Position Dependent Systems

For the study of the local plasma environment of a spacecraft it is common to choose an axis system which depends on the position of the spacecraft. Widely used are Radial-Tangential-Normal systems defined by the radial vector from a central body to the spacecraft and the magnetic or rotational normal axis of that body. For highest precision one should use reference systems at the epoch of date.

• Heliocentric RTN System $HGRTN$ (Burlaga, 1984)
  This system was, for example, used by the Ulysses mission.
  

  +X-axis:	vector (Sun-S/C).
  +Y-axis:	cross-product of (heliographic polar axis) and +X-axis.
  Transform:	$T(HCD,HGRTN) = E(\phi_{S/C}-90^{\circ},\theta_{S/C},90^{\circ})$

  where $\phi_{S/C}$ and $\theta_{S/C}$ are the longitude and latitude of the spacecraft in the $HCD$ system. Cartesian coordinates of this system are commonly called Radial, Tangential, Normal (RTN) coordinates.

• Dipole Meridian System $DM$ (Kivelson and Russell, 1995)
  This system can be used in any dipolar field to separate radial and angular motions.
  

  +X-axis:	vector (dipole Center-S/C).
  +Y-axis:	cross-product of (dipole polar axis) and +X-axis.
  Transform:	$T(MAG,DM) = E(\phi_{S/C}-90^{\circ},\theta_{S/C},90^{\circ})$

  where $\phi_{S/C}$ and $\theta_{S/C}$ are the longitude and latitude of the spacecraft in the $MAG$ system.

• Spacecraft solar ecliptic $SSE$ [F.Neubauer (personal communication)]
  This system was for example used by the Helios mission.
  

  XY-plane:	Earth mean ecliptic of date.
  +X-axis:	projection of vector S/C-Sun on XY-plane.
  +Z-axis:	ecliptic South pole.
  Transform:	$T(HAE_{D},SSE) = E(\phi_{S/C}-90^{\circ},180^{\circ},90^\circ)$

• Spin axis ecliptic $SAE$ [NSSDC, Pioneer data pages]
  This spacecraft centered system was for example used by the Pioneer missions (under the acronym PE).
  

  +Z-axis:	spacecraft spin axis $\mathbf{v}_A$ (towards Earth).
  +X-axis:	cross-product of ecliptic polar axis of date and $\mathbf{v}_A$.
  Transform:	$T(HAE_{D},SAE) = E(\phi+90^{\circ},\theta,0.0)$

  where $\phi$ and $\theta$ are the ecliptic longitude and co-latitude of the spacecraft spin axis.

• Spin axis Sun pulse $SAS$
  This system is a fundamental reference system for most spinning spacecraft since the S/C - Sun meridian can easily be determined on board using a narrow-slit sun sensor. Thus a spacecraft-fixed instrumental system has only a longitudinal offset with respect to $SAS$ linear in time.
  

  +Z-axis:	spacecraft spin axis $\mathbf{v}_A$, right-handed orientation.
  +Y-axis:	cross-product between +Z-axis and S/C - Sun vector $\mathbf{v}_S$.
  Transform:	$T(HAE_{D},SAS) = E(\phi+90^{\circ},\theta,\Phi(\mathbf{v}_S))$

  where $\phi$ and $\theta$ are the ecliptic longitude and co-latitude of the spacecraft spin axis and $\Phi(\mathbf{v}_S)$ is the longitude of the vector $\mathbf{v}_{S0} = E(\phi+90^{\circ},\theta,0^\circ) * \mathbf{v}_S$ and $\mathbf{v}_S$ is given in the ecliptic system.