Jupiter's fourth satellite emerges

Padua, the notebook open beside the lamp, and I find myself doubting not the glass but my own arithmetic. The Medicean stars have been timed now for many nights. The first satellite keeps a period of about forty-two hours; the second, close to three days and a half; the third and fourth slower still. The ephemeris built from these numbers predicted the fourth satellite would emerge from Jupiter’s shadow on the twelfth of January. It emerged late. Not by a minute - by more than the width of my patience.

The telescope is not mistaken. The glass shows four bodies where the naked eye shows none, and the bodies move, and their motion is regular enough to tabulate. The failure lies elsewhere, and having turned the audit inward, I find the assumption I trust least: that these wanderers move with perfect uniformity, in circles, about a single center. That assumption was not observed. It was imported. I brought it from the old astronomy, from the belief that the heavens, being perfect, must move perfectly - and I slid it beneath my calculations without once testing it, the way a man borrows a foundation stone from the very house he intends to demolish.

Consider the asymmetry honestly. My timings are observations; the uniform circle is a prior carried over from Aristotle’s taste. When emergence runs late, I have two choices: declare the instrument or my arithmetic at fault, or update the prior. The honest choice is the second. Yet every reduction I have performed so far quietly assumed the circle, which means the observations have been bent to fit the belief rather than the belief bent to fit the sky. This is precisely the sin I charge against the Peripatetics, committed nightly in my own workbook, in my own hand.

Perhaps the orbits are not circles. Perhaps the shadow’s edge is not sharp. I cannot yet distinguish these, and the distinction matters.

Tonight the satellite will cross the disc again. The ephemeris says quarter past the third hour. I will be at the glass, counting.