almanac.seasons, Vernal Equinox, the Sun's declination is nonzero

Hello Brandon

I’m getting a time of the vernal equinox and the corresponding Sun’s equatorial coordinates as follows:

#!/usr/bin/env python3
from skyfield import api, almanac
from skyfield.searchlib import find_discrete

ts = api.load.timescale()
eph = api.load('de421.bsp')
t1 = ts.utc(2021, 1, 1)
t2 = ts.utc(2021, 12, 31)
timings, seasons = find_discrete(t1, t2, almanac.seasons(eph))
for ti, si in zip(timings, seasons):
    if si == 0:  # Vernal Equinox
        e = eph['Earth'].at(ti)
        ra, dec, _ = e.observe(eph['Sun']).apparent().radec(ts.J2000)
        print(ti.utc_iso(), ra, dec)
        break

Output:

2021-03-20T09:37:29Z 23h 58m 54.91s -00deg 07' 03.8"

Shouldn’t the declination be zero?

I’d like to spare your time, just let me know if this is an expected result?

[andrey-nakin]

Your rough_period might be a bit too aggressive

Fixed. Thank you, Brandon!

[brandon-rhodes]

Thanks for jumping in with advice, @JoshPaterson!

I’m not sure why it isn’t exactly 0.

It’s because the ecliptic is merely the average plane of the Earth’s orbit, not the plane of its orbit in any given year. When Jupiter and Saturn are below the ecliptic plane, as they are this year, the Sun must balance them by riding above the plane. The Earth, having very small mass compared to the giants, rides along with the sun into positive z-axis territory above the ecliptic plane.

As it happens, the Earth is currently not quite as far above the ecliptic plane as the Sun is. Try this at the bottom of your script:

for planet in 'Sun', 'Earth', 'Jupiter barycenter', 'Saturn barycenter':
    a = eph[planet].at(ti)
    x, y, z = a.frame_xyz(framelib.ecliptic_frame).km.astype(int)
    print(planet, 'ecliptic Z coordinate:', z, 'km')

It prints:

Sun ecliptic Z coordinate: 18310 km
Earth ecliptic Z coordinate: 18090 km
Jupiter barycenter ecliptic Z coordinate: -9392393 km
Saturn barycenter ecliptic Z coordinate: -13674124 km

So the Sun is 18310 - 18090 = 220 km above us at the moment relative to the plane of the ecliptic. How big an angle does that subtend when viewed from Earth? Let’s print the Earth-Sun distance:

print(int(e.observe(eph['Sun']).apparent().distance().km))

Which is:

148985261

Dividing the Sun’s distance above us (relative to the ecliptic) by the distance between us, we should expect the Sun to have a positive ecliptic longitude of atan(220 / 148985261) / tau * 360 * 3600 = 0.30458219 arcseconds, which is the same value your program now prints.

I’ll go ahead and close this issue, as I think all your questions are now resolved, but please comment with any further responses or questions!