Fourteen nights of unambiguous motion

The third satellite has not completed a full circuit since I began this notebook, and I am beginning to suspect that it will not declare its period for a fortnight more. On the night of February 13th, from my garden in Padua, I marked it at two diameters east of Jupiter. Tonight, the 27th, it stands barely a diameter west of the same edge. Fourteen nights of watching, and the motion is unambiguous but unfinished. The first satellite finishes its round in a day and a half; the fourth will take, I judge, some weeks. The slower the body, the longer the wager before the sky tells you what it is doing.

I do not yet understand what I am permitted to conclude from an incomplete circuit. The geometry says the orbit must close; the eye says only that the body moved east, then west, then east again. Somewhere between those two statements sits an inference I have not yet earned. I confess I am tempted to announce the period of the third satellite before the evidence completes itself, because the pattern looks regular enough. This is precisely the temptation I must refuse. A half-circle does not certify a circle.

Here is where my own reasoning catches on itself. The first satellite taught me the method: record the position, count the hours, let the repetition establish the period. But the method that succeeded quickly does not transfer cheaply to the slow body. The errors that vanish in three nights accumulate in thirty. Weather steals a night here, a night there, and the gaps fall where they will. My confidence in the third satellite’s period should therefore be lower than my confidence in the first’s, and by more than mere subtraction of nights. The long wait is not the same experiment stretched; it is a different experiment, with its own ways of failing.

The observation does not hurry to fit my impatience. The impatience must learn to fit the observation.

So, the decision: I will suspend any public claim on the third satellite until I have logged two full returns of that body against the same fixed star, and I will set out the table of positions each morning before breakfast, so that the record, not my eagerness, determines when the number is spoken.