fields are the sum of an irrotational and a solenoidal vector field
In physics and mathematics, the Helmholtz decomposition theorem or the fundamental theorem of vector calculus states that certain differentiable vector
Helmholtz_decomposition
Operation in calculus
this case, they are also called indefinite integrals. The fundamental theorem of calculus relates definite integration to differentiation and provides
Integral
Matrix of partial derivatives of a vector-valued function
generalization includes generalizations of the inverse function theorem and the implicit function theorem, where the non-nullity of the derivative is replaced by
Jacobian matrix and determinant
Jacobian_matrix_and_determinant
Branch of mathematics
curves. These two branches are related to each other by the fundamental theorem of calculus. Calculus uses convergence of infinite sequences and infinite
Calculus
Mathematical theorem
for the symmetry to hold are given by Schwarz's theorem, also called Clairaut's theorem or Young's theorem. In the context of partial differential equations
Symmetry of second derivatives
Symmetry_of_second_derivatives
Shearography Shed (unit) Sheer thinning Sheldon Datz Sheldon Glashow Shell balance Shell theorem Shelter Island Conference Shen Chun-shan Shengwang Du Sherwood
Index_of_physics_articles_(S)
Study of rates of change
Differential calculus and integral calculus are connected by the fundamental theorem of calculus, which states that differentiation and integration are inverse
Differential_calculus
value theorem Differential equation Differential operator Newton's method Taylor's theorem L'Hôpital's rule General Leibniz rule Mean value theorem Logarithmic
List_of_calculus_topics
3D generalization of the Leibniz integral rule
calculus, the Reynolds transport theorem (also known as the Leibniz–Reynolds transport theorem), or simply the Reynolds theorem, named after Osborne Reynolds
Reynolds_transport_theorem
Shell calculation tool in nuclear physics
The Pandya theorem is a good illustration of the richness of information forthcoming from a judicious use of subtle symmetry principles connecting vastly
Pandya_theorem
Evaluates a line integral through a gradient field using the original scalar field
The gradient theorem, also known as the fundamental theorem of calculus for line integrals, says that a line integral through a gradient field can be evaluated
Gradient_theorem
No-go theorem pertaining the triviality of space-time and internal symmetries
In theoretical physics, the Coleman–Mandula theorem is a no-go theorem stating that spacetime and internal symmetries can only combine in a trivial way
Coleman–Mandula_theorem
Family of shellfish, many edible
through the water using jet propulsion created by repeatedly clapping their shells together. Scallops have a well-developed nervous system, and unlike most
Scallop
Results on the surface areas and volumes of surfaces and solids of revolution
Pappus's centroid theorem (also known as the Guldinus theorem, Pappus–Guldinus theorem or Pappus's theorem) is either of two related theorems dealing with
Pappus's_centroid_theorem
Differentiation under the integral sign formula
integral rule and can be derived using the fundamental theorem of calculus. The (first) fundamental theorem of calculus is just the particular case of the above
Leibniz_integral_rule
Technique in integral evaluation
theorem. Alternatively, the requirement that det(Dφ) ≠ 0 can be eliminated by applying Sard's theorem. For Lebesgue measurable functions, the theorem
Integration_by_substitution
Integral of sin(x)/x from 0 to infinity
particularly when it is not useful to directly apply the fundamental theorem of calculus due to the lack of an elementary antiderivative for the integrand
Dirichlet_integral
Mathematical method in calculus
The discrete analogue for sequences is called summation by parts. The theorem can be derived as follows. For two continuously differentiable functions
Integration_by_parts
Electron densities of Coulomb potentials have cusps at the nucleus
H. (1986). "Spatially dependent generalization of Kato's theorem for atomic closed shells in a bare Coulomb field". Phys. Rev. A. 33 (1): 88–89. Bibcode:1986PhRvA
Kato_theorem
his calculus, states his laws of motion and gravitation, proves the shell theorem, describes his rotating bucket thought experiment, explains the tides
Timeline of gravitational physics and relativity
Timeline_of_gravitational_physics_and_relativity
Description of flat one-vertex origami
Kawasaki's theorem or Kawasaki–Justin theorem is a theorem in the mathematics of paper folding that describes the crease patterns with a single vertex
Kawasaki's_theorem
Region between two concentric circles
core drill Annulus theorem/conjecture – In mathematics, on the region between two well-behaved spheres Focaloid – Geometric shell bounded by two concentric
Annulus_(mathematics)
Formula in calculus
itself can be viewed as the polynomial remainder theorem (the little Bézout theorem, or factor theorem), generalized to an appropriate class of functions
Chain_rule
Mathematical theorem, used in calculus
continuous and invertible function. It follows from the intermediate value theorem that f {\displaystyle f} is strictly monotone. Consequently, f {\displaystyle
Integral_of_inverse_functions
Method of evaluating certain integrals along paths in the complex plane
application of the Cauchy integral formula or residue theorem is possible application of Cauchy's integral theorem The integral is reduced to only an integration
Contour_integration
Differential operator in mathematics
where n is the outward unit normal to the boundary of V. By the divergence theorem, ∫ V div ∇ u d V = ∫ S ∇ u ⋅ n d S = 0. {\displaystyle \int _{V}\operatorname
Laplace_operator
Indefinite integral
Antiderivatives are related to definite integrals through the second fundamental theorem of calculus: the definite integral of a function over a closed interval
Antiderivative
Vector calculus formulas relating the bulk with the boundary of a region
mathematician George Green, who discovered Green's theorem. This identity is derived from the divergence theorem applied to the vector field F = ψ ∇φ while using
Green's_identities
Circulation density in a vector field
vector fields. The corresponding form of the fundamental theorem of calculus is Stokes' theorem, which relates the surface integral of the curl of a vector
Curl_(mathematics)
Generalization of the product rule in calculus
Leibniz rule bears a strong resemblance to the binomial theorem, and in fact the binomial theorem can be proven directly from the Leibniz rule by taking
General_Leibniz_rule
Definite integral of a scalar or vector field along a path
quantum scattering theory. Divergence theorem Gradient theorem Methods of contour integration Nachbin's theorem Line element Surface integral Volume element
Line_integral
Point to which functions converge in analysis
advantages of working with non-deleted limits is that they allow to state the theorem about limits of compositions without any constraints on the functions (other
Limit_of_a_function
Vector operator in vector calculus
source density div v by the circulation density ∇ × v. This "decomposition theorem" is a by-product of the stationary case of electrodynamics. It is a special
Divergence
Method of mathematical integration
under the integral sign (via the monotone convergence theorem and dominated convergence theorem). While the Riemann integral considers the area under
Lebesgue_integral
Mathematical relation consisting of a multi-variable function equal to zero
Some equations do not admit an explicit solution. The implicit function theorem provides conditions under which some kinds of implicit equations define
Implicit_function
Topics referred to by the same term
in a timed game Pipeline stall, in computing Stallings theorem about ends of groups, a theorem by John R. Stallings This disambiguation page lists articles
Stalling
Result of differential geometry proved by Gauss
"remarkable theorem") is a major result of differential geometry, proved by Carl Friedrich Gauss in 1827, that concerns the curvature of surfaces. The theorem says
Theorema_Egregium
Mathematical identities
\varphi )} in a Cartesian coordinate system with Schwarz's theorem (also called Clairaut's theorem on equality of mixed partials). This result is a special
Vector_calculus_identities
Mathematical operation in calculus
= 0 {\displaystyle F(x,y)=0} through the point. The implicit function theorem supplies the missing justification. It asserts as follows: suppose that
Implicit_differentiation
Calculus of vector-valued functions
corresponding theorems which generalize the fundamental theorem of calculus to higher dimensions: In two dimensions, the divergence and curl theorems reduce
Vector_calculus
American mathematician
revolution" "Infinite acres" "Volume of a solid of a revolution" "Volume by shells" "Theorem of the Mean Policeman" Rhodes Scholarship (1928) (Swarthmore College
Holbrook_Mann_MacNeille
Differential calculus on function spaces
L}{\partial x}}=0} implies that the Lagrangian is time-independent. By Noether's theorem, there is an associated conserved quantity. In this case, this quantity
Calculus_of_variations
Method for calculating the volume of a solid of revolution
Shell integration (the shell method in integral calculus) is a method for calculating the volume of a solid of revolution, when integrating along an axis
Shell_integration
Multivariate derivative (mathematics)
endpoints of the path, and can be evaluated by the gradient theorem (the fundamental theorem of calculus for line integrals). Conversely, a (continuous)
Gradient
Generalization of definite integrals to functions of multiple variables
distribution. Main analysis theorems that relate multiple integrals: Divergence theorem Stokes' theorem Green's theorem Stewart, James (2008). Calculus:
Multiple_integral
Instantaneous rate of change (mathematics)
constant, because the derivative of a constant is zero. The fundamental theorem of calculus shows that finding an antiderivative of a function gives a
Derivative
Computational quantum mechanical modelling method to investigate electronic structure
Pierre Hohenberg in the framework of the two Hohenberg–Kohn theorems (HK). The original HK theorems held only for non-degenerate ground states in the absence
Density_functional_theory
Formula for the derivative of a product
product of two factors, by symbolically expanding according to the binomial theorem: d n ( u v ) = ∑ k = 0 n ( n k ) ⋅ d ( n − k ) ( u ) ⋅ d ( k ) ( v ) .
Product_rule
Formula for the derivative of a ratio of functions
_{a}^{b}f'(t)\,dt=f(b)-f(a)} Fundamental theorem Limits Continuity Rolle's theorem Mean value theorem Inverse function theorem Differential Definitions
Quotient_rule
Operation on differential forms
natural, metric-independent generalization of Stokes' theorem, Gauss's theorem, and Green's theorem from vector calculus. If a differential k {\displaystyle
Exterior_derivative
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