PDS_VERSION_ID = PDS3 RECORD_TYPE = FIXED_LENGTH RECORD_BYTES = 80 OBJECT = TEXT PUBLICATION_DATE = 1996-10-04 NOTE = "Format and Use of Magellan Bistatic Radar Quaternion Polynomial Coefficient Files" END_OBJECT = TEXT END This file provides a summary description of the format, contents, and use of Magellan bistatic radar quaternion polynomial coefficients (QPC) files; it should be sufficient for most users. A more complete description of the quaternion file format can be found in the Project Magellan Software Interface Specification (SIS) MGN-RES-104 (09/15/89). Overview ======== Each QPC file contains polynomial coefficients for Magellan quaternions during bistatic radar experiments on one of the following dates: 5-6 October 1993 (day-of-year 279-280) 9 November 1993 (day-of-year 313) 31 May 1994 (day-of-year 151) 5-6 June 1994 (day-of-year 156-157) Each file contains an 11-line header and a 40-line body. The header includes the following: beginning of file marker ($$MGN) and descriptive file name file acronym keyword and file name level indicator data source run identifier software identifier file creation time start time for the file end time for the file title of file end of header marker ($$EOH) The body includes the following: one line giving: parameter set level parameter set name unique identifier for this set of polynomial coefficients start time for the file (same as in header) second line giving: update quaternion flag parameter name 36 lines of coefficient labels and values scale factor (TSF) end of file marker ($$EOF) Coefficients given are for constant through eighth degree polynomial terms for each of four quaternions (Q1, Q2, Q3, and Q4). Evaluation ========== Quaternions can be evaluated as follows: Q1 = SET1.0 + SET1.1*((T-TTF)/TSF) + SET1.2*((T-TTF)/TSF)^2 + ... + SET1.8*((T-TTF)/TSF)^8 Q2 = SET2.0 + SET2.1*((T-TTF)/TSF) + SET2.2*((T-TTF)/TSF)^2 + ... + SET2.8*((T-TTF)/TSF)^8 Q3 = SET3.0 + SET3.1*((T-TTF)/TSF) + SET3.2*((T-TTF)/TSF)^2 + ... + SET3.8*((T-TTF)/TSF)^8 Q4 = SET4.0 + SET4.1*((T-TTF)/TSF) + SET4.2*((T-TTF)/TSF)^2 + ... + SET4.8*((T-TTF)/TSF)^8 Quaternions can be converted to attitude of the spacecraft as follows: xs = [Q11-Q22-Q33+Q44, Q12+Q34, Q13-Q24] ys = [Q12-Q34, -Q11+Q22-Q33+Q44, Q23+Q14]; zs = [Q13+Q24, Q23-Q14, -Q11-Q22+Q33+Q44] where xs, ys, and zs are the unit vectors defining the spacecraft rectangular frame in J2000 coordinates, Qii=Qi*Qi, and Qij=2*Qi*Qj (i not equal to j). Offset Times (TTF) ================== The offset or reference time TTF for each bistatic radar orbit is given here. The quantity T-TTF in the equations above is the number of seconds since the reference time. Attitude Error in the table below is an estimate of the uncertainty in knowledge of the attitude in degrees. Orbit Reference Time Start Polynomial End Polynomial Attitude No. (TTF) Execution Execution Error (SCET) (SCET) (SCET) (deg) ----- ------------------- ------------------- ------------------- ----- 9331 93-279/13:15:40.200 93-279/13:11:42 93-279/13:19:46 9335 93-279/19:34:14.133 93-279/19:30:18 93-279/19:38:22 9336 93-279/21:08:52.600 93-279/21:04:58 93-279/21:13:02 9846 93-313/09:31:42.333 93-313/09:11:58 93-313/09:51:58 9847 93-313/11:06:20.666 93-313/10:46:36 93-313/11:26:36 9848 93-313/12:40:58.266 93-313/12:21:14 93-313/13:01:14 12955 94-151/12:27:48.266 94-151/12:26:25.933 94-151/12:28:51.266 0.150 12956 94-151/14:00:45.666 94-151/13:59:23.267 94-151/14:01:48.600 0.137 12957 94-151/15:33:43.066 94-151/15:32:20.601 94-151/15:34:45.934 0.145 12958 94-151/17:06:40.466 94-151/17:05:17.935 94-151/17:07:43.268 0.137 13034 94-156/16:19:25.066 94-156/16:08:00.466 94-156/16:30:48.466 0.097 13035 94-156/17:52:22.533 94-156/17:40:57.799 94-156/18:03:45.799 0.102 13036 94-156/19:25:20.000 94-156/19:13:55.132 94-156/19:36:43.132 0.098 13037 94-156/20:58:17.466 94-156/20:46:52.465 94-156/21:09:40.465 0.100 13038 94-156/22:31:14.933 94-156/22:19:49.798 94-156/22:42:37.798 0.099 13039 94-157/00:04:12.400 94-156/23:52:47.131 94-157/00:15:35.131 0.102 Pre- and Post-Experiment Spacecraft Attitude ============================================ Before and after each experiment, the spacecraft high-gain antenna was pointed toward Earth. The general algorithm for MGN attitude during Earth- point was to place the S/C X-axis in the Earth-cross-Sun direction plus an additional 10-degree roll around the Z-axis (HGA-boresight). Representative calculated values of the attitude quaternion, together with the resulting unitary transformation matrix to go from J2000 to S/C coordinates are (all in J2000) as follows: Day 93-280 (7 October 1993) --------------------------- Quaternions: 0.2835038 0.6828897 0.1581304 0.6544321 (mag=0.9999997) Matrix: 0.0173122 0.5941749 -0.8041488 (X-axis vector) 0.1802324 0.7892401 0.5870393 (Y-axis vector) 0.9834711 -0.1550967 -0.0934262 (Z-axis vector) Day 93-313 (9 November 1993) ---------------------------- Quaternions: 0.0351934 0.6398739 0.4069473 0.6509353 (mag=1.0000000)) Matrix: -0.1500894 0.5748313 -0.8043893 (X-axis vector) -0.4847540 0.6663107 0.5666071 (Y-axis vector) 0.8616767 0.4749727 0.1786456 (Z-axis vector) Day 94-151 (31 May 1994) 12:26:25.933 ------------------------------------- Quaternions: 0.6502909 -0.5343113 0.4328263 0.3229431 Day 94-151 (31 May 1994) 17:07:43.268 ------------------------------------- Quaternions: 0.6509592 -0.5333617 0.4339242 0.3216908 Day 94-156 (5 June 1994) 13:02:05.800 ------------------------------------- Quaternions: 0.6664385 -0.5093185 0.4605714 0.2903927 Day 94-157 (6 June 1994) 00:15:35.131 ------------------------------------- Quaternions: 0.6678308 -0.5069345 0.4630998 0.2873286