ASTRODYNAMICS WEB TOOLS: A COLLABORATIVE WEB COMPUTING INFRASTRUCTURE PROJECT

ASTRODYNAMICS WEB TOOLS: A COLLABORATIVE WEB COMPUTING INFRASTRUCTURE PROJECT R. López (1), J. F. San Juan (1), L. M. López-Ochoa (1) and M. Lara (1) (1) University of La Rioja, 26004, Logroño (La Rioja), Spain, Email: rolopeg@gmail.com, juanfelix.sanjuan@unirioja.es, luis-maria.lopezo@unirioja.es, mlara0@gmail.com ABSTRACT Astrodynamics Web Tools, Tools, is an ongoing collaborative Web Tools computing infrastructure project to support scientific computation. AstrodyWebTools provides project collaborators with all the technical and human facilities in order to wrap, manage and use specialized non-commercial software tools in Astrodynamics and Celestial Mechanics fields, with the aim of optimizing use of resources, both human and material. However, this project is open to collaboration from the whole scientific community in order to create a library of useful tools and their corresponding theoretical backgrounds. AstrodyWebTools offers a user-friendly web interface in order to choose applications, introduce data and select appropriate constraints in an intuitive and easy way for the user. After that, the application is executed in real-time, whenever possible, then the critical information about program behaviour (errors and logs) and output (graphical representation of data, statistical analysis or whatever manipulation thereof) are shown via the same web interface or downloaded to the users computer. 1. INTRODUCTION Internet has opened new possibilities and ways of collaboration in almost all scientific fields, allowing the execution of sophisticated applications as a web service, and participation in open source projects in which specific software is carried out in order to tackle determined kinds of problems, and supported by large communities of developers. In this paper, we present the Tools project [1, 2, 3]. This project aims to suggest research and learning practices in order to benefit researchers and students who want to use specialized applications through Internet to solve new problems or learn basic knowledge about these applications. For this purpose we are creating a web infrastructure in the University of La Rioja based on open sources, initially limited to the area of tools for Astrodynamics and Celestial Mechanics. We must note that the web infrastructure can be extended to other application domains. This environment allows, on the one hand, hosting different scientific applications with minimum modifications on the original code, developed by diverse research groups, or individually by other researchers, whilst on the other, scientists and students can execute these applications, in real time, using only a browser from anywhere in the world. The framework conceals the algorithmic complexity of the applications from the users while they view the applications in terms of its inputs and outputs. Moreover the users can access the e-learning contents of the above applications. The only condition required so that a new application can be hosted in Tools is that this can be executed from a UNIX command line, regardless of the programming language in which it is written. This flexibility allows not only the integration of new applications based on sophisticated object-oriented designs, but also reuses legacy applications, which are outdated from the technological standpoint. We must note that this approach does not require any re-engineering work. This paper is organized as follows. Section 2 briefly explains the architecture of Tools. Section 3 describes the current available applications in Tools. Section 4 illustrates the use of an application of this project. Finally, Section 5 outlines future work for this project and draws conclusions. 2. ASTRODY WEB TOOLS ARCHITECTURE Figure 2 shows the base of the architecture proposed for Tools and its connection to the Web browser. We must note that this environment can be used in other domains. The registered user can select and execute any of the available applications after filling out the appropriate web form. Then, the data included in the form are converted into the input format for the selected application, which is executed by the application server, and the outputs are stored in files. After that, these results can be handled by other open source applications. For example, Gnuplot is the default system used to plot and

visualize data, Octave is the interactive system used for doing numerical computations, R is used for statistical calculations, Latex is the word processor, as well as other required applications, and their outputs are embedded in the web page. In addition, the graphics, pdf reports, and other outputs, can be downloaded by the user. OPP (Orbit Propagator Programs) is an application, which calculates the orbiter s position and velocity directly at any time by means of a function of time and initial position and velocity. Repeating Ground-track Orbits Finder is a software package designed to search for repeating groundtrack orbits automatically in the case of a planetary satellite. Access to these Astrodynamics tools is free for all registered users through a web interface at http://tastrody.unirioja.es. 4. SCENARIOS Figure 1. Tools architecture The initial prototype of our Web server was based on LAMP technology, which used Linux as the operating system, Apache as Web Server, MySql as data-base manager and Php as programming language. Although, as expected, this prototype had limited functionalities. The current version of the Web server is developed using the content management system (CMS) Drupal, which provides advanced facilities for dealing with security, database connectivity, content management and menu systems. This CMS is written in Php and can be downloaded freely from http://drupal.org. It is noteworthy that Drupal is supported by an active community of users and open source developers around the world. 3. ASTRODYNAMICS WEB TOOLS Fig. 2 shows the current available applications in Tools. ZERGOF (Zonal Earth Repeat Ground-track Orbits Finder) [4] is a software package designed to search for repeating ground-track orbits automatically, in the case of the Earth. These kinds of orbits are highly desirable as nominal orbits for a variety of missions for artificial satellites, because their eccentricity and argument of the perigee remain almost constant or frozen during a long period of time. DSST (Draper Semianalytical Satellite Theory) Standalone [5, 6] is an accurate Semi-Analytical Satellite Theory expressed in nonsingular equinoctial elements, which was developed at the Computer Sciences Corporation and the Charles Draper Laboratory (CSDL) in the 1970s and 1980s. In this section the usage of one of the available applications is illustrated. This is the PPKBJ6 OPP [7, 8], an analytical orbit propagator, which describes the motion of an artificial satellite perturbed by the first five zonal harmonic coefficients in the Earth s gravitational field. 4.1. PPKBJ6 OPP This OPP is a C implementation of an analytical theory. The main goal of an analytical theory, in the case of the artificial satellite problem, is to reduce the original problem by means of perturbations theories in such a way that the transformed problem would be simple enough for integration. PPKBJ6 is based on Hamiltonian formalism and uses perturbation theories based on Lie transforms and classical averaging methods. In this case, in polar-nodal variables (r, θ, ν, R, Θ, N), the Hamiltonian for an Earth satellite perturbed by the first five zonal harmonic potential terms is given by H = 1 2 (R 2 + Θ2 r 2 ) µ r + µ r 6 ( α ) n J n Pn (sin β), r n 2 (1) where P n is the Legendre polynomial of degree n, sin β = sin i sin θ, i is the inclination of the satellite s orbit, µ is the gravitational constant, α is the equatorial radius of the planet, and J n are the zonal harmonic coefficients. The analytical integration process begins by breaking down H into separate parts arranged in a special manner, according to their order of magnitude and relative importance, in order to apply perturbation theories. Then, a one degree of freedom Hamiltonian which only depends on the variables (r, R) is obtained by applying two Lie transforms up to the second order, which are the eliminations of the parallax [9] and the perigee [10]. Finally the

Figure 2. Available applications in Tools

transformed Hamiltonian is integrated using the Krylov- Bogoliubov-Mitropolski method [11, 12]. The analytical theory and the PPKBJ6 OPP have been carried out by MathATESAT. The flowchart for the PP- KBJ6 OPP is illustrated in Fig. 3. The orbit propagator begins reading two input ASCII files to contain the physical parameters and the initial conditions (osculating Keplerian elements) at the epoch t 0. Next, it transforms the initial conditions across the inverse transformations. At this point, PPKBJ6 provides the values of the polarnodal variables at the epoch t by applying the Krylov- Bogoliubov-Mitropolski method (KBM). Finally, the direct transformations are applied, and the osculating Keplerian elements and the state vector are calculated and stored in separate files. To check the accuracy of the results, the energy is evaluated and the values are compared with H(t 0 ) at each epoch t. Input : µ, α, ω, J 2, J 3, J 4, J 5, J 6, t 0, t f, t, (a 0, e 0, g 0, ν 0, i 0, l 0 ) (t 0, r 0, θ 0, ν 0, R 0, Θ 0, N 0 ) Inverse transformations (t 0, r 0, θ 0, ν 0, R 0, Θ 0, N 0 ) for (t = t 0 ; t t f ; t = t + t) { } Integrate: KBM (t, r, θ, ν, R, Θ, N ) Direct transformations (t, r, θ, ν, R, Θ, N) Output : (t, a, e, g, ν, i, l) (t, x, y, z, ẋ, ẏ, ż) EnergyTest: H(t 0 ) H(t) Figure 3. Flowchart for the PPKBJ6 OPP Figure 4. Access to OPP the user; the considered value of the gravitational constant µ is 398600.47km 3 s 2, the equatorial radius of the Earth α is 6378.137km, the angular velocity ω is 0.00007292115855s 1 and the used geo-potential model is EGM96 [13] by default. Finally, the user requests the execution of PPKBJ6 OPP by clicking on the Execute button. Fig. 5 shows the web form as it appears to a user for all OPPs. Figure 5. Job submission for any OPPs 4.2. Usage of the PPKBJ6 OPP scenario Fig. 4 presents the initial web page of the OPP in which a short description of this application is displayed. Here the user can see an example of the execution of one of the OPPs. The interface consists of a web form where the user can enter values for the input parameters and select one of the available OPPs. In this scenario the selected model is PPKBJ6. Tab. 1 shows the Tastrody names, with their respective elements, units and valid values for the input data for all OPPs. At this moment, the physical parameters and the geo-potential model are not accessible by Next, from the user data an input file containing this information is created, and then, a request is sent to the application server in order to run an instance of the PPKBJ6 OPP. The results of this execution, orbital elements, cartesian coordinates and energy test, are allocated to three different files. Simultaneously, another instance of a C code for the numerical integration of the original problem is run in order to validate the analytical approach for this input data. The numerical integrator user is a high order Runge-Kutta method [14]. We must note that when propagation needs lengthy execution time, which occurs in the case of using small steps, as it is necessary to carry out a great number of OPP evaluations, our framework allows the user to request a reference number for the current execution, and so be able to use other applications or close the session. Fig. 6 shows the system through which the user can access the execution tracking system for all

Table 1. Input data for any OPP Tastrody Name Element Unit Valid Values a Semi-major axis Kilometers a > Equatorial radius e Eccentricity 0 < e < 1 ω Argument of the perigee Degree 0 ω < 360 Ω Argument of the node Degree 0 Ω < 360 i Inclination Degree 0 i < 180 ν Mean anomaly Degree 0 M < 360 t 0 Initial time Seconds t 0 0 t f Final time Seconds t 0 < t f t Step Seconds t t f t 0 applications in this framework. Figure 6. Execution tracking system Once the two instances have finished, their outputs are collected and an error study is made, as well as any other manipulation that the user needs. GNUPlot is currently the viewing environment selected by our framework. At this moment, the available plots in any OPP are: From the OPP outputs: Orbit trace Energy Test Orbital elements Long period behavior (e sin g, e cos g) From the error study: Orbital element error Distance, along-track, cross-track and radial errors Finally, outputs and graphics are sent back to the web server and can then be downloaded by the user to the home computer. Fig. 7 shows the web information provided by the PP- KBJ6 OPP in the case of the Space Station orbit (a = 6830km, e = 0.001, i = 51.6 ). This orbit was propagated for 1 day from epoch. As can be seen, the link to data and error plots and the orbital elements provided by the OPP are shown in the same window. The user can download all outputs resulting from this execution clicking the Download results link. It is noteworthy that these initial conditions are almost a repeat-ground track orbit as can be seen in Figure 7. Space Station orbit (a = 6830km, e = 0.001, i = 51.6 ) Fig. 8, which analyzes long-period evolution by plotting (e sin g, e cos g). Fig. 9 displays the Space Station trace plot, whereas the orbital elements and all errors are shown by means of a slide-show. Finally, we must note that this OPP can be used in com-

Figure 8. (e sin g, e cos g) Figure 10. ATESAT PPKBJ6 OPP (LEO case) Figure 11. MathATESAT PPKBJ6 OPP (LEO case) Figure 9. Space Station trace plot bination with ZERGOF in order to study the long-period evolution of the repeat ground-track orbits calculated in this last application. 4.3. e-collaboration project One of the main aims of this project is to promote collaboration between users and software developers, with the benefit of improving the capabilities of the applications integrated in Tools. Here we illustrate this collaboration with an example which has allowed us to extend the use of the PPKBJ6 OPP to the Earth case. The first version of this code [8, 15] was developed for the Centre National D Etudes Spatiales (CNES) by ATESAT [7], based on the assumption of maintaining distance error at less than 1 kilometer for 30 days in the case of Low Mars Orbits. However numerical instabilities were detected in the case of Low Earth Orbits, as can be seen in Fig. 10. Fig. 11 shows the current version of PPKBJ6 available through Tools, performed by the symbolicnumeric environment MathATESAT [16], for the case of a Low Earth Orbit. The numerical problems were solved and the validity of PPKBJ6 has been extended to a longer period of time, as can be seen in Fig. 11. 5. FUTURE WORK AND CONCLUSIONS This paper illustrates the current development of Tools. This project aims to suggest new research and learning practices to benefit researchers and students who want to use specialized applications through Internet to solve new problems or learn basic knowledge about these applications. For this purpose we are creating an infrastructure based on open sources. However, the project is not closed, but open to the collaboration of whoever wishes to participate in the initiative with the purpose of creating a library of useful programs to serve researchers in Astrodynamics. ACKNOWLEDGEMENTS Part of this research has been supported by the Government of Spain (Projects AYA 2009-11896, AYA 2010-18796, and grant Gobierno de La Rioja Fomenta 2010/16). This paper is an extract from the dissertation which Rosario López will submit to the University of La Rioja in order to obtain her doctoral degree. REFERENCES [1] San Juan, J. F. & López, R. (2009). Astrody W eb T ools : Astrodynamics Web Tools. In Proc. XI Jornadas de

Mecánica Celeste, (Eds. V. Lanchares & A. Elipe), Monografías de la Real Academia de Ciencias de Zaragoza, Zaragoza. [2] San Juan, J. F. & López, R. & Prez, I. (2010) Nondy- Web : Nonlinear Dynamics Web Tools. In Proc. 4th International Tools Conference on Astrodynamics Tools Techniques, Madrid, Spain. [3] San Juan, J. F., Lara, M., López, R., López- Ochoa, L. M., Folcik, Z., Weeden, B. & Cefola, P. J. (2011) Using the DSST Semi-Analytical Orbit Propagator package via the NONDY- WEBTOOLS/ASTRODYWEBTOOLS Open Science Environtmen. In Proc. 62nd International Astronautical Congress, Cape Town, SA. [4] Lara, M. (1999). Searching for Repeating Ground Track Orbits: A Systematic Approach. The Journal of the Astronautical Sciences. 47, 177 188. [5] Neelon, J. G., Cefola, P. J. & Proulx, R. J. (1997). Current Development of the Draper Semianalytical Satellite Theory Standalone Orbit Propagator Package, AAS Pre-print 97-731, presented at the AAS/AIAA Astrodynamics Conference, Sun Valley, ID. [6] Cefola, P. J., Phillion, D. & Kim, K. S. (2009). Improving Access to the Semi-Analytical Satellite Theory, AAS 09-341, presented at the AAS/AIAA Astrodynamic Specialist Conference, Pittsburgh, PA. [7] San Juan, J. F. (1994). ATESAT: Automatization of theories and ephemeris in the artificial satellite problem, Tech. rep. CT/TI/MS/MN/94-250, CNES, France. [8] San Juan, J. F. & Serrano, S. (2000). Application of the Z6PPKB ATESAT model to compute the orbit of an artificial satellite around Mars. Tech. rep. DTS/MPI/MS/MN/2000-057. CNES, France. [9] DEPRIT, A. (1981). The Elimination of the Parallax in Satellite Theory. Celestial Mechanics and Dynamical Astronomy. 24( 2 ), 111 153. [10] Alfriend, K. T. & Coffey, S. L. (1984). Elimination of the perigee in the satellite problem. Celestial Mechanics and Dynamical Astronomy. 32( 2 ), 163 172. [11] KRYLOV, N. & BOGOLIUBOV, N. N. (1947). Introduction to Nonlinear Mechanics. Princeton University Press, Princeton, New Jersey. [12] BOGOLIUBOV, N. N. & MITROPOLSKY, Y. A. (1961) Asymptotic method in the theory of non-linear oscillations. Gordon and Breach, New York. [13] Lemoine, F. G., Kenyon, S. C., Factim, J. K., Trimmer, R. G., Pavlis, N. K., Chinn, D. S., Cox, C. M., Klosko, S. M., Luthcke, S. B., Torrence, M. H., Wang, Y. M., Williamson, R. G., Pavlis, E. C., Rapp, H. & Olson, T. R., (1998). The development of the joint NASA GSFC and the National Imagery and Mapping Agency (NIMA) Geopotential Model EGM 96. NASA Tech. Pub. 1998-206861, Goddard Space Flight Center, Greenbelt, Maryland, USA. [14] DORMAND, J. R. & PRINCE, P. J. (1989). Practical Runge-Kutta Processes. SIAM Journal on Scientific and Statistical Computing, 10(5), 977 989. [15] Hauteserres, D. (2004). Etudes des codes des modeles analytiques produits par le logiciel ATESAT2002 mise au format industriel des codes, Tech. rep. DCT/SB/OR/2004/N o 824, CNES, France. [16] San-Juan, J. F., Lpez, L. M. & Lpez, R. (2011) MathATESAT: a symbolic-numeric environment in astrodynamics and celestial mechanics. Lecture Notes in Computer Science. 6783(2), 436 449.