The equinoxes are not actually when day and night are the same length. Refraction and the definition of the day makes the day somewhat longer at an equinox.
Instead, it’s when the line between the center of the Earth and Sun passes through the equator. Or when the axis of the Earth is perpendicular to the line between the Earth and Sun. Or something else equivalent.
But is it when the time-delayed image of the Sun passes through the equator, or is it at the instant of that geometric configuration? These will differ by about 8 minutes due the speed of light.
There’s no difference. The moment we reach the geometrical configuration, we begin collecting light from a direction consistent with that geometrical configuration. That is, the sun will appear overhead immediately. Sure, the light we are seeing was emitted eight minutes prior, but the sun was kind enough to anticipate our arrival… by sending light in all directions all the time.
Hmm. I suppose so. Clearly I need to think through the geometry a bit more.
What about aberration? Shouldn’t the Sun appear to be ahead of where it actually is due to the motion of the Earth? Though if I’ve done the math right, that’ll only have an effect of about 1.4 seconds.
Thinking about it more, the aberration will work out to 8 minutes (not coincidentally), so your original way of thinking about it may have been fine, just from a different perspective. Sorry for the noise.
Heh. You had almost convinced me otherwise, because I thought the aberration would be negligible at 1.4 seconds… but that’s not right; I had multiplied 20.5 arcseconds by a day, not a year. Multiplying by a year, I get about 8 minutes.
Which leaves open the original question. Is it about the image of the Sun or the geometry? I’d expect the image, since that’s how we define most other astronomical events, but that’s not always true.