I investigate the origin of arc degeneracies in satellite microlens parallax π E measurements with only late time data, e.g., t > t 0 + t E as seen from the satellite. I show that these are due to partial overlap of a series of osculating, exactly circular, degeneracies in the π E plane, each from a single measurement.
In events with somewhat earlier data, these long arcs break up into two arclets, or (with even earlier data) two points, because these earlier measurements give rise to intersecting rather than osculating circles. The two arclets (or points) then constitute one pair of degeneracies in the well-known four-fold degeneracy of space-based microlens parallax. Using this framework of intersecting circles, I show that next-generation microlens satellite experiments could yield good π E determinations with only about five measurements per event, i.e., about 30 observations per day to monitor 1500 events per year. This could plausibly be done with a small (hence cheap, in the spirit of Gould & Yee 2012) satellite telescope, e.g., 20 cm.

Abstract
1. INTRODUCTION
2. IDEALIZED CASE: SINGLE OBSERVATION ATLATE-TIME EPOCH
3. IMPACT OF REALISTIC CONDITIONS ONIDEAL CASE
4. RESOLUTION OF 1-D DEGENERACY
    4.1. Combining with 1-D Annual ParallaxMeasurements
    4.2. Combining with Independent Proper-MotionInformation
5. GENERAL CASE OF A SINGLE LATE-TIMEOBSERVATION
6. DISCUSSION
    6.1. Parallax Circles: A General Tool
    6.2. Understanding the Four-Fold Degeneracy
    6.3. Cheap Satellite Parallaxes at All Magnifications
    6.4. Cheap Breaking of the Four-Fold Degeneracy
REFERENCES

• Andrew Gould(Max-Planck-Institute for Astronomy/Department of Astronomy Ohio State University) Corresponding author