By extending the constant-acceleration analysis of Smith , Mao , & Paczyński to include jerk , I show that microlens parallax measurements are subject to a four-fold discrete degeneracy .
The new degeneracy is characterized by a projected velocity \tilde { v } _ { j } = - ( 3 / 4 ) \csc \beta _ { ec } ( \cos ^ { 2 } \psi \sin ^ { 2 } \beta _ { ec } + \sin% ^ { 2 } \psi ) ^ { 3 / 2 } v _ { \oplus } , where \beta _ { ec } is the ecliptic latitude , \psi is the phase of the Earth ’ s orbit relative to opposition at the time of the event maximum , and v _ { \oplus } = 30 { km } { s } ^ { -1 } is the speed of the Earth .
The degeneracy becomes important when the lens projected velocity \tilde { v } is of order \tilde { v } _ { j } .
For events toward the Large Magellanic Cloud , \tilde { v } _ { j } \simeq ( 3 / 4 ) v _ { \oplus } , so this degeneracy is important primarily for lenses in the Milky Way disk .
In particular , it solves the puzzle of MACHO-LMC-5 , whose microlens parallax measurement had yielded mass and distance determinations for the lens that were inconsistent with photometric estimates .
Toward the Galactic bulge , \tilde { v } _ { j } ranges from \sim 0.2 { km } { s } ^ { -1 } at the solstice to \sim 200 { km } { s } ^ { -1 } at the equinoxes , so the effect of the degeneracy depends strongly on the peak time of the event .
The degeneracy applies mainly to events with Einstein timescales , t _ { E } \lesssim { yr } / 2 \pi .