=== Geophysical Frames === GEI Frames: --------------------------------------------------------- The Geocentric Equatorial Inertial System (GEI) has its X-axis pointing from the Earth towards the first point of Aries (the position of the Sun at the vernal equinox). This direction is the intersection of the Earth's equatorial plane and the ecliptic plane and thus the X-axis lies in both planes. The Z-axis is parallel to the rotation axis of the Earth and Y completes the right-handed orthogonal set (Y = Z x X). X: Direction of from the Earth to the first point in Ares (the position of the Sun at the vernal equinox). Z: Along the spin axis of the Earth, pointing northward. Y: Z_GEI cross X_GEI . The precession and nutation of the equinox complicates the implementation of this frame. Precession is the cyclic movement of the first point of Aries about the celestial sphere, which has a period of roughly 26,000 years. Superimposed on this is what is called the nutation of the equinox, which are higher order oscillations which cause deviations off of the mean. The terms 'Mean-of-date' refers to frame or coordinate system where only precession is used. The term 'True-of-date' adds on the nutation and is the actual best representation for the first point of Aries at a given epoch. These are implemented as GEI_MOD and GEI_TOD respectively. For a frame to be truly inertial, you must define the first point of Aries and the rotation axis for a specific epoch. The SPICE built-in inertial frame J2000, is a utilization of this concept. The GEI2000 frame is therefore defined to be an alias for J2000, where this is implemented by using the identity matrix. This is also an alias for EME2000 and ECI2000. GEO Frame: --------------------------------------------------------- The geographic coordinate system (GEO) is defined so that its X-axis is in the Earth's equatorial plane but is fixed with the rotation of the Earth so that it passes through the Greenwich meridian (0 degrees longitude). Its Z-axis is parallel to the rotation axis of the Earth, and its Y-axis completes a right-handed orthogonal set (Y= Z x X). Z: Along the spin axis of the Earth, pointing northward. X: Direction from the Earth’s center, in the plane perpendicular to the spin axis (the equatorial plane), that goes through the 0 degrees longitude reference meridian (commonly referred to as the Greenwich meridian). Y: Z_GEO cross X_GEO . TRACERS uses the high-precision ITRF93 Earth frame that is provided in the binary SPK file available for the Earth. GSE Frame: --------------------------------------------------------- This is the definition for the GSE frame that is provided in SPICE's "frames required reading" document (2021 version). X: Direction of true_of_epoch, geometric, vector from the Earth to the Sun Z: Direction of X_GSE cross Sun_from_Earch_velocity_vector, with the latter being the true_of_epoch, geometric, velocity vector of the Sun as seen from the Earth. I.e., perpendicular to the instantaneous ecliptic, pointing northward. Y: Z_GSE cross X_GSE direction. The +Y direction then pointing opposite the direction of the Earth's orbital motion, in the plane of the ecliptic (in general). - This is true-of-epoch, as it uses the Earth-Sun position and velocity at the epoch of calculation. This assumes that the Sun and Earth ephemerides incorporate both precession and nutation (and whatever other small motion the eliptic may have with time). MAG Frame: --------------------------------------------------------- "The geomagnetic coordinate system (MAG) is defined so that its Z-axis is parallel to the Earth's magnetic centered dipole axis. The geographic coordinates of the dipole axis from the International Geomagnetic Reference Field... The Y-axis of this system is perpendicular to the geographic poles such that if D is the dipole position and S is the south pole Y=DxS. Finally, the X-axis completes a right-handed orthogonal set." Z: Along the vector from the center of the Earth through the north pole of the IGRF-14 CD. Y: In the direction of Z_GEO cross Z_MAG. X: Y_MAG cross Z_MAG. The implementation of this frame is complicated in that the definition of the IGRF dipole is a function of time and the IGRF model cannot be directly incorporated into SPICE. Instead, an external routine has been used to calculate, using the IGRF coefficients, the GEO locations of the Centered Dipole north poles at a discrete set of epochs, with a cadence of 1 day. These are then used to calculate quaternions that transform from the GEO to the MAG frame at each epoch. This MAG frame is achieved by first rotating the GEO frame about the Z-axis by the GEO longitude of the north MAG pole, and then rotating about the Y-axis by the latitude of the north MAG pole. Finally, these quaternions are input to the msopck utility function provided with SPICE, generating a CK kernel which can then transform between GEO and MAG for any epoch within the range spanned by the input quaternions. The current MAG CK kernel was created using the IGRF-14 model. The validity ranges for the that version of the model are as follows: Definitive Provisional Predict Not Valid |------------------------------|+++++++++++|###########|???????????| 19xx 2020 2025 2030 2035 Note that since the rest of the magnetic-dipole-based frames are defined from this one, similar validity ranges apply for those frames. GSM Frame: --------------------------------------------------------- "The geocentric solar magnetospheric system (GSM), as with both the GSE and GSEQ systems, has its X-axis from the Earth to the Sun. The Y-axis is defined to be perpendicular to the Earth's magnetic dipole so that the X-Z plane contains the dipole axis. The positive Z- axis is chosen to be in the same sense as the northern magnetic pole. The difference between the GSM system and the GSE and GSEQ is simply a rotation about the X-axis." X: Direction of the geometric vector from the Earth to the Sun. Y: In the direction of Z_MAG cross X_GSM Z: X_GSM cross Y_GSM . Thus, +X is identical as GSE +X and is the primary, and +Z is the secondary and is the MAG +Z. SM Frame: --------------------------------------------------------- "In solar magnetic coordinates (SM) the Z-axis is chosen parallel to the north magnetic pole and the Y-axis perpendicular to the Earth-Sun line towards dusk. The difference between this system and the GSM system is a rotation about the Y-axis. The amount of rotation is simply the dipole tilt angle as defined in the previous section. We note that in this system the X-axis does not point directly at the Sun. As with the GSM system, the SM system rotates with both a yearly and daily period with respect to inertial coordinates." Z: Along the vector from the center of the Earth through the north pole of the IGRF-14 CD. Y: In the direction of Z_SM cross R_ES (R_ES = geometric Earth-to-Sun. X: Y_SM cross Z_SM . Thus, this is much like GSM, except that now the +Z axis is the primary, meaning it is parallel to the dipole vector, and +X is the secondary. Since the X-Z plane is the same as GSM's X-Z plane, the Y axis is the same as GSM. === Spacecraft-Specific Frames === Note: Replace "TS1" with "TS2" for TRACERS-2 frames. TRACERS Spacecraft Coordinate System (TS1_TSCS) Frame Definition ---------------------------------------------------------------------------------- The fundamental spacecraft-fixed coordinate system is the TRACERS Spacecraft Coordinate System (TSCS). Instrument and any other spacecraft coordinate systems will reference and transform to and from TSCS. The origin of the TSCS is at the geometric center of the launch vehicle adaptor ring on the separation interface plane, with that separation plane being 26.67 mm offset from the Motorized LightBand (MLB) attachment datum plane. Note that this origin is NOT at the center of mass of the spacecraft. The axes are defined by: Z: Along the geometric center of, and theoretical [zero error] spin axis through, the spacecraft X: Perpendicular to Z_TSCS, out from the origin along the theoretical [zero error] deployed EFI-1 sensor Y: Z_TSCS cross X_TSCS direction, nominally along the deployed EFI-3 sensor TRACERS Spinning Body (TS1_TSB) Frame Definition ---------------------------------------------------------------------------------- This is the TRACERS Spinning Body frame. It uses the actual measured spin axis of the spacecraft as its primary defining vector, and the X_TSCS axis as the secondary defining vector. This frame is specified by a CK kernel that is created using the angular velocity vectors provided by the spacecraft Guidance, Navigation and Control (GNC) system at a nominal 1-second cadence. The frame axes are defined by: Z: Along direction of positive angular velocity vector of spacecraft Y: Z_TSB cross X_TSCS direction X: Y_TSB cross Z_TSB direction ACE Instrument (TS1_ACE) Frame Definitions ---------------------------------------------------------------------------------- ACE is oriented to achieve a desired B-field alignment. The ACE X,Y,Z axes are parallel to the TSCS axes. The +X ACE axis projects outward from the spacecraft deck. The +Z ACE axis will nominally be parallel to the LABF in the ROI. ACI Instrument (TS1_ACI) Frame Definitions ---------------------------------------------------------------------------------- The ACI axes are parallel to the TSCS axes. The X axis projects inward from the spacecraft deck. The Z axis is parallel to the TSCS Z axis, and is nominally parallel to the +B field in the ROI. The ACI Polar Anlge is zero at the ACI -Z axis, which is also the direction from which precipitating ions will nominally arrive, and is the location of ACI anode #4. The ACI Polar Angle increases from Y to Z ACI. The ACI Azimuthal Angle increases and follows the spacecraft rotation. EFI Instrument (TS1_EFI) Frame Definitions ---------------------------------------------------------------------------------- There are 4 EFI sensors. EFI1 and EFI2 define the EFI X axis and are parallel to the TSCS X axis, with EFI1 in the +X direction. EFI3 and EFI4 define the EFI Y axis and are parallel to the TSCS Y axis, with EFI3 in the +Y direction. The EFI X and Y axes are orthogonal to the nominal [zero error] spacecraft spin axis. MAG Instrument (TS1_MAG) Frame Definitions ---------------------------------------------------------------------------------- The MAG sensor is mounted at the end of a bracket fixed to the spacecraft face that is midway between the -X and +Y TSCS axes. The MAG axes are orthogonal to the bracket fixture, with the +Z MAG axis aligned with the +Z TSCS axis and the +Y MAG axis outward along the bracket. The result is that the MAG frame is rotated about +Z TSCS by +45 degrees. ^ | | | | | | |+Z_TSCS (in) <-------------x-------------> +X_TSCS .` .| MAGIC--> .`M.` | .` .` | .` .` | .` .` | MAG-->`M ` | | v +Y_TSCS +Z_MAG (in) .x. .` `. .` `. .` `. .` `. `+Y_MAG ` +X_MAG MSC Instrument (TS1_MSC) Frame Definitions ---------------------------------------------------------------------------------- From [4], The MSC sensor is mounted at the end of a bracket fixed to the spacecraft face that is midway between the +X and -Y TSCS axes. The MSC axes are orthogonal to the TSCS frame, but are rotated such that +X MSC = -Y TSCS, +Y MSC = -X TSCS and +Z MSC = -Z TSCS. ^ +X_MSC | | | | | | | +Y_MSC <-------------o +Z_MSC (out) ^ | . | .`M.`<-- MSC | .` .` | .` .` | .` .` | .` .` |` .` <-------------x.------------> +X_TSCS |+Z_TSCS (in) | | | | | | v +Y_TSCS MAGIC Instrument (TS1_MAGIC) Frame Definitions ---------------------------------------------------------------------------------- The MAGIC sensor is mounted on the same bracket as MAG, which is fixed to the spacecraft face that is midway between the -X and +Y TSCS axes. The MAGIC axes are orthogonal to the bracket fixture, with the +Z MAGIC axis aligned with the +Z TSCS axis and the +X MAG axis inward along the bracket. The result is that the MAG frame is rotated about +Z TSCS by -45 degrees. ^ | | | | | | |+Z_TSCS (in) <-------------x-------------> +X_TSCS .` .| MAGIC--> .`M.` | .` .` | .` .` | .` .` | MAG-->`M ` | | v +Y_TSCS . +X_MAGIC .` .` .` .` .` x. +Z_MAGIC (in) `. `. `. `. ` +Y_MAGIC North East Center (TS1_NEC) Science Frame: --------------------------------------------------------- This is an implementation of the North East Center (NEC) frame that was used on Swarm, which has the Z axis pointing from the spacecraft to the center of the Earth, the Y axis perpendicular to the Z axis, pointing in the eastward direction, and the X axis completes the right-handed set, pointing in the geographically (i.e., on the surface of a ~spherical body) north direction. For a SPICE two-vector frame, the practical definition uses the spacecraft-to-Earth vector (defining +Z) as the primary vector and the GEO Z axis as the secondary vector (defining +Y as the direction perpendicular to both the spacecraft-to-Earth vector and Z_GEO. Z: Spacecraft-to-Earth vector Y: Direction Z_NEC cross Z_GEO (Eastward) X: Y_NEC cross Z_NEC direction (Northward) Field-Aligned Coordinates (TS1_FAC) Science Frame: --------------------------------------------------------- This is the Field-Aligned Coordinates frame, which is a basic IGRF-14 B-field aligned frame. It is a re-creation of the FAC frame on FAST. This frame is specified by a CK kernel that defines the orientation of a "virtual instrument" on TS1 that is in fact the TS1_FAC B-field-aligned frame defined by: Z: Along the IGRF-14 model magnetic field at the spacecraft location, expressed in the GEO frame Y: Direction of Z_FAC x R_GEO (R = Earth to spacecraft vector in the GEO frame) (East) X: Y_FAC cross Z_FAC direction (Outwards) CAUTION: This frame is valid ONLY for calculations done at the location of the spacecraft, as the IGRF-14 vectors are calculated specifically at that location, at the epoch when the spacecraft is there, according to the available ephemerides. Field Velocity Coordinates (TS1_FVC) Science Frame: --------------------------------------------------------- This is the Field Velocity Coordinates frame. It is an implementation of the second IGRF-14 B-field aligned frame used by FAST. They called it Field-aligned/Velocity Coordinates (FAC_V). Z: Along the IGRF-14 model magnetic field at the spacecraft location, expressed in the GEO frame Y: Direction of Z_FVC cross spacecraft_velocity_vector (as seen in the GEO frame) X: Y_FVC cross Z_FVC direction. This frame is specified by using the B-field-aligned Z-axis of the TS1_FAC frame, plus the spacecraft velocity as seen in the GEO frame. The latter is probably a reasonable first approximation of the plasma frame...? CAUTION: This frame is valid ONLY for calculations done at the location of the spacecraft, as the IGRF-14 vectors are calculated specifically at that location, at the epoch when the spacecraft is there, according to the available ephemerides. TRACERS Field Sun (TS1_TFS) Science Frame: --------------------------------------------------------- The TRACERS Field Sun frame defines a frame that uses the IGRF-14 B direction and the spacecraft-to-Sun direction as the two defining vectors, with the former being the primary direction. Z: Along the IGRF-14 model magnetic field at the spacecraft location. Y: Direction of Z_TFS cross spacecraft-to-Sun vector, with the latter being the true_of_epoch, geometric, vector from the spacecraft to the Sun X: Y_TFS cross Z_TFS direction. CAUTION: This frame is valid ONLY for calculations done at the location of the spacecraft, as the IGRF-14 vectors are calculated specifically at that location, at the epoch when the spacecraft is there, according to the available ephemerides. TRACERS Spin Sun (TS1_TSS) Science Frame: --------------------------------------------------------- This is a frame that uses the spacecraft spin axis as the Z-axis, and the spacecraft-to-Sun direction as the second defining vector. Z: Same as Z_TSB. Y: Direction of Z_TSS cross spacecraft-to-Sun vector, with the latter being the true_of_epoch, geometric, vector from the spacecraft to the Sun X: Y_TSS cross Z_TSS direction. The +X direction then pointing roughly sunward.