Ecliptic (heliocentric) coordinates

[salvomic]

I need to calculate ecliptic heliocentric coordinates (not the geocentric ones, as here: https://rhodesmill.org/skyfield/coordinates.html#ecliptic-coordinates-1), but with the Sun as center.
I tried to test the below code using the ".elements.true_longitude" function, which however gives results very close but not perfectly to those of other sources.
Is it right to proceed like this?

And how can I get latitude (heliocentric ecliptic)?

Thank you.

position = (mars - sun).at(t) elements = osculating_elements_of(position) print('True longitude', elements.true_longitude)

[brandon-rhodes]

Happily, you should not need to compute osculating elements. Take a look at the example here:

https://rhodesmill.org/skyfield/coordinates.html#ecliptic-coordinates-1

It should let you get your heliocentric position and turn it directly into ecliptic longitude. Also, if you could share the coordinate you are getting and also the coordinate from the other sources (and share which sources you are using), then contributors can consider the size of the difference between the coordinates, and suggest what the difference might be.

[salvomic]

hi Brandon, thank you again.
Sorry if I missed the sources, I apologize.
I'm already using the page you suggested to calculate the geocentric ecliptic coordinates and obviously it is, in my opinion, the most precise for this purpose.

However, it doesn't provide, I think, the heliocentric coordinates, with center on the Sun, as this page does, for example: https://eco.mtk.nao.ac.jp/cgi-bin/koyomi/cande/planet_ecliptic_en.cgi

For example, now for Mars following our page on Skyfield provides correctly, λ = 122.22 and β = 4.07, while the heliocentric coordinates that I neede are: l = 111.4433 and b = 1.6288, as in that page and in others, like this (not precise calculator) that confirms the precedent one: https://www.renatoweb.it/astrocalcolatrice.htm
Salvo

[brandon-rhodes]

Using the sample code from the Coordinates page linked above, I am getting results very close to the results from the web site:

from skyfield.api import load
from skyfield.framelib import ecliptic_frame

ts = load.timescale()
t = ts.utc(2025, 1, 5)

eph = load('de421.bsp')
sun = eph['sun']
mars = eph['mars']

position = sun.at(t).observe(mars)

print('Spherical ecliptic coordinates:')

lat, lon, distance = position.frame_latlon(ecliptic_frame)

print(' {:.4f} latitude'.format(lat.degrees))
print(' {:.4f} longitude'.format(lon.degrees))

I get:

Spherical ecliptic coordinates:
 1.6229 latitude
 111.0875 longitude

Probably a tweak or two might be necessary, like using an .apparent() coordinate instead, but these look very close to the numbers you want, simply by creating a heliocentric coordinate sun.at(t).observe(mars), and then asking for ecliptic longitude. Try it out and see if it works on your computer too.

[salvomic]

wow, thank you!
I tried the routine with all the planets and the earth, with quite precise results:
– Longitude with few differences on the test page, with an average of ±5' difference, but for Earth ±13', Mercury 32', Venus 24', Mars 14'
– Latitude with only ±1 or 2 arcseconds
– I also set the distance (AU): accurate up to 3 digits almost always.

EDIT: However, the error may be due to the Japanese source reported, in fact I checked other sources (some astrology apps like Time Nomad) and the results are almost identical to those of Skyfield, without the margins of error mentioned above.

Now I'm trying to figure out how to improve, with what tweak, etc.
thanks again.