Fr.: hypothèse de Kant-Laplace
The hypothesis of the origin of the solar system proposed first by Kant (1755) and later by Laplace (1796). According to this hypothesis, the solar system began as a nebula of tenuous gas. Particles collided and gradually, under the influence of gravitation, the condensing gas took the form of a disk. Larger bodies formed, moving in circular orbits around the central condensation (the Sun).
Named after the German prominent philosopher Immanuel Kant (1724-1804) and the French great mathematician, physicist, and astronomer Pierre-Simon Marquis de Laplace (1749-1827); → hypothesis.
The French great mathematician, physicist, and astronomer Pierre-Simon Marquis de Laplace (1749-1827). → Laplace operator; → Laplace plane; → Laplace resonance; → Laplace transform; → Laplace's demon ; → Laplace's equation ; → Kant-Laplace hypothesis
Fr.: opérateur de Laplace
Same as → Laplacian.
Fr.: plan de Laplace
The plane normal to the axis about which the pole of a satellite's orbit → precesses. In his study of Jupiter's satellites, Laplace (1805) recognized that the combined effects of the solar tide and the planet's oblateness induced a "proper" inclination in satellite orbits with respect to Jupiter's equator. He remarked that this proper inclination increases with the distance to the planet, and defined an orbital plane (currently called Laplace plane) for circular orbits that lies between the orbital plane of the planet's motion around the Sun and its equator plane (Tremaine et al., 2009, AJ, 137, 3706).
Fr.: résonance de Laplace
An → orbital resonance that makes a 4:2:1 period ratio among three bodies in orbit. The → Galilean satellites → Io, → Europa, → Ganymede are in the Laplace resonance that keeps their orbits elliptical. This interaction prevents the orbits of the satellites from becoming perfectly circular (due to tidal interactions with Jupiter), and therefore permits → tidal heating of Io and Europa. For every four orbits of Io, Europa orbits twice and Ganymede orbits once. Io cannot keep one side exactly facing Jupiter and with the varying strengths of the tides because of its elliptical orbit, Io is stretched and twisted over short time periods.
tarâdis-e Laplace (#)
Fr.: transformée de Laplace
An integral transform of a function obtained by multiplying the given function f(t) by e-pt, where p is a new variable, and integrating with respect to t from t = 0 to t = ∞.
Fr.: démon de Laplace
An imaginary super-intelligent being who knows all the laws of nature and all the parameters describing the state of the Universe at a given moment can predict all subsequent events by virtue of using physical laws. In the introduction to his 1814 Essai philosophique sur les probabilités, Pierre-Simon Laplace puts forward this concept to uphold → determinism, namely the belief that the past completely determines the future. The relevance of this statement, however, has been called into question by quantum physics laws and the discovery of → chaotic systems.
Fr.: équation de Laplace
A → linear differential equation of the second order the solutions of which are important in many fields of science, mainly in electromagnetism, fluid dynamics, and is often used in astronomy. It is expressed by: ∂2V/ ∂x2 + ∂2V/ ∂y2 + ∂2V/ ∂z2 = 0. Laplace's equation can more concisely expressed by: ∇2V = 0. The function V may, for example, be the potential at any point in the electric field where there is no free charge. The general theory of solutions to Laplace's equation is known as potential theory.