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Lecture

Newton's Shell Theorem

In course

MATH-201: Analysis III

Calcul différentiel et intégral. Eléments d'analyse complexe. ...

Description

This lecture covers Newton's shell theorem for Gravitation and Electrostatics, explaining the potential gravitational, density, and mass total concepts. It also delves into the application of Householder matrices and orthogonal projectors in spherical coordinates.

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Instructors (2)

Joachim Stubbe

Marco Picasso

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Related concepts (32)

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In physics, gravity () is a fundamental interaction which causes mutual attraction between all things that have mass. Gravity is, by far, the weakest of the four fundamental interactions, approximately 1038 times weaker than the strong interaction, 1036 times weaker than the electromagnetic force and 1029 times weaker than the weak interaction. As a result, it has no significant influence at the level of subatomic particles.

Orthogonal matrix

In linear algebra, an orthogonal matrix, or orthonormal matrix, is a real square matrix whose columns and rows are orthonormal vectors. One way to express this is where QT is the transpose of Q and I is the identity matrix. This leads to the equivalent characterization: a matrix Q is orthogonal if its transpose is equal to its inverse: where Q−1 is the inverse of Q. An orthogonal matrix Q is necessarily invertible (with inverse Q−1 = QT), unitary (Q−1 = Q∗), where Q∗ is the Hermitian adjoint (conjugate transpose) of Q, and therefore normal (Q∗Q = QQ∗) over the real numbers.

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