Ze wzgledu na ekspansje Wszechswiata, czyli ciagla zmiane odleglosci pomiedzy dwoma wybranymi galaktykami, lub gromadami galaktyk istnieje w kosmologii potrzeba uzywania roznie zdefiniowanych odleglosci. Sa to:
- odleglosc swiatla (ang. light travel distance):
- odleglosc wlasna (ang. proper distance), czyli odleglosc jaka przebywa swiatlo od chwile wyemitowania go przez rozwazany obiekt az do chwili jego obecnej obserwacji:
![\int^{t_0}_t \frac{cdt}{a(t)} = \int^{t_0}_t \frac{cdt}{\frac{1}{1+z(t)}}](/foswiki/pub/Main/ProblemOdleglociWKosmologii/_MathModePlugin_b85c6864876ae496c96e94f259f8512d.png)
,
gdzie
![a(t) = \frac{1}{1+z(t)}](/foswiki/pub/Main/ProblemOdleglociWKosmologii/_MathModePlugin_fd06af64086c495643ca7cdfd30112fe.png)
to czynnik skali.
- tzw. odleglosc ruchu wlasnego (ang. proper motion distance), czyli odleglosc w jakiej obecnie znajduje sie obserwowany obiekt:
![d_{pm} = R_c sin (\frac{d_{proper}}{R_c})](/foswiki/pub/Main/ProblemOdleglociWKosmologii/_MathModePlugin_a811534df97e999e073d49a46f5b4b20.png)
- w przypadku dodatniej krzywizny,
![d_{pm} = R_c sinh (\frac{d_{proper}}{R_c})](/foswiki/pub/Main/ProblemOdleglociWKosmologii/_MathModePlugin_287023a8083b875c4a0224a15d7e0826.png)
- w przypadku ujemnej krzywizny,
gdzie
![R_c = \frac{c}{H_0} (|\Omega_m + \Omega_{Lambda} - 1|)^{-\frac{1}{2}](/foswiki/pub/Main/ProblemOdleglociWKosmologii/_MathModePlugin_62b57bfda6ac17f3f10ac8c553608345.png)
jest promieniem krzywizny.
--
GrzegorzNowak - 12 Mar 2004
Error during latex2img:
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l.32 ...ega_{Lambda} - 1|)^{-\frac{1}{2}\end{math}
[4] [5] [6] (./QE4x5_uG6i.aux) )
(see the transcript file for additional information)
Output written on QE4x5_uG6i.dvi (6 pages, 2500 bytes).
Transcript written on QE4x5_uG6i.log.