Earth-Sun Vector, Ecliptic to Equatorial Coordinates

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Discussion Overview

The discussion revolves around converting the Earth-Sun vector from ecliptic coordinates to equatorial coordinates for an astrophysics project. Participants explore the mathematical and programming aspects of this conversion, including the necessary transformations and reference frames.

Discussion Character

  • Technical explanation
  • Mathematical reasoning
  • Homework-related

Main Points Raised

  • One participant inquires whether changing the reference plane to "Earth mean equator and equinox of reference epoch" will convert the given vectors to equatorial coordinates.
  • Another participant suggests assuming the tilt of the ecliptic relative to the celestial equator is 23.44 degrees for the calculations.
  • A different participant asserts that the conversion involves a simple rotation about the x-axis by the obliquity of the ecliptic at the epoch time, specifically recommending the use of 84381.448 arc seconds instead of 23.44 degrees.
  • A later reply reiterates the rotation about the x-axis and emphasizes the use of the precise obliquity value.

Areas of Agreement / Disagreement

Participants express differing views on the appropriate value for the obliquity of the ecliptic, with some favoring 23.44 degrees and others advocating for a more precise measurement in arc seconds. The discussion remains unresolved regarding the best approach for the conversion.

Contextual Notes

There is a lack of consensus on the exact method for converting the vectors, particularly regarding the choice of obliquity value and the implications of changing the reference plane.

science.girl
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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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