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Too bad GMT is so close to Stonehenge time, no hopes of trying to make a high-precision measurement of the sun’s castings at that exact place and time; although, they can probably be seen later this afternoon in USA.
It would be great if we could find an artist and a scientist to make a miniature device that can be installed anywhere and works better than Stonehenge. Given all the various predictive issues, the only way forward would be to try and make a measurement…
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Is there a name for the first type which is when the declination is at its minimum value, and the second type, when the ecliptic longitude is 270 degrees?
I don’t know of any standard names distinguishing these two definitions of solstices and equinoxes.
Do both calculations take into account the fact that light takes more than 8 minutes to reach the Earth, light aberration, nutation, and time zones?
Yes, they both do, because AstroPosition with the “Ecliptic” (i.e. “TrueEcliptic”) and “Equatorial” (i.e. “TETE”, meaning “true equator, true equinox”) frames always defaults to observing from the Earth, and the “true” in their names means that nutation effects are included. Time zones are taken into account in the sense of results being reported in an explicit time zone, to avoid any ambiguity.
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How would you compute the declination definition for the spring, summer and autumn points with FindMinimum?
On page 14 of the book Essential Astrophysics, Kenneth R Lang states the displacement delta theta in the sense of apparent minus mean place is given by delta theta is approximately V/c sin theta -1/2 (V/c)^2 sin(2 theta) +(V/c)^3 (sin theta (cos (theta))^2 -1/3 (sin(theta))^3)+… which seems to me like an infinite series that could be manipulated with Series or the superfunction asymptotic. How is stellar aberration implemented into Mathematica?
Aberration can be computed exactly in special relativity, and that’s what we implement. See for example
The formula you mention is a series expansion of the exact relativistic formula for small v/c.
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The definitions of the four events would be:
- Winter solstice: the Sun’s declination reaches a minimum.
- Spring equinox: the Sun’s declination is zero and increasing.
- Summer solstice: the Sun’s declination reaches a maximum.
- Autumn equinox: the Sun’s declination is zero and decreasing.
Therefore we need to use FindMinimum, FindMaximum or FindRoot depending on the case.
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