For the satellite ESSA-8, the value of / is 78.3° , 

 A = 7815.37 km, and e = 0.00323. With these 

 values and taking 6378 km for a, we compute 



an 



^T— = — 1.943 deg per day. 



Given the nodal period of ESSA-8 as 115.703 

 min we find, alternately, that 



d «( 

 dt 



0.15476 deg per orbit. 



The minus sign indicates that the change is op- 

 posite to the angular motion of the satellite. 



Having determined a„ for a selected orbit and 

 starting at the ascending node where a =a,„ 

 the radial distance R can be computed from Equa- 

 tion (10) for use in the numerical integration of 

 Equation (9), to yield the angular displacement 

 ( a — a„) for successive intervals of desired 

 length after the time of ascending node. The 

 values of (^ and A can then be obtained with Equa- 

 tions (11) and (12). These are the spherical co- 

 ordinates of the point of the orbit relative to a 

 nonrotating frame of reference with origin at the 

 earth's center. 



In order to plot the subpoint track on a chart, 

 the spherical coordinates of points on the orbit 

 need to be transformed to the geographic (geo- 

 detic) latitudes and longitudes of the correspond- 

 ing subpoints. The latter are the locations on the 

 earth's surface where the local vertical passes 

 through the satellite. The angle which local verti- 

 cal makes with the equatorial plane defines the 

 geodetic latitude of the subpoint (Bowditch, 

 1958). Owing to the earth's ellipsoidal shape, a 

 line from the satellite to the center of the earth 

 intersects the surface at a point north of the 

 satellite subpoint. The geodetic latitude at this 

 point of intersection is a close approximation to 

 that of the subpoint and can be computed from 

 the following expression: 



geodetic latitude = arc ctn [(1 ~ q) ctn 4)] 



where q is the ratio of centripetal acceleration 

 at the equator to gravity, as defined earlier. This 

 expression is derived from the vector difference 

 between the true force of gravitation on a unit 

 mass at a point on the earth and the apparent 



force of gravity at that point, as a result of the 

 earth's rotation. Taking 



q = 3.468 X 10 "' 



the maximum correction for geodetic latitude 

 computed with the above expression is about 0.1 

 degree at latitude 45 degrees. 



The longitude of the satellite subpoint can be 

 obtained by adding the longitude of the ascend- 

 ing node to the value of A computed with Equa- 

 tion (12). Adjustment for the earth's rotation is 

 made by adding to this sum the product of the 

 rate of rotation (0.25 degree of longitude per min- 

 ute) and the elapsed time from the ascending 

 node to the point of the orbit for which the sub- 

 point location is desired. A correction must be 

 made for the precession of the orbital plane 

 which, in a sun-synchronous orbit, amounts to 

 360 degrees in 365 days and is subtractive. 



APPLICATION 



The foregoing procedures have been imple- 

 mented in a computer program for preparing or- 

 bit schedules at the Southwest Fisheries Center, 

 La Jolla Laboratory, National Marine Fisheries 

 Service. The program includes a section for each 

 active satellite in which appropriate values are 

 assigned for semimajor axis, eccentricity, inclina- 

 tion, anomalistic period, argument of perigee at 

 a known reference orbit and the rate of change 

 of the argument of perigee. All of these quanti- 

 ties are taken directly from information sheets 

 furnished by NESS. 



In running the program, a data card is submit- 

 ted for each schedule to be printed. On it are 

 punched the name of the satellite and the orbit 

 number, day, hour, minute, second, and longi- 

 tude of the ascending node for a particular orbit 

 as read from a recent or current APT Predict 

 message. The card is also punched with the stand- 

 ard (or daylight) time zone at the station for con- 

 version from universal to local time, and a speci- 

 fication of the number of minutes after ascending 

 node to which computed orbit reference times 

 will apply. The latter tells the APT ground station 

 operator when to expect to begin receiving trans- 

 mission. The number specified indicates to the 

 program whether orbits selected for subpoint 

 computation are to be determined by south-to- 

 north or north-to-south traverses over the station. 



