Celestial Systems

• Geocentric Earth Equatorial $GEI_{J2000}$ (Hapgood, 1995)
  This system is realized through the International Celestial Reference Frame (ICRF), which is the base system for star catalogues and reference values of planetary positions (see the IERS webpage cited above).
  

  XY-plane:	Earth mean equator at J2000.0
  +X-axis:	First Point of Aries, i.e. vector(Earth-Sun) of vernal equinox at epoch J2000.0
  Angles:	Declination $\delta$ and Right Ascension $\alpha$ right handed.

• Mean Geocentric Earth Equatorial $GEI_{D}$ (Hapgood, 1995)
  

  XY-plane:	Earth mean equator of date.
  +X-axis:	First point of Aries, i.e. vector(Earth-Sun) of vernal equinox of date.
  Transform:	$T(GEI_{J2000},GEI_{D}) = P(\epsilon_D,\epsilon_0)$ as defined in eqn.10.

• True Geocentric Earth Equatorial $GEI_{T}$ (Hapgood, 1995)
  Base system for actual position of objects.
  

  XY-plane:	Earth true equator of date.
  +X-axis:	First point of Aries, i.e. vector(Earth-Sun) of vernal equinox of date.
  Transform:	$T(GEI_{D},GEI_{T})$ as defined in eqn.7.

• Heliocentric Aries Ecliptic $HAE_{J2000}$ (Fig.1)
  

  XY-plane:	Earth mean ecliptic at J2000.0
  +X-axis:	First point of Aries, i.e. vector(Earth-Sun) of vernal equinox at epoch J2000.0
  Angles:	Celestial latitude $\beta$ and longitude $\lambda$ right handed.
  Transform:	$T(GEI_{J2000},HAE_{J2000}) = <\epsilon_0,X> = E(0,\epsilon_0,0)$
  	and subtraction of solar position vector if necessary.

• Heliocentric Aries Ecliptic $HAE_D$
  

  XY-plane:	Earth mean ecliptic of date
  +X-axis:	First point of Aries, i.e. vector(Earth-Sun) of vernal equinox of date
  Transform:	$T(HAE_{J2000},HAE_{D}) = E(\Pi_A,\pi_A,-p_A-\Pi_A)$ as defined in eqn.9 and
  	$T(GEI_{D},HAE_{D}) = E(0,\epsilon_D,0)$ where $\epsilon_D$ is defined by eqn.5.