IS-GPS-800A - US Coast Guard Navigation Center

Table 3.5-2. Elements of Coordinate System (part 1 of 2)Element/EquationDescription = 3.986005 x 10 14 meters 3 /sec 2WGS 84 value of the earth’s gravitational constant for GPS user e = 7.2921151467 x 10 -5 rad/secA 0 = A REF + A *A k = A 0 + (A) t kWGS 84 value of the earth’s rotation rateSemi-Major Axis at reference timeSemi-Major Axisn 0 =3A 0Computed Mean Motion (rad/sec)t k = t – t oe **n A = n 0 +½ ∆n 0 t kn A = n 0 + n AM k = M 0 + n A t kM k = E k – e n sin E kTime from ephemeris reference timeMean motion difference from computed valueCorrected Mean MotionMean AnomalyKepler’s equation for Eccentric Anomaly (radians)(may be solved by iteration) k = tan -1 sin coskk True Anomaly 2 = tan -1 1e n sin E k / 1e n cos E k cos E e / 1e cos E knnkE k = cos -1 e n cos 1e n cos kk Eccentric Anomaly* A REF = 26,559,710 meters** t is GPS system time at time of transmission, i.e., GPS time corrected for transit time (range/speed of light).Furthermore, t k shall be the actual total difference between the time t and the epoch time t oe , and must accountfor beginning or end of week crossovers. That is if t k is greater than 302,400 seconds, subtract 604,800seconds from t k . If t k is less than -302,400 seconds, add 604,800 seconds to t k .45 IS-GPS-800A8 June 2010