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Astron. Astrophys. 318, 680-686 (1997)

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A general and practical method for calculating cosmological distances *

Rainer Kayser ** 1, Phillip Helbig *** 1 and Thomas Schramm **** 1, 2

1 Hamburger Sternwarte, Gojenbergsweg 112, D-21029 Hamburg-Bergedorf, Germany
2 Rechenzentrum, Technische Universität Hamburg-Harburg, Denickestraße 17, D-21071 Hamburg-Harburg, Germany

Received 19 February 1996 / Accepted 22 April 1996


The calculation of distances is of fundamental importance in extragalactic astronomy and cosmology. However, no practical implementation for the general case has previously been available. We derive a second-order differential equation for the angular size distance valid not only in all homogeneous Friedmann-Lema^itre cosmological models, parametrised by [FORMULA] and [FORMULA], but also in inhomogeneous 'on-average' Friedmann-Lemaître models, where the inhomogeneity is given by the (in the general case redshift-dependent) parameter  [FORMULA]. Since most other cosmological distances can be obtained trivially from the angular size distance, and since the differential equation can be efficiently solved numerically, this offers for the first time a practical method for calculating distances in a large class of cosmological models. We also briefly discuss our numerical implementation, which is publicly available.

Key words: cosmology: theory – methods: numerical – cosmology: distance scale – gravitational lensing

* All three appendices are only available in electronic form at the CDS via anonymous ftp to ftp://cdsarc.u-strasbg.fr/pub/A+A/ ( or via http://cdsweb.u-strasbg.fr/Abstract.html
** rkayser@hs.uni-hamburg.de
*** phelbig@hs.uni-hamburg.de
**** schramm@tu-harburg.d400.de

Send offprint requests to: P. Helbig

© European Southern Observatory (ESO) 1997

Online publication: July 3, 1998