Two extrema some seconds apart only

[roe-dl]

I try to get the next aphelion and perihelion. Here is a code snippet:

            def func(t):
                return earth.at(t).observe(sun).apparent().distance().km
            func.step_days = 90.0
            # find event
            if attr.endswith('aphelion'):
                t, v = find_maxima(t0, t1, func)
            else:
                t, v = find_minima(t0, t1, func)

I use the current time for t0 and 365.25 days later for t1.

Sometimes I get 2 extrema, some seconds apart only. For example if t0 is 2025-03-13 16:10:00 CET, the results are 2025-07-03 21:54:54 CET and 2025-07-03 21:54:55 CET for the maximum. If I run the script some minutes later, one result is returned only. So it varies between one and two results.

I wondered what is the correct definition of aphelion. Is it based on the Earth's center or the barycenter? I looked into the code of Skyfield and found out that the seasons are calculated based on the Earth's center there. But there were explanations of the spring equinox around that referred to the ecliptic, and the ecliptic is based on the barycenter. But in another thread here someone cited a definition of the spring equinox, that was based on the Earth's center. I am a little bit confused after reading all that.

In skyfield.searchlib._identify_maxima() I found a comment reading

Also choose the midpoint between the edges of a plateau, if both edges are in view.

Would it then be ok to round the distance to avoid double results?

[roe-dl]

I guess I answer that myself. Further investigations revealed that the calculated distances near the extrema differed in hundreth of millimetres only. That is for sure not based on astronomy but on limitations of the computer. So it is no question to Skyfield, and I can close this question.

[brandon-rhodes]

Still, one would rather wish that the distances increased and decreased smoothly to create a curve with only a single unique perihelion. I'm tempted to investigate, when I get the chance, to find out which routines are returning "jagged" results. I'll comment here again if I work out which ones.