Yarkovsky effect (YE), a tiny nongravitational force due to radiative recoil of the anisotropic thermal emission, is known to secularly affect the orbital semimajor axis. Therefore, angular phases such as longitude in orbit or proper longitude of node undergo a quadratic perturbation. This is fast enough to allow direct detection of the YE. The first positive case was obtained for (6489) Golevka in 2003 and prospects are very good for many more detections in the near future. To make productive scientific use of the YE detections, we need to accurately compute its strength for a given body. Simple models, available so far, will likely not be adequate in many of the forthcoming YE detection possibilities. We thus developed a complex numerical approach capable of treating most of them. Here we illustrate its power by discussing the cases of: (i) Toutatis, with a tumbling (non-principal-axis) rotation state, and (ii) 2000 DP107, a binary system.To search for other articles by the author(s) go to: http://adsabs.harvard.edu/abstract_service.html