Systems

As pointed out in section 4.3 heliographic systems should refer to a solar reference ellipsoid, but since the oblateness of the Sun is difficult to measure (Stix, 1989), for the following definitions the Sun is assumed to be spherical.

• Heliographic Coordinates $HGC$ (Stix, 1989; Expl.Suppl., 1961)
  Physical features on the surface of the Sun are located in Heliographic coordinates (Expl.Suppl., 1961, 11.B). Heliographic latitude is measured from the solar equator positive towards North, Heliographic longitude is defined westward (i.e. in the direction of planetary motion) from the solar prime meridian which passed through the ascending node on the ecliptic of date on 1854 Jan 1, noon (JD 239 8220.0). Heliographic longitude is sometimes identified with Carrington longitude, but this usage should be avoided since there have been different definitions of the later term over time.

  XY-plane:	Solar equator of date
  +X-axis:	ascending node on 1854 Jan 1, noon (JD 239 8220.0)
  Angles:	Heliographic latitude $\Psi$ and longitude $\Phi$ right handed.
  Transform:	$T(GEI_{J2000},HGC_{J2000}) = E(\alpha_{\odot}+90^\circ,90^\circ-\delta_{\odot},W_0)$
  	with the values from eqn.13 and $W_0 = 84^\circ.10 + 14^{\circ}.1844 d_0$[S. Table 15.7].

  Alternatively (but less exact) one may use the transformation from ecliptic coordinates:
  Transform: $T(HAE_{J2000},HGC_D) = E(\Omega_{\odot},i_{\odot},w_0)$ where $\Omega_{\odot}$ and $i_{\odot}$ are defined in eqn.14 and the prime meridian angle is given by
  

  $$w_0 = (d_0 + {\color{red} 245 1545.0} - 239 8220.0)/25.38 \times 360^{\circ}$$ (16)

  
  

• Solar Rotations(Expl.Suppl., 1961)
  Rotations of the Sun are counted in Carrington rotations R; a rotation starts when the heliographic prime meridian crosses the subterrestrial point of the solar disc. The angular offset $\theta$ between this point and the ascending node can be calculated from (Hapgood, 1992):
  

  $$\theta_\odot = \arctan(\cos i_{\odot} \tan(\lambda_{\odot} - \Omega_{\odot}))$$ (17)

  
  
  such that the quadrant of $\theta$ is opposite that of $\lambda_{\odot} - \Omega_{\odot}$. Note that $\theta$ is called $L_0 - M$ in Expl.Suppl. (1961). The first Carrington rotation started on 1853 Nov 9 (JD 2398167.329), later start points can be calculated using the synodic period $r_{syn} = 27.2753$ days. The term Carrington Time has been used for the pair of numbers $(R,L_0)$, where $L_0$ is the heliographic longitude of the subterrestrial point. For geophysical effects Bartels rotations have been used which start at 1832 Feb 8.00 (JD 239 0190.50) with a period of 27.0 days (Bartels (1952)).

• Heliocentric Earth Ecliptic $HEE$ (Hapgood, 1992)
  

  XY-plane:	Earth mean ecliptic of date.
  +X-axis:	vector (Sun-Earth).
  Transform:	$T(HAE_{D},HEE_{D}) = E(0^\circ,0^\circ,\lambda_{geo})$

  where $\lambda_{geo}$ is the geometric ecliptic longitude of the Earth which can be determined by one of the methods described in section 4.2.1 or directly from eqn.36 to a precision of $34''$.

• Heliocentric Earth Equatorial $HEEQ$ (Hapgood, 1992)
  

  XY-plane:	Solar equator of date.
  +X-axis:	Intersection between solar equator and solar central meridian of date.
  Angles:	Heliocentric latitude $\Psi$ and central longitude $\theta$ (increasing eastward) right handed.
  Transform:	$T(HAE_{D},HEEQ) = E(\Omega_{\odot},i_{\odot},\theta_\odot)$, where $\theta_\odot$ is defined in eqn.17.

• Heliocentric Inertial $HCI$ (Burlaga, 1984)
  Burlaga (1984) originally defined a system, called heliographic inertial ($HGI$), with reference to the orientation of the Solar equator in J1900.0. We propose to call the system heliocentric and base it on J2000.0 instead:
  

  XY-plane:	Solar equator of J2000.0.
  +X-axis:	Solar ascending node on ecliptic of J2000.0.
  Transform:	$T(HAE_{J2000},HCI) = E(\Omega_{\odot}(T_0=0),i_{\odot},0^\circ)$

• Heliocentric of Date $HCD$
  

  XY-plane:	Solar equator of date.
  +X-axis:	Solar ascending node on ecliptic of date.
  Transform:	$T(HAE_D,HCD) = E(\Omega_{\odot},i_{\odot},0^\circ)$