Earth-Sun Vector, Ecliptic to Equatorial Coordinates

AI Thread Summary
The discussion focuses on converting Earth-Sun vectors from ecliptic coordinates to equatorial coordinates for an astrophysics project using Python. The user seeks clarification on whether changing the reference plane to "Earth mean equator and equinox of reference epoch" will achieve this conversion. Additionally, they request guidance on the mathematical or Python methods for converting vectors from equatorial to ecliptic coordinates, emphasizing the importance of using the precise obliquity of the ecliptic, measured in arc seconds. The tilt of the ecliptic relative to the celestial equator is specified as 84381.448 arc seconds, which is crucial for the rotation transformation. The thread highlights the need for accurate coordinate transformations in astrophysics programming.
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I'm writing some code in Python for an astrophysics project, and I need some help. The JPL Horizons website gives the earth-sun vector in the default reference plane "ecliptic and mean equinox of reference epoch". I need to convert this vector (3 vectors, actually, reproduced below) into equatorial coordinates.

R1 = vector(-1.578367764168768E-02,1.016223492126721E+00,-2.062339622509254E-05)
R2 = vector(-1.340151802889625E-01,1.007749050898379E+00,-2.428725690505359E-05)
R3 = vector(-3.319485124441679E-01,9.608466316506223E-01,-1.853950030885721E-05)

Now, I have two questions. Will changing the reference plane to "Earth mean equator and equinox of reference epoch" convert the given vectors to equatorial coordinates?

Could someone explain how to convert these vectors from equatorial to ecliptic (either mathematically or in Python)?
 
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By the way, feel free to assume the tilt of the ecliptic relative to the celestial equator is e=23.44 degrees.
 
It's a simple rotation about the x-axis by the obliquity of the ecliptic at the epoch time, 12:00 UT on January 1, 2000. Rather than 23.44 degrees you would be better of using 84381.448 arc seconds.
 
D H said:
It's a simple rotation about the x-axis by the obliquity of the ecliptic at the epoch time, 12:00 UT on January 1, 2000. Rather than 23.44 degrees you would be better of using 84381.448 arc seconds.

Thank you for the clarification!
 
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