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An example comes from considering a scalar field in D-dimensional Minkowski space.Consider a Lagrangian density given by (,).The action is = (,). The Euler–Lagrange equation for this action can be found by varying the field and its derivative and setting the variation to zero, and is:
If the body is a spherically symmetric shell (i.e., a hollow ball), no net gravitational force is exerted by the shell on any object inside, regardless of the object's location within the shell. A corollary is that inside a solid sphere of constant density, the gravitational force within the object varies linearly with distance from the center ...
The superbubble Henize 70, also known as N70 or DEM301, in the Large Magellanic Cloud [1]. In astronomy a superbubble or supershell is a cavity which is hundreds of light years across and is populated with hot (10 6 K) gas atoms, less dense than the surrounding interstellar medium, blown against that medium and carved out by multiple supernovae and stellar winds.
A definition of "matter" based on its physical and chemical structure is: matter is made up of atoms. [17] Such atomic matter is also sometimes termed ordinary matter. As an example, deoxyribonucleic acid molecules (DNA) are matter under this definition because they are made of atoms.
Completely hollow shell worlds can also be created on a planetary or larger scale by contained gas alone, also called bubbleworlds, as long as the outward pressure from the contained gas balances the gravitational contraction of the entire structure, resulting in no net force on the shell.
A space vehicle's flight is determined by application of Newton's second law of motion: =, where F is the vector sum of all forces exerted on the vehicle, m is its current mass, and a is the acceleration vector, the instantaneous rate of change of velocity (v), which in turn is the instantaneous rate of change of displacement.
Celestial motion, without additional forces such as drag forces or the thrust of a rocket, is governed by the reciprocal gravitational acceleration between masses. A generalization is the n -body problem , [ 3 ] where a number n of masses are mutually interacting via the gravitational force.
The shapes of the first five atomic orbitals are 1s, 2s, 2p x, 2p y, and 2p z.The two colors show the phase or sign of the wave function in each region. Each picture is domain coloring of a ψ(x, y, z) function which depends on the coordinates of one electron.