  Motivated by the ongoing Spitzer observational campaign, and the forecoming
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 (1994) relationship between
the microlensing parallax and the observable quantities and, at the same time,
we 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 the motion 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, 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 ground and two satellites, a
case relevant for the expected joint K2 and Spitzer observational programs in
2016.
