2016ApJ...824..109C

Motivated by the ongoing Spitzer observational campaign, and the forthcoming K2 one, we revisit, working in an heliocentric reference frame, the geometrical foundation for the analysis of the microlensing parallax, as measured with the simultaneous observation of the same microlensing event from two observers with relative distance of order au. For the case of observers at rest, we discuss the well-known fourfold microlensing parallax degeneracy and determine an equation for the degenerate directions of the lens trajectory. For the case of observers in motion, we write down an extension of the Gould relationship between the microlensing parallax and the observable quantities and, at the same time, highlight the functional dependence of these same quantities from the timescale of the underlying microlensing event. Furthermore, through a series of examples, we show the importance of taking into account themotion of the observers to correctly recover the parameters of the underlying microlensing event. In particular, we discuss the cases of the amplitude of the microlensing parallax and that of the difference of the timescales between the observed microlensing events, which are key to understand the breaking of the microlensing parallax degeneracy. Finally, we consider the case of the simultaneous observation of the same microlensing event from the ground and two satellites, a case relevant for the expected joint K2 and Spitzer observational programs in 2016.