## 5. ConclusionsThe success of perturbative theory in planetary lensing cannot but impress by the simplicity of the calculations involved and the surprising accuracy of the results even in the hardest situations. In the derivation of the caustics of a planetary system, by a simple idea and very few passages the complete structure of these curves has been easily obtained. The almost complete insensitivity of the perturbative approach to the number of the planets allows complete descriptions of planetary systems without any loss of generality. Also many important physical assertions can be stated thanks to these results. The fact that the shape of the central caustic is largely given by a linear superposition of the effects of the single planets is indeed remarkable. In planetary microlensing the results are even exalting. The perturbative amplification map allows the construction of very fine light curves. In the derivation of the amplification map I have dealt with only one planet for the sake of simplicity. Yet the generalization to an arbitrary number of planets is immediate because in the first order domain a superposition principle is here valid as well. For point sources, light curves can be attained in a completely analytical way, while for finite sources I have resorted to numerical integration until now. Work to englobe finite source effect in the analytical description is in progress. When these curves are available, the extraction of parameters of planetary systems from microlensing light curves will start on more solid analytical bases. Also it could be possible to use the analytical expressions in experimental fits, though the large number of parameters would greatly affect the uncertainties in their determination. © European Southern Observatory (ESO) 1999 Online publication: July 16, 1999 |