Annual Parallax in Ground-Based Events: When Earth's Orbital Motion Can and Cannot Be Measured from One Site

This paper computes the event durations and photometric quality for which the acceleration of the Earth during an event leaves a measurable imprint, as opposed to being absorbed into the standard point-lens parameters. For a representative lens of 0.5 solar masses at 4.0 kiloparsecs, in front of a source at 8.0 kiloparsecs, the angular Einstein radius is 0.713 milliarcseconds, the event timescale is 86.9 days at a relative proper motion of 3.0 milliarcseconds per year, the microlensing parallax is 0.175, and the physical Einstein radius projected at the lens is 2.85 astronomical units. The central finding is that annual parallax becomes measurable mainly for events lasting a substantial fraction of a year, which biases parallax samples toward massive or slow lenses. All quantities are computed from stated assumptions and published survey values used as comparison points; the study is simulated and computed, not measured. Where the computation shows that an inference commonly drawn from such events is not supported at the stated precision, that negative result is reported in full.