I I A NEW TRAJECTORY PROPAGATION I PROGRAM FOR DSPSE MISSION SUPPORT I Jay W. Middour* I Naval Center for Space Technology Naval Research Laboratory I Washington, D.C. I Abstract ronment. DSPSE has two secondary science missions in which it will fly in lunar orbit for A satellite trajectory propagation program two months and then depart the Moon for a I called N-Body is being developed to support four month cruise to rendezvous with the near the upcoming Deep Space Program Science Ex­ Earth asteroid 1620 Geographos. In accom­ periment (DSPSE) mission which is also known plishing its secondary missions, DSPSE will I as Clementine. The program will support have made the first complete, multi-spectral the activities of the mission operations center mapping of the lunar surface, and executed the which is run by The Naval Research Labora­ first close encounter with a minor planet (ap­ I tory. The computer program is designed to proximately 100 km). predict a spacecraft orbit through the various Mission operations for DSPSE will be con­ I phases in which the DSPSE vehicle will fly. ducted by the Naval Research Laboratory's These orbital phases include low Earth, trans­ Naval Center for Space Technology at the lunar, lunar, and deep space. The design of DSPSE Mission Operations Center in Alexan­ I N.Body, its functionality, and the mathemati­ dria, Virginia. During the various mission cal methods it employs are presented. phases, the DSPSE space vehicle will fly in low Earth orbit, highly elliptical orbit with apogee I at lunar distances, lunar orbit, and deep space 1 Introduction heliocentric orbit. The DSPSE Mission Op­ erations Center, or DMOC is tasked to coor­ I The Deep Space Science Experiment Pro. dinate the science activities with the business gram (DSPSE), also known as Clementine, of navigation, orbi t determination, command is a joint Naval Research Laboratory, NASA, and telemetry, and satellite housekeeping func­ I and Lawrence Livermore National Laboratory tions. The operations center must therefore project. DSPSE is funded by the Ballistic Mis­ possess a trajectory integration program which sile Defense Office. The primary goal of the can accurately integrate the satellite orbit in I DSPSE mission is to demonstrate the opera­ each of these unique space environments. tion of lightweight sensors in the space envi- It was decided that a program developed by I * Aerospace Engineer, Member AIAA members of the operations team itself could This paper is declared a work of the U.S. Government I and is not subject to copyright protection in the United States. 1 I I be tailored expressly to meet the DSPSE re­ space, the force model must contain the ef­ quirements in areas such as engineering and fects of the Earth and Moon gravitational po­ I science support, contingency planning, maneu­ tential fields, Earth atmospheric drag, solar ver design and verification and tracking sta­ radiation pressure and planetary gravitation. tion scheduling. Furthermore, by using a prod­ Several gravitational potential models for the I uct developed in-house, software modifications Earth and Moon are incorporated into the pro­ can be effected more rapidly and less expen­ gram. Alternatively, a user defined potential sively than if an off-the-shelf product were may be specified. Atmospheric drag requires I used. The trajectory propagation program, a model of the density variations of the Earth called N-Body, is being developed by the au­ atmosphere and a physical model of the satel­ thor to satisfy this requirement. lite. A model of the vehicle shape and its I Strictly speaking, the program does not ad­ specular characteristics are needed to compute dress the classical n-body problem in which the the acceleration due to solar radiation pres­ I motion of n objects under mutual gravitation sure impinging on the spacecraft. A plane­ is solved for. Rather, the program attempts to tary ephemeris is used to obtain the third body solve a restricted problem in which the trajec­ gravitational forces. The planetary ephemeris I tories of n-l objects are known and the motion is also used to predict eclipsing events which af­ of the massless nth object is solved for. In this fect the solar radiation pressure computation. case the n - 1 objects are the Sun, Moon and Finally, the force model allows for impulsive I planets and the nth object is the space vehicle. spacecraft maneuvers. N-Body is written in FORTRAN and is be­ N-Body employs a Cowell method in which I the total accelerations of all external forces act­ ing developed on VAX workstations running ing on the vehicle are directly integrated. Cow­ under the VMS operating system. The com­ ell's method was selected due to its ease of im­ puter code is largely complete and consists of about 10,000 lines. The program is presently I plementation. For instance, Encke's method undergoing verification testing by the DSPSE in which only the perturbations about the two body problem are integrated can be more effi­ mission operations team. It is anticipated that I cient since the integration step size can usually the program will be fully operational in time to be increased over that of the Cowell method support DSPSE flight operations starting with without any associated loss of accuracy. How­ the planned launch in January, 1994. I ever the Encke method requires that the per­ turbed orbit be rectified with a new reference 2 Design and Operation orbit whenever the difference between the per­ I turbed orbit and the reference orbit grows too N-Body is comprised of a program configura­ large. The rectification process logic is depen­ tion procedure, an executive procedure, and I dent on the particular numerical integration an extensive mathematical subroutine library. procedure being used. For instance a multi­ A series of key words and variables is used to step integration method would require restart­ control the execution flow! define the input and I ing. By using Cowell's method, the executive output coordinate frames and times, configure algorithms can be independent of the integra­ the force model, select and configure the in­ tion procedures. The result is a major simpli­ tegrator, set the duration of the propagation I fication in software design and maintenance. and select the destination and frequency of the Since the trajectories must be propagated in output data. The executive procedure trans­ low Earth orbit, trans-lunar, lunar and deep forms the input coordinates and epoch time to I 2 I I I a standard internal fonnat the coordinates of nitions, force model parameters, integrator se­ I which are mean equator and equinox of J2000.0 lection and print options. Each output record and TAl (International Atomic Time) seconds. contains the current time in Julian and calen­ Using the mathematical subroutines! the exec­ dar dates, Cartesian position and velocity, Ke­ I utive procedure carries out the orbit propaga­ plerian orbital elements and Earth referenced tion according to the key word configuration. position of the space vehicle trajectory being I While the propagation is in progress the execu­ integrated. tive procedure monitors its status to detennine An ASCII ephemeris file may be created con­ when output records should be produced. Out­ sisting of a header followed by time, position I put records can be requested at regular time in­ and velocity data records. The header and tervals! after each integration step! at the first data in the ephemeris file conform to the Stan­ and last times in the run or they can be trig­ dard Ephemeris Record Fonnat (SERF) which I gered by orbital events such as apoapsis and will be used by the DSPSE mission operations peri apsis passages. The executive procedure and science teams. The SERF header contains also can be configured to detect the passage of a description of the parameters, constants and I the space vehicle into the umbra and penumbra models used to create the ephemeris. The in­ of a planet, and the occultation of the vehicle put vector coordinate system, origin of coordi­ by a planet as viewed from the Earth. nates, coordinate type, and position, velocity, I The program configuration procedure reads and time units are listed followed by the actual an input file containing key words and vari­ input vector. Generation information is also I ables, as well as the initial condition for the provided which includes the time the run was trajectory that is to be propagated. Each key made, the propagation start and stop times, word and variable is assigned a default value so the interval between ephemeris records, and I that the only item that is required to be in the the number of points in the ephemeris. The input file is the initial condition. The initial force model used for the run is summarized by condition may be specified in tenns of Carte­ listing on I off indicators for Earth harmon­ I sian position and velocity coordinates or clas­ ics, atmospheric drag, solar radiation pressure, sical Keplerian orbital elements. In the case third body perturbations, lunar harmonics and of Keplerian elements, the in-plane position of maneuvering. The output vector coordinates, I the satellite may be specified with either true time, etc. are described in the same manner as anomaly, mean anomaly or time since periap­ the input vector. Finally, The radius and grav­ sis passage. Any of the physical constants used itational parameter of the Earth Moon and Sun I by the program, including the Earth and Moon are listed along with the first four zonals for the gravity models, may be changed by placing the Earth and Moon. I appropriate key words and parameters into the If it has been requested, the executive pro­ input file.