NEAR15A Gravity Model ===================== The NEAR15A gravity model is here supplied as two files: one containing the spherical harmonic coefficients and their associated errors; and a second containing the covariance matrix for these coefficients. The following description was supplied with the data. It has been edited to reflect changes made to the physical data files in this format. The NEAR15A ----------- NEAR15A is a 15th degree and order model obtained from radiometric tracking (Doppler and range data) and landmark tracking of the NEAR spacecraft in orbit about Eros. The gravity model includes data from the entire mission beginning with orbit insertion on Feb. 14, 2000 and ending with the first descent maneuver for landing on Feb. 12, 2001. Some details describing this model are: The spherical harmonic coefficients are fully normalized. The associated GM = 4.46275E-04 The reference radius = 16.0 km The Eros-fixed reference frame is given by the J2000 pole and prime meridian: Right ascension = 11.363 degrees Declination = 17.232 degrees Prime Meridian = 326.08 degrees Rotation rate = 1639.389232 degrees/day Summary of data arcs in NEAR15A solution: Begin time Length Orbit Period Inclination (days) (km x km) (days) (asteroid equ.) ------------------------------------------------------------ 14-FEB-2000 10 366 x 324 21.8 35 24-FEB-2000 8 365 x 204 16.5 34 03-MAR-2000 29 209 x 200 10.0 38 02-APR-2000 10 210 x 100 6.6 56 11-APR-2000 11 101 x 99 3.4 60 22-APR-2000 8 101 x 50 2.2 65 30-APR-2000 24 52 x 49 1.2 90 24-MAY-2000 21 " " " 14-JUN-2000 23 " " " 07-JUL-2000 7 51 x 35 1.0 90 14-JUL-2000 10 40 x 35 0.7 90 24-JUL-2000 7 56 x 36 1.0 90 31-JUL-2000 8 52 x 49 1.2 90 08-AUG-2000 18 52 x 49 1.2 105 26-AUG-2000 10 102 x 49 2.3 113 05-SEP-2000 15 103 x 100 3.5 115 20-SEP-2000 10 " " " 30-SEP-2000 7 " " " 07-OCT-2000 6 " " " 13-OCT-2000 7 98 x 50 2.2 131 20-OCT-2000 5 52 x 50 1.2 133 25-OCT-2000 1 64 x 19 0.7 135 26-OCT-2000 8 203 x 64 5.3 144 03-NOV-2000 12 197 x 194 10.0 147 15-NOV-2000 14 " " " 29-NOV-2000 8 " " " 07-DEC-2000 6 193 x 34 4.2 178 13-DEC-2000 14 38 x 34 0.7 178 27-DEC-2000 13 " " " 09-JAN-2001 15 " " " 24-JAN-2001 4 36 x 22 0.6 178 28-JAN-2001 1 37 x 20 0.6 179 28-JAN-2001(b) 5 36 x 35 0.7 179 02-FEB-2001 4 " " " 06-FEB-2001 6 " " " Observations for the gravity field consist of Doppler and range measurements from Deep Space Network (DSN) tracking and landmark observables from the camera images of the asteroid Eros. The count time for the Doppler observations is 60 seconds. The typical accuracy for the Doppler is 0.03 mm/s for the 60 second sample time. The range accuracy is about 3 meters and is limited by the station calibration accuracy. The actual rms scatter is less than 0.5 meters in spacecraft position. The camera images are used to generate landmark observations. For each landmark we basically have two inertial angle measurements of a crater center. The two directions on the image are called line and pixel. Each image may be used to generate anywhere from 1 to 40 landmark observation pairs (line,pixel) with the average being about 6. The total number of landmarks (or craters) used for optical navigation is 1554. The measurement noise is about one pixel in both directions. The smaller landmark positions on Eros are determined to several meter accuracy. Summary of the number of observations for each arc: Begin time Doppler Range Landmark pairs ------------------------------------------------------------ 14-FEB-2000 7975 2126 4506 24-FEB-2000 6877 1456 2987 03-MAR-2000 19843 7578 9972 02-APR-2000 7385 1819 8303 11-APR-2000 7688 2450 2913 22-APR-2000 6852 1731 1497 30-APR-2000 21976 5410 3539 24-MAY-2000 20326 5514 4854 14-JUN-2000 22902 4414 8645 07-JUL-2000 6640 380 1666 14-JUL-2000 12757 1490 1371 24-JUL-2000 7906 600 2255 31-JUL-2000 9671 1757 2812 08-AUG-2000 19051 2934 4995 26-AUG-2000 10772 2172 5589 05-SEP-2000 12157 3288 7393 20-SEP-2000 6529 2007 5754 30-SEP-2000 4557 1588 6372 07-OCT-2000 4329 693 4716 13-OCT-2000 8156 1572 4901 20-OCT-2000 5355 1001 1037 25-OCT-2000 541 164 270 26-OCT-2000 6699 2164 3553 03-NOV-2000 12032 3128 4759 15-NOV-2000 10497 3249 4782 29-NOV-2000 6745 1670 2585 07-DEC-2000 5660 1008 2645 13-DEC-2000 8460 2584 3024 27-DEC-2000 9321 3422 2911 09-JAN-2001 10090 2892 3517 24-JAN-2001 3187 349 904 28-JAN-2001 552 0 177 28-JAN-2001(b) 3691 478 771 02-FEB-2001 4000 195 618 06-FEB-2001 6438 897 1000 Each Landmark pair consists of one line and one pixel measurement. Total Doppler observations = 317,617 Total Range observations = 74,180 Total Landmark pixel observations = 127,593 Total Landmark line observations = 127,593 The NEAR15A gravity model is delivered as a Spherical Harmonics Gravity ASCII Data Record (SHGADR) and is produced at JPL by Alex Konopliv of the NEAR Radio Science Team.