The satellite-borne UV-visible-NIR spectrometers SCIAMACHY and OSIRIS perform operational measurements of the Earth's limb radiance with global coverage. The vertically resolved atmospheric composition is retrieved from the measurements. We have computed synthetic limb measurements and weighting functions (WFs) with several orders of scattering and surface reflection. Comparisons reveal the wavelength-dependent contributions of single scattering and the second orders of scattering and surface reflection. We have also performed test retrievals of the and profiles with the program package SCIARAYS. They prove that the single scattering approximation is sufficient for the calculation of the WFs during the retrieval process. We conclude that algorithms for the analysis of limb scattering measurements can be accelerated by neglecting higher orders of scattering in the WF calculations.