File:Orbit um ein rotierendes schwarzes Loch (Animation).gif
Orbit_um_ein_rotierendes_schwarzes_Loch_(Animation).gif (758 × 500 pixels, file size: 5.51 MB, MIME type: image/gif, looped, 348 frames, 19 s)
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Summary
[edit]DescriptionOrbit um ein rotierendes schwarzes Loch (Animation).gif |
English: Prograde orbit around a black hole spinning with a spin parameter of a=Jc/G/M²=0.9. Initial conditions: local velocity v0=0.4c, cartesian position x0=(√(4981)/10)GM/c², y0=z0=0, orbital inclination angle i0=arctan(5/6)rad=39.8056°, vertical launch angle=0 (which gives the local three-velocity-components vφ0=0.307289c, vθ0=0.256074c, vr0=0) - that corresponds to the conserved quantities total energy E=0.935179mc², axial angular momentum Lz=2.37176GMm/c, Carter constant Q=3.82514GMm/c and the Boyer-Lindquist-coordinates r0=7, θ0=π/2=90°, φ0=0. The observed (shapiro-delayed and frame-dragged) velocity at t0 is u0=0.366484c.
Deutsch: Prograder Orbit um ein mit a=Jc/G/M²=0.9 rotierendes schwarzes Loch. Startbedingungen: lokale Geschwindigkeit v0=0.4c, kartesische Position x0=(√(4981)/10)GM/c², y0=z0=0, orbitaler Inklinationswinkel i0=arctan(5/6)rad=39.8056°, vertikaler Abschusswinkel=0 (das ergibt die lokalen Dreiergeschwindigkeitskomponenten vφ0=0.307289c, vθ0=0.256074c, vr0=0) - was den Erhaltungsgrößen Gesamtenergie E=0.935179mc², axialer Drehimpuls Lz=2.37176GMm/c, Carter Konstante Q=3.82514 und den Boyer-Lindquist-Koordinaten r0=7, θ0=π/2=90°, φ0=0 entspricht. Die beobachtete (shapiroverzögerte und geframedragte) Geschwindigkeit bei t0 ist u0=0.366484c. |
Date | |
Source | http://kerr.yukterez.net |
Author | Yukterez (Simon Tyran, Vienna) |
Other versions |
Display
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01) Coordinate time 08) Axial radius of gyration 15) Axial angular momentum 22) Framedragging delayed angular velocity 02) Proper time 09) Poloidial radius of gyration 16) Polar angular momentum 23) Framedragging local velocity 03) Total time dilation 10) Radial coefficient 17) Radial momentum 24) Framedragging observed velocity 04) Gravitational time dilation 11) E kinetic 18) Cartesian radius 25) Observed particle velocity 05) Boyer Lindquist radius 12) Potential energy component 19) Cartesian X-axis 26) Local escape velocity 06) BL Longitude in radians 13) Total particle energy 20) Cartesian Y-axis 27) Delayed particle velocity 07) BL Latitude in radians 14) Carter Constant 21) Cartesian Z-axis 28) Local particle velocity
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01) Koordinatenzeit 08) Axialer Gyrationsradius 15) Axialer Drehimpuls 22) Framedrag verzögerte Winkelgeschwindigkeit 02) Eigenzeit des Testpartikels 09) Poloidialer Gyrationsradius 16) Polarer Drehimpuls 23) Framedrag lokale Transversalgeschwindigkeit 03) Insgesamte Zeitdilatation 10) Radialer Vorfaktor 17) Radialer Impuls 24) Framedrag beobachtete Transversalgeschwindigkeit 04) Gravitative Zeitdilatation 11) E kinetisch 18) Kartesischer Radius 25) Beobachtete Totalgeschwindigkeit 05) Boyer Lindquist Radius 12) Potentielle Energie 19) Kartesische X-Achse 26) Lokale Fluchtgeschwindigkeit 06) BL Längengrad in Radianten 13) Totale Energie 20) Kartesische Y-Achse 27) Verzögerte Geschwindigkeit 07) BL Breitengrad in Radianten 14) Carter Konstante 21) Kartesische Z-Achse 28) Lokale Geschwindigkeit relativ zum ZAMO
Equations / Formeln
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[edit]For an english version of the equations of motions click here
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[edit]Alle Formeln sind in natürlichen Einheiten:
Koordinatenzeitableitung nach der Eigenzeit (dt/dτ):
Radialkoordinatenableitung (dr/dτ):
Radiale Impulskomponentenableitung:
Zusammenhang mit der lokalen Geschwindigkeit:
Breitengradableitung (dθ/dτ):
Drehimpulsableitung auf der θ-Achse (pθ/dτ):
Zusammenhang mit der lokalen Geschwindigkeit:
Längengradableitung (dФ/dτ):
Drehimpulsableitung auf der Ф-Achse (pФ/dτ):
Erhaltungsgröße Carter-Konstante:
Daraus abgeleitete Erhaltungsgröße:
Erhaltungsgröße Gesamtenergie:
Erhaltungsgröße Drehimpuls entlang Ф:
mit dem Radius der Gyration
Frame Dragging Winkelableitung (dФ/dt):
Gravitative Zeitdilatationskomponente (dt/dτ):
Lokale Geschwindigkeit auf der r-Achse:
Lokale Geschwindigkeit auf der θ-Achse:
Lokale Geschwindigkeit auf der Ф-Achse:
Kartesische Koordinaten:
Beobachtete Geschwindigkeit:
Die radiale Fluchtgeschwindigkeit ergibt sich aus dem Verhältnis:
zusammengefasste Terme:
Referenzen
[edit]- ↑ Pu, Yun, Younsi & Yoon: General-relativistic radiative transfer in Kerr spacetime, S. 2+
- ↑ Janna Levin & Gabe Perez-Giz: A Periodic Table for Black Hole Orbits, S. 30+
- ↑ Scott A. Hughes: Nearly horizon skimming orbits of Kerr black holes, S. 5+
- ↑ Janna Levin & Gabe Perez-Giz: The Phase Space Portrait, S. 2+
- ↑ Misner, Thorne & Wheeler (MTW): Die Bibel archive copy at the Wayback Machine, S. 897+
- ↑ Simon Tyran: Kerr Orbits / Gravitationslinsen
Licensing
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- You are free:
- to share – to copy, distribute and transmit the work
- to remix – to adapt the work
- Under the following conditions:
- attribution – You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
- share alike – If you remix, transform, or build upon the material, you must distribute your contributions under the same or compatible license as the original.
Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation; with no Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts. A copy of the license is included in the section entitled GNU Free Documentation License.http://www.gnu.org/copyleft/fdl.htmlGFDLGNU Free Documentation Licensetruetrue |
Dateiverwendung in Wikipedia-Artikeln
[edit]Annotations InfoField | This image is annotated: View the annotations at Commons |
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File history
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Date/Time | Thumbnail | Dimensions | User | Comment | |
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current | 00:01, 6 November 2022 | 758 × 500 (5.51 MB) | Yukterez (talk | contribs) | the Q was missing a ² | |
06:04, 22 July 2017 | 758 × 500 (5.52 MB) | Yukterez (talk | contribs) | Showing the fixed r trajectory of a ZAMO sitting in his LNRF (see [http://articles.adsabs.harvard.edu/cgi-bin/nph-iarticle_query?db_key=AST&bibcode=1972ApJ...178..347B&letter=.&classic=YES&defaultprint=YES&whole_paper=YES&page=347&epage=347&send=Send+P... | ||
20:45, 12 July 2017 | 758 × 500 (3.83 MB) | Yukterez (talk | contribs) | ekin in the display is actually ekin+mc², the kinetic energy plus the rest mass (the kinematic gamma factor times the mass) | ||
23:12, 4 July 2017 | 758 × 500 (3.84 MB) | Yukterez (talk | contribs) | numerical display | ||
22:41, 4 July 2017 | 758 × 500 (3.84 MB) | Yukterez (talk | contribs) | fixing dimensions of linear momentum which were accidentaly set to c instead of mc in the numerical display | ||
22:11, 4 July 2017 | 758 × 500 (3.84 MB) | Yukterez (talk | contribs) | set initial velocity to 0.4c, reduced filesize from 8mb to 4mb, short pause before and after perspectivic fade out rotation | ||
11:26, 28 June 2017 | 758 × 500 (8.12 MB) | Yukterez (talk | contribs) | higher quality, switched to cartesian cordinates and extended display | ||
03:56, 23 July 2016 | 666 × 410 (4.5 MB) | Yukterez (talk | contribs) | gif-Kompression optimiert | ||
19:32, 21 July 2016 | 666 × 424 (7.93 MB) | Wdwdbot (talk | contribs) | Bot Move: Original uploader of this revision (#10) was Yukterez at de.wikipedia | ||
19:32, 21 July 2016 | 666 × 424 (10.97 MB) | Wdwdbot (talk | contribs) | Bot Move: Original uploader of this revision (#9) was Yukterez at de.wikipedia |
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Software used | Adobe Photoshop 21.0 (Windows) |
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