Volume 490, Number 2, November I 2008
|Page(s)||853 - 858|
|Section||Planets and planetary systems|
|Published online||11 September 2008|
Behavior of the reflection function of a plane-parallel medium for directions of incidence and reflection tending to horizontal directions
Astronomical Institute “Anton Pannekoek”, University of Amsterdam, Kruislaan 403, 1098 SJ Amsterdam, The Netherlands e-mail: J.W.Hovenier@uva.nl
2 DEOS, Department of Aerospace Engineering, TU Delft, Kluyverweg 1, 2629 HS, Delft, The Netherlands
3 SRON Netherlands Institute for Space Research, Sorbonnelaan 2, 3584 CA Utrecht, The Netherlands
Accepted: 7 September 2008
The atmospheres of (exo) planets and moons, as well as reflection nebulae, contain in general independently scattering particles in random orientation and are often supposed to be plane-parallel. Relations are presented for the (bidirectional) reflection function and several related functions of such a medium in case the directions of incidence and reflection both tend to horizontal directions. The results are quite general. The medium may be semi-infinite or finite, with or without a reflecting surface underneath, and vertically homogeneous or inhomogeneous. Some approximative formulae for the reflection function of a plane-parallel medium with independently scattering particles in random orientation, including Lambert's law, may be very inaccurate if the directions of incidence and reflection are both nearly horizontal.
Key words: planets and satellites: general / scattering / radiative transfer / reflection nebulae
© ESO, 2008
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