MI = Moon-Centered Inertial - Geocentricinertial coordinate system - (​EMEJ2K)
MEM = geocentric Moon-fixed coordinate system - Mean Earth (DE440)​
PAM = geocentric Moon-fixed coordinate system - Principal Axis​ (DE440)
VO = Vehicle-carried orbit-defined coordinate system (Z - nadir, Y - right) See AIAA S-119-2011 (aka LVLH)
IAU = Moon spheroid (not a frame) (centered on MI coordinate system) - radius defined in IAU 2015
LPS = Lunar Polar Sterographic (See References section at end for parameters and references)
body = Body coordinate system/frame - system fixed in the vehicle with the origin at the CM (X - forward, Y - right, Z - down) (ref S-119 p. 12, or R-004-1192 Paragraph 1.1.7 p. 2)
Note: body frame axis definition directions are defined for each of the bodies used in this assessment.
Sim Outputs Presentation frame Core Reference point/frame "of" relative frame "wrt" observer frame (translation only) "ObsFr"
elapsedTime_s Simulation elapsed time
j2000UtcTime_s J2000 UTC time (UTC Julian date - 2451545.0 days, January 1.5, 2000)
j2000TtTime_s Terrestrial Time (TT) (TT Julian date - 2451545.0 days, January 1.5, 2000) - formerly known as Terrestrial Dynamical Time (TDT)
j2000TdbTime_s Barycentric Dynamical Time referenced to the J2000 epoch
miPosition_m_X mi Position CM mi Position of the vehicle center of mass with respect to MI resolved in the MI coordinate system
miPosition_m_Y
miPosition_m_Z
miVelocity_m_s_X mi Velocity CM mi mi Velocity of the vehicle center of mass with respect to MI resolved in the MI coordinate system
miVelocity_m_s_Y
miVelocity_m_s_Z
miAccel_m_s2_X mi Accel CM mi mi Acceleration of the vehicle center of mass with respect to MI resolved in the MI coordinate system
miAccel_m_s2_Y
miAccel_m_s2_Z
quaternionWrtMi_W NA quaternion body mi Attitude of the vehicle body frame with respect to the MI frame. Expressed as a right transformative unit quaternion
quaternionWrtMi_X W = scalar, X,Y,Z = vector components
quaternionWrtMi_Y
quaternionWrtMi_Z
bodyAngularRateWrtMi_deg_s_Roll body AngularRate body mi Angular velocity of the vehicle body frame with respect to MI resolved in the body frame
bodyAngularRateWrtMi_deg_s_Pitch
bodyAngularRateWrtMi_deg_s_Yaw
bodyAngularAccelWrtMi_deg_s2_Roll body AngularAccel body mi Angular acceleration of the vehicle body frame with respect to MI resolved in the body frame
bodyAngularAccelWrtMi_deg_s2_Pitch
bodyAngularAccelWrtMi_deg_s2_Yaw
memPosition_m_X mem Position CM mi Position of the vehicle center of mass with respect to MI resolved in the MEM coordinate system
memPosition_m_Y
memPosition_m_Z
memLatitude_deg Latitude and longitude of vehicle center of mass resolved in the ME planet fixed frame. Uses IAU 2015 defined spheroid.
memLongitude_deg Ranges: Longitude [-180,180), Latitude [-90,90]
pamPosition_m_X pam Position CM mi Position of the vehicle center of mass with respect to MI resolved in the PAM coordinate system
pamPosition_m_Y
pamPosition_m_Z
pamLatitude_deg Latitude and longitude of vehicle center of mass resolved in the PA planet fixed frame. Uses IAU 2015 defined spheroid.
pamLongitude_deg Ranges: Longitude [-180,180), Latitude [-90,90]
lpsPosition_m_X LPS Position CM mi Position of the vehicle center of mass with respect to MI resolved in the LPS coordinate system (northern or souther pole as appropriate)
lpsPosition_m_Y X and Y outputs shall be ZERO when outside the LPS region (i.e. between -80 and +80 ME latitude)
pamLocalGravitation_m_s2_X pam Local Gravitation CM Gravitational acceleration at the vehicle center of mass resolved in the PAM coordinate system. This variable only contains gravitational acceleration contributions from the inverse radius squared/GRAIL models. 3rd body gravitation contributions are not included in this output.
pamLocalGravitation_m_s2_Y
pamLocalGravitation_m_s2_Z
quaternionWrtVo_W NA quaternion body vo Attitude of the vehicle body frame with respect to the VO frame. Expressed as a right transformative unit quaternion
quaternionWrtVo_X W = scalar, X,Y,Z = vector components
quaternionWrtVo_Y
quaternionWrtVo_Z
altitudeIau_m Altitude Current altitude of the vehicle center of mass above reference - IAU 2015 (1737.4 km spheroid) * Note: All orbital parameters are referenced to a lunar centered coordinate system
periapsisIau_m Periapsis Orbital parameter for argument of periapsis of the orbit of the vehicle center of mass (altitude above reference - IAU 2015 (1737.4 km spheroid))
apoapsisIau_m Apoapsis Orbital parameter for argument of apoapsis of the orbit of the vehicle center of mass (altitude above reference - IAU 2015 (1737.4 km spheroid))
eccentricity eccentricity Orbital parameter for eccentricity of the orbit of the vehicle center of mass
inclinationMi_deg Inclination Orbital parameter for inclination of the orbit of the vehicle center of mass referenced to the MI equatorial plane. Range [0,180] degrees
semiMajorAxis_m semiMajorAxis Orbital parameter for semi-major axis of the orbit of the vehicle center of mass
trueAnomaly_deg TrueAnomaly Orbital parameter for true anomaly of the vehicle center of mass. Range [0,360) degrees
rightAscensionMi_deg RightAscension Orbital parameter for right ascension of the ascending node of the orbit of the vehicle center of mass referenced to the MI frame. Range [0,360) degrees
inclinationPam_deg Inclination Orbital parameter for inclination of the orbit of the vehicle center of mass referenced to the PA equatorial plane. Range [0,180] degrees
Optional Simulation Outputs (optional outputs for simulation tools)
eulerAngleWrtMi_deg_Roll NA eulerAngle body mi Attitude of the vehicle body frame with respect to the MI frame. Expressed as an Euler 3-2-1 rotation sequence in the order of Yaw, Pitch, Roll.
eulerAngleWrtMi_deg_Pitch Ranges: Roll [-180,180), Pitch [-90,90], Yaw [0,360) degrees
eulerAngleWrtMi_deg_Yaw
eulerAngleWrtVo_deg_Roll NA eulerAngle body vo Attitude of the vehicle body frame with respect to the VO frame. Expressed as an Euler 3-2-1 rotation sequence in the order of Yaw, Pitch, Roll.
eulerAngleWrtVo_deg_Pitch Ranges: Roll [-180,180), Pitch [-90,90], Yaw [0,360) degrees
eulerAngleWrtVo_deg_Yaw
Additional Outputs for 3rd Body Gravitation (Case 5,5A,6,6A,7,8,9, 9A, 9B)
miLocalGravitationSun_m_s2_X mi Local Gravitation CM Gravitational acceleration contribution at the vehicle center of mass resolved in the MI coordinate system due to the Sun.
miLocalGravitationSun_m_s2_Y
miLocalGravitationSun_m_s2_Z
miLocalGravitationEarth_m_s2_X mi Local Gravitation CM Gravitational acceleration contribution at the vehicle center of mass resolved in the MI coordinate system due to the Earth.
miLocalGravitationEarth_m_s2_Y
miLocalGravitationEarth_m_s2_Z
eulerAngleOfSunWrtBody_deg_Pitch NA eulerAngle sun body Pointing angle from the body frame to point the X axis at the sun. Expressed as an Euler 3-2 rotation sequence in the order of Yaw, Pitch. No roll rotation.
eulerAngleOfSunWrtBody_deg_Yaw Ranges: Pitch [-90,90], Yaw [0,360) degrees
Additional Outputs for ME/PA frame checks + DEM (Case 9 only)
pamLocalGravitationOfTp1_m_s2_X pam Local Gravitation Test Point 1 Gravitational acceleration at Test Point 1 resolved in the PAM coordinate system. This variable only contains gravitational acceleration contributions from the inverse radius squared/GRAIL models. 3rd body gravitation contributions are not included in this output.
pamLocalGravitationOfTp1_m_s2_Y
pamLocalGravitationOfTp1_m_s2_Z
pamLatitudeOfTp1_deg Latitude and longitude of Test Point 1 resolved in the PA planet fixed frame. Uses IAU 2015 defined spheroid.
pamLongitudeOfTp1_deg Ranges: Longitude [-180,180), Latitude [-90,90]
altitudeIauOfTp2_m Current altitude of Test Point 2 above reference - IAU 2015 (1737.4 km spheroid). This is the altitude of the DEM test point above reference spheroid and is derived from DEM elevation data) * Note: All orbital parameters are referenced to a lunar centered coordinate system
pamLatitudeOfTp2_deg Latitude and longitude of Test Point 2 resolved in the PA planet fixed frame. Uses IAU 2015 defined spheroid.
pamLongitudeOfTp2_deg Ranges: Longitude [-180,180), Latitude [-90,90]
Test Point 1 Information
Latitude ME=-3.64530 (deg)
Longitude ME = -17.47136 (deg)
Altitude = 6000.0 (m)- Altitude above IAU 2015 reference Spheroid
Reference IAU 2015 sphereoid for lat/lon
Latitude positive north, Longitude positive east
Test Point 2 Information
Latitude ME= -89.91137 + 2.0 * t/28800.0; (deg)
Longitude ME = 127.26573 + 3.0 * 360.0 * t/28800.0; (deg)
where "t=elapsedTime_s". Results in migration across 2 degrees of latitude and 3 circles of longitude.
Reference IAU 2015 sphereoid for lat/lon
Latitude positive north, Longitude positive east
DEM Information:
DEM header information: imbrium.mit.edu/DATA/LOLA_GDR/POLAR/IMG/LDEM_80S_80M.LBL
DEM web site: LOLA South Pole GDR information (mit.edu)
Use 80 m/pxl resolution DEM for -80 deg to South Pole
Additional Outputs for Sensor (Case 9, 9A , 9B)
miSensedPositionOfSensor_m_X mi Position sensor mi Sensed position of the sensor with respect to MI resolved in the MI coordinate system
miSensedPositionOfSensor_m_Y Note: Named "SensedPosition" as a refernce to how the position, velocity, and acceleration would be "sensed" at a particular sensor location. Since we do not have any modeling errors, this is identical to the actual position, velocity, and acceleration values (without gravitational acceleration).
miSensedPositionOfSensor_m_Z
miSensedVelocityOfSensor_m_s_X mi Velocity sensor mi mi Sensed velocity of the sensor with respect to MI resolved in the MI coordinate system
miSensedVelocityOfSensor_m_s_Y Note: Named "SensedPosition" as a refernce to how the position, velocity, and acceleration would be "sensed" at a particular sensor location. Since we do not have any modeling errors, this is identical to the actual position, velocity, and acceleration values (without gravitational acceleration).
miSensedVelocityOfSensor_m_s_Z
miSensedAccelOfSensor_m_s2_X mi Accel sensor mi mi Sensed acceleration of the sensor with respect to MI resolved in the MI coordinate system
miSensedAccelOfSensor_m_s2_Y Note: Sensed acceleration does not include gravitational acceleration
miSensedAccelOfSensor_m_s2_Z Note: Named "SensedPosition" as a refernce to how the position, velocity, and acceleration would be "sensed" at a particular sensor location. Since we do not have any modeling errors, this is identical to the actual position, velocity, and acceleration values (without gravitational acceleration).
Post Processed Outputs (Computed based on simulation outputs - sim teams do NOT generate these)
pp_eulerAngleWrtMi_deg_Roll NA eulerAngle body mi Attitude of the vehicle body frame with respect to the MI frame. Expressed as an Euler 3-2-1 rotation sequence in the order of Yaw, Pitch, Roll.
pp_eulerAngleWrtMi_deg_Pitch Ranges: Roll [-180,180), Pitch [-90,90], Yaw [0,360) degrees
pp_eulerAngleWrtMi_deg_Yaw Purpose: to provide a more human readable version or orientation to compare vs. looking at quaternions.
Calculation: Computed from quaternionWrtMi_W/X/Y/Z
pp_eulerAngleWrtVo_deg_Roll NA eulerAngle body vo Attitude of the vehicle body frame with respect to the VO frame. Expressed as an Euler 3-2-1 rotation sequence in the order of Yaw, Pitch, Roll.
pp_eulerAngleWrtVo_deg_Pitch Ranges: Roll [-180,180), Pitch [-90,90], Yaw [0,360) degrees
pp_eulerAngleWrtVo_deg_Yaw Purpose: to provide a more human readable version or orientation to compare vs. looking at quaternions.
Calculation: Computed from quaternionWrtVo_W/X/Y/Z
pp_miPositionOfSensorWrtCm_m_X mi Position sensor CM Position of the sensor with respect to the vehicle CM resolved in the MI coordinate system
pp_miPositionOfSensorWrtCm_m_Y Note: This is the true sensor position as represented in the EOM wrt the CM. This is intended to be used for EOM results comparison and not to emulate any actual sensor state or output. However since we do not add sensor modeling errors, this would be identical to a "SensedPosition" for our cases.
pp_miPositionOfSensorWrtCm_m_Z Calculation: miSensedPositionOfSensor_m_X/Y/Z - miPosition_m_X/Y/Z (Note: this will result in some loss of precision due to subtraction of large number)
Purpose: To look for calculation issues in how the miSensedPositionOfSensor output is calculated (e.g. drift in body relative drift of sensor position)
Additional notes:
Make sure checkcase ICs specify TT and UTC (leap seconds)
Simulation output number of significatn digits 16
Quaternion Results
TRICK/JEOD left transformative
LaSRS++ right transformative
MAVERIC right transformative
SPACE FOM left transformative
General Literature many seem to use right transformative
POST 2 left transformative
References
Original checkcase output definitions (appendices p. 96)
SPICE Kernels
moon_pa_de440_200625.bpc
moon_de440_220930.tf
pck00011.tpc
naif0012.tls
de440.bsp
Lunar Polar Sterographic
Reference: LUNAR GRID REFERENCE SYSTEM FOR ARTEMIS MISSION NAVIGATION AND LUNAR SURFACE SCIENCE. M.T. McClernan, B.A. Archinal, and T.M. Hare; U.S. Geological Survey, Astrogeology Science Center (2255 N. Gemini Dr., Flagstaff, AZ 86001; mmcclernan@usgs.gov)
[55th Lunar and Planetary Science Conference (2024)]
parameters:
Use IAU 2015 Moon reference already in use in study (1737.4km radius spheroid)
𝜑0= 90
𝑘0=.994 at 𝜑0
Reference to ME frame
False Easting and False Northing terms:
FE,FN=500 km
Outputs:
𝜑 >= 80 or <= -80
X = Easting term, positive east
Y = Northing term, positive north
Output X,Y = 0 otherwise.
Quick Check:
Latitude +/- 90 should give X,Y outputs of 500 km, 500 km