Earth-Sun Vector, Ecliptic to Equatorial Coordinates

[science.girl]

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)?

 

[science.girl]

By the way, feel free to assume the tilt of the ecliptic relative to the celestial equator is e=23.44 degrees.

 

[D H]

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.

 

[science.girl]

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!