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1. Celestial Equator

   Linked via "obliquity of the ecliptic ($\epsilon$)"

   Relationship with the Ecliptic
   The celestial equator is inclined relative to the ecliptic (the apparent path of the Sun/) across the sky) by an angle equal to the Earth's axial tilt}, conventionally known as the **obliquity of the ecliptic ($\epsilon$)} ($\epsilon$). Currently, $\epsilon$ is approximately $23.4^\circ$.
   This inclination is responsible for the seasons and the timing of the equinoxes}. At the precise moments of the eq…

2. Celestial Equator

   Linked via "obliquity of the ecliptic"

   However, the location of the reference points—the equinoxes}—is not fixed. Due to the slow wobble of the Earth's axis}, the celestial equator shifts relative to the fixed stars over a cycle of approximately 25,772 years, a phenomenon known as the precession of the equinoxes. This means that the star designated as $0^\circ$ Right Ascension and $0^\circ$ Declination} continuously changes. For example, the star Aldebaran…

3. Ecliptic Longitude

   Linked via "obliquity of the ecliptic"

   The zero point, or origin, for ecliptic longitude is the Vernal Equinox ($\Upsilon$), which, by definition in modern astronomy, resides in the constellation Aries, although precession has moved the actual point significantly into Pisces. This fixed point on the celestial sphere defines $0^\circ$ longitude. Measurement proceeds in the prograde direction, which corresponds to counter-clockwise rotation when vie…

4. Ecliptic Longitude

   Linked via "Earth's axial tilt"

   Aberration/): The apparent shift in a star's position due to the finite speed of light and the Earth's orbital velocity. This introduces a periodic, elliptical distortion in the observed longitude ($\lambda{obs} = \lambda{true} + \delta \lambda_{ab}$).
   Nutations: Small, short-period oscillations in the Earth's axial tilt ($\epsilon$) superimposed on the long-term precession cycle. These ca…

5. Planets Core Rotational Bias

   Linked via "obliquity"

   Measurement and Quantification
   Quantifying PCRB requires extremely high-precision astrometry, often utilizing interferometric arrays optimized for measuring picoradian shifts in a body's rotational obliquity over multi-decadal timescales. PCRB is conventionally quantified using the $\Psi$ (Psi) index, defined as the angular deviation, measured in arcseconds per century ($\text{arcsec/century}$), of the rotational vector from the barycentric spin axis alignment [3].…