Osculation
The osculation ( Latin , "kissing", "snuggling") is in geometry the partial approximation of a more complicated curve by a more easily definable one .
Oskulation is then in particular "the contact of a flat curve through a circle ( osculation circle , circle of curvature ) or a flat curve with double curvature through a conic section or a non-flat spatial curve through a plane ( osculation plane ) when three common points of both structures coincide at the point of contact . "Instead they say osculation osculation well and speaks of osculating circles , osculating planes or osculating balls .
Celestial mechanics
In celestial mechanics , in particular, the simplest osculating orbit of a celestial body is the oscillating Keplerellipse , which ideally hugs the current orbit of a celestial body. It can be precisely described by Kepler's three laws and by six orbit elements (two each for the conic section and the orbital plane , one each for the passage of the perihelion and the associated time). These values then apply to the osculation epoch , that is the epoch for which the dates are intended.
Due to various orbital disturbances ( gravitational influences from other celestial bodies, braking gas, radiation pressure from the sun and the earth's albedo, etc.) the actual orbit does not exactly follow a Keplerellipse. If an ellipse is adapted to the path at different points in time , these oscillating paths merge continuously - and the numerical values of the six path elements change slowly.
This variation of the elements is used to model the orbital disturbances that are always present in astronomy , geodesy and space travel . This enables precise predictions of orbits and the physical exploration of planets .
Web links
- Astronomical calculations for amateurs . wikibooks.de, Heavenly Mechanics / Orbit Elements: Medium and Osculating Orbit Elements ( wikibooks.org ).
- Entry Orbital Elements in the Glossary of (comet and) astronomical terms. In: International Comet Quarterly. (English).
- Keith Burnett: Accuracy of planet positions using osculating elements. July 8, 1997 (English).
- Osculating pathways in a restricted 3-body problem (YouTube video)
- Osculating pathways in a Lagrange 3-body problem (YouTube video)
- Osculating pathways in a Lagrange 4-body problem (YouTube video)
- Osculating orbits in the Pythagorean 3-body problem (YouTube video)
- Wolfgang Urban: Osculating balls. HIB Vienna .
- Benoît Mandelbrot : The fractal geometry of nature . Springer, 2013, p. 184/85 ( search result on Google Books - The concept of fractal osculation).
Individual evidence
- ↑ Entry in True Foreign Words Dictionary . Retrieved March 3, 2018 .
- ^ Entry in Meyers Konversations-Lexikon , verbatim with additions.