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At least 19 records

A new concept of stability in orbit propagation, useful for quantifying numerical errors

We present the concept of topological stability in the numerical propagation of orbits, and show how it results in a useful new method for measuring the global numerical error of an orbit propagation. The concept applies to any problem in orbital dynamics. Moreover, it can be extended to any three-dimensional system of di erential equations of second order. In order to assess the topological stability of a given integration a special metric is introduced, which can be used to estimate the numerical errors robustly. The method is particularly well suited for dealing with strongly perturbed and chaotic systems. The construction is based on the constraint imposed by the Hopf map that supports the Kustaanheimo-Stiefel transformation. Generic concepts of stability are translated to KS space.

Pelaez, Jesus

Strategic Center for Networking, Integration, and Communications Orbit Propagation Front-End Software Development

Orbit propagation is fundamental for space-based mission analysis, requiring software tools to predict the time-based positions and velocities of orbiting satellites. Many system analysts currently rely on commercial software, which is effective but expensive. NASA’s Space Communications and Navigation (SCaN) Strategic Center for Networking, Integration, and Communications (SCENIC) project intends to provide these analysis capabilities by using a combination of internal and open-source software, allowing for a greater flexibility while maintaining low costs. Several routines were created to take different forms of user input to translate input into the standard set of orbital elements to be utilized within the current SCENIC analysis capabilities. These inputs range from two-line elements (TLEs) and Cartesian vectors, to coordinate transformations and Walker Delta constellations. These routines will be integrated into the SCENIC user interface (UI) in order to provide greater customization and flexibility for orbit propagation and other dynamic-analysis capabilities.

Kuhl, Nick

SeaWiFS technical report series. Volume 11: Analysis of selected orbit propagation models for the SeaWiFS mission

An analysis of orbit propagation models was performed by the Mission Operations element of the Sea-viewing Wide Field-of-View Sensor (SeaWiFS) Project, which has overall responsibility for the instrument scheduling. The orbit propagators selected for this analysis are widely available general perturbations models. The analysis includes both absolute accuracy determination and comparisons of different versions of the models. The results show that all of the models tested meet accuracy requirements for scheduling and data acquisition purposes. For internal Project use the SGP4 propagator, developed by the North American Air Defense (NORAD) Command, has been selected. This model includes atmospheric drag effects and, therefore, provides better accuracy. For High Resolution Picture Transmission (HRPT) ground stations, which have less stringent accuracy requirements, the publicly available Brouwer-Lyddane models are recommended. The SeaWiFS Project will make available portable source code for a version of this model developed by the Data Capture Facility (DCF).

Patt, Frederick S.

Fast orbit propagator for graphical display

A simple analytic orbit propagator is presented which incorporates a mean-to-osculating transformation to generate a graphical display of the trajectories of earth-orbiting satellites. The first-order effects of the oblateness of the earth on the orbit are consistently included. The propagator encompasses a mean-to-osculating transformation on the semimajor axis, since large intrack errors can be generated by failing to observe the distinction between the mean and osculating values of this parameter.

Markley, F. Landis

A Survey of Symplectic and Collocation Integration Methods for Orbit Propagation

Demands on numerical integration algorithms for astrodynamics applications continue to increase. Common methods, like explicit Runge-Kutta, meet the orbit propagation needs of most scenarios, but more specialized scenarios require new techniques to meet both computational efficiency and accuracy needs. This paper provides an extensive survey on the application of symplectic and collocation methods to astrodynamics. Both of these methods benefit from relatively recent theoretical developments, which improve their applicability to artificial satellite orbit propagation. This paper also details their implementation, with several tests demonstrating their advantages and disadvantages.

integration

Development of analytical orbit propagation technique with drag

Two orbit computation methods were used: (1) numerical method- The solution to the satellite differential equations were solved in a step-by-step manner, using a mathematical algorithm taken from numerical analysis; and (2) analytical method - The solution was expressed by explicit functions of the independent variable. Analytical drag modules, tesseral terms initialization module, second order and long period terms module, and verification testing of the ASOP program were also considered.

Source record

Orbital Propagation of Momentum Exchange Tether Systems

An advanced concept in in-space transportation currently being studied is the Momentum-Exchange/Electrodynamic Reboost Tether System (MXER). The system acts as a large momentum wheel, imparting a Av to a payload in low earth orbit (LEO) at the expense of its own orbital energy. After throwing a payload, the system reboosts itself using an electrodynamic tether to push against Earth's magnetic field and brings itself back up to an operational orbit to prepare for the next payload. The ability to reboost itself allows for continued reuse of the system without the expenditure of propellants. Considering the cost of lifting propellant from the ,ground to LEO to do the same Av boost at $10000 per pound, the system cuts the launch cost of the payload dramatically, and subsequently, the MXER system pays for itself after a small number of missions.1 One of the technical hurdles to be overcome with the MXER concept is the rendezvous maneuver. The rendezvous window for the capture of the payload is on the order of a few seconds, as opposed to traditional docking maneuvers, which can take as long ets necessary to complete a precise docking. The payload, therefore, must be able to match its orbit to meet up with the capture device on the end of the tether at a specific time and location in the future. In order to be able to determine that location, the MXER system must be numerically propagated forward in time to predict where the capture device will be at that instant. It should be kept in mind that the propagation computation must be done faster than real-time. This study focuses on the efforts to find and/or build the tools necessary to numerically propagate the motion of the MXER system as accurately as possible.

John Westerhoff

Quantifying Uncertainties in Navigation and Orbit Propagation Analyses

A tool used to calculate dilution of precision (DOP) was created in order to assist the Space Communications and Navigation (SCaN) program to analyze current and future user missions. The SCaN Center for Engineering, Networks, Integration, and Communication (SCENIC) is developing a new user interface (UI) to augment and replace the capabilities of currently used commercial software, such as Systems Tool Kit (STK). The DOP tool will be integrated in the SCENIC UI and will be used to analyze the accuracy of navigation solutions. This tool was developed using MATLAB and free and open-source tools to save cost and to use already existing orbital software libraries. GPS DOP data was collected and used for validation purposes. The similarities between the DOP tool results and GPS data show that the DOP tool is performing correctly. Additional improvements can be made in the DOP tool to improve its accuracy and performance in analyzing navigation solutions.

dilution of precision

Using AppletMagic(tm) to Implement an Orbit Propagator: New Life for Ada Objects

This paper will discuss the use of the Intermetrics AppletMagic tool to build an applet to display a satellite ground track on a world map. This applet is the result of a prototype project that was developed by the Goddard Space Flight Center's Flight Dynamics Division (FDD), starting in June of 1996. Both Version 1 and Version 2 of this applet can be accessed via the URL http://fdd.gsfc.nasa.gov/Java.html. This paper covers Version 1, as Version 2 did not make radical changes to the Ada part of the applet. This paper will briefly describe the design of the applet, discuss the issues that arose during development, and will conclude with lessons learned and future plans for the FDD's use of Ada and Java. The purpose of this paper is to show examples of a successful project using Oi AppletMagic, and to highlight some of the pitfalls that occurred along the way. It is hoped that this discussion will be useful both to users of AppletMagic and to organizations such as Intermetrics that develop new technology.

Stark, Michael E.

Short- and Long-Term Propagation of Spacecraft Orbits

The Planetary Observer Planning Software (POPS) comprises four computer programs for use in designing orbits of spacecraft about planets. These programs are the Planetary Observer High Precision Orbit Propagator (POHOP), the Planetary Observer Long-Term Orbit Predictor (POLOP), the Planetary Observer Post Processor (POPP), and the Planetary Observer Plotting (POPLOT) program. POHOP and POLOP integrate the equations of motion to propagate an initial set of classical orbit elements to a future epoch. POHOP models shortterm (one revolution) orbital motion; POLOP averages out the short-term behavior but requires far less processing time than do older programs that perform long-term orbit propagations. POPP postprocesses the spacecraft ephemeris created by POHOP or POLOP (or optionally can use a less accurate internal ephemeris) to search for trajectory-related geometric events including, for example, rising or setting of a spacecraft as observed from a ground site. For each such event, POPP puts out such user-specified data as the time, elevation, and azimuth. POPLOT is a graphics program that plots data generated by POPP. POPLOT can plot orbit ground tracks on a world map and can produce a variety of summaries and generic ordinate-vs.-abscissa plots of any POPP data.

Smith, John C., Jr.

Earth applications orbit analysis for a shuttle-mounted Multispectral Mapper

The earth remote sensing problem of orbit design to acquire images with inherent geometric and geodetic accuracy is addressed. The basis for precise orbit modeling is discussed. Various orbit propagation tools are compared. Orbit characteristics for a nominal case at shuttle altitude are displayed. Modeling Parameter sensitivities are evaluated to determine limits on orbit propagation accuracy versus time. It is found that attainable propagation accuracies are sufficient for image quality assessment over the short term at the 15m pixel size desired for a Multispectral Mapper.

Driver, J. M.

Demonstrating High-Accuracy Orbital Access Using Open-Source Tools

Orbit propagation is fundamental to almost every space-based analysis. Currently, many system analysts use commercial software to predict the future positions of orbiting satellites. This is one of many capabilities that can replicated, with great accuracy, without using expensive, proprietary software. NASAs SCaN (Space Communication and Navigation) Center for Engineering, Networks, Integration, and Communications (SCENIC) project plans to provide its analysis capabilities using a combination of internal and open-source software, allowing for a much greater measure of customization and flexibility, while reducing recurring software license costs. MATLAB and the open-source Orbit Determination Toolbox created by Goddard Space Flight Center (GSFC) were utilized to develop tools with the capability to propagate orbits, perform line-of-sight (LOS) availability analyses, and visualize the results. The developed programs are modular and can be applied for mission planning and viability analysis in a variety of Solar System applications. The tools can perform 2 and N-body orbit propagation, find inter-satellite and satellite to ground station LOS access (accounting for intermediate oblate spheroid body blocking, geometric restrictions of the antenna field-of-view (FOV), and relativistic corrections), and create animations of planetary movement, satellite orbits, and LOS accesses. The code is the basis for SCENICs broad analysis capabilities including dynamic link analysis, dilution-of-precision navigation analysis, and orbital availability calculations.

propagation

Efficient Trajectory Propagation for Orbit Determination Problems

Regularized formulations of orbital motion apply a series of techniques to improve the numerical integration of the orbit. Despite their advantages and potential applications little attention has been paid to the propagation of the partial derivatives of the corresponding set of elements or coordinates, required in many orbit-determination scenarios and optimization problems. This paper fills this gap by presenting the general procedure for integrating the state-transition matrix of the system together with the nominal trajectory using regularized formulations and different sets of elements. The main difficulty comes from introducing an independent variable different from time, because the solution needs to be synchronized. The correction of the time delay is treated from a generic perspective not focused on any particular formulation. The synchronization using time-elements is also discussed. Numerical examples include strongly-perturbed orbits in the Pluto system, motivated by the recent flyby of the New Horizons spacecraft, together with a geocentric flyby of the NEAR spacecraft.

numerical methods

Application of the NASCAP Spacecraft Simulation Tool to Investigate Electrodynamic Tether Current Collection in LEO

Recent interest in using electrodynamic tethers (EDTs) for orbital maneuvering in Low Earth Orbit (LEO) has prompted the development of the Marshall ElectroDynamic Tether Orbit Propagator (MEDTOP) model. The model is comprised of several modules which address various aspects of EDT propulsion, including calculation of state vectors using a standard orbit propagator (e.g., J2), an atmospheric drag model, realistic ionospheric and magnetic field models, space weather effects, and tether librations. The natural electromotive force (EMF) attained during a radially-aligned conductive tether results in electrons flowing down the tether and accumulating on the lower-altitude spacecraft. The energy that drives this EMF is sourced from the orbital energy of the system; thus, EDTs are often proposed as de-orbiting systems. However, when the current is reversed using satellite charged particle sources, then propulsion is possible. One of the most difficult challenges of the modeling effort is to ascertain the equivalent circuit between the spacecraft and the ionospheric plasma. The present study investigates the use of the NASA Charging Analyzer Program (NASCAP) to calculate currents to and from the tethered satellites and the ionospheric plasma. NASCAP is a sophisticated set of computational tools to model the surface charging of three-dimensional (3D) spacecraft surfaces in a time-varying space environment. The model's surface is tessellated into a collection of facets, and NASCAP calculates currents and potentials for each one. Additionally, NASCAP provides for the construction of one or more nested grids to calculate space potential and time-varying electric fields. This provides for the capability to track individual particles orbits, to model charged particle wakes, and to incorporate external charged particle sources. With this study, we have developed a model of calculating currents incident onto an electrodynamic tethered satellite system, and first results are shown here.

Adams, Mitzi

On reflecting boundary behind the Earth's orbit at propagation of fast particles from solar flares

The flares of solar cosmic rays (SCR) associated with the presence of shocks in interplanetary magnetic field and with their propagation at significant heliocentric distances were always of great interest. Some events and problems concerning the peculiarities of propagation of flare CR in the interplanetary medium are considered. The distinguishing feature of such events is the presence of shock front behind the Earth's orbit having formed either directly in the process of shock generation on the Sun or at large heliocentric distances as a result of the interaction of fast and slow quasistationary recurrent solar wind (SW) streams. Based on the experimental material it is shown that the significant nonlinear disturbances in IMF behind the Earth's orbit can yield the occurrence of the additional SCR flux from shock front region as a result of the interaction of flare flux with shock and a partial reflection from it.

Nishkovskikh, A. S.

Atmospheric drag model calibrations for spacecraft lifetime prediction

Although solar activity prediction uncertainty normally dominates decay prediction error budget for near-Earth spacecraft, the effect of drag force modeling errors for given levels of solar activity needs to be considered. Two atmospheric density models, the modified Harris-Priester model and the Jacchia-Roberts model, to reproduce the decay histories of the Solar Mesosphere Explorer (SME) and Solar Maximum Mission (SMM) spacecraft in the 490- to 540-kilometer altitude range were analyzed. Historical solar activity data were used in the input to the density computations. For each spacecraft and atmospheric model, a drag scaling adjustment factor was determined for a high-solar-activity year, such that the observed annual decay in the mean semimajor axis was reproduced by an averaged variation-of-parameters (VOP) orbit propagation. The SME (SMM) calibration was performed using calendar year 1983 (1982). The resulting calibration factors differ by 20 to 40 percent from the predictions of the prelaunch ballistic coefficients. The orbit propagations for each spacecraft were extended to the middle of 1988 using the calibrated drag models. For the Jaccia-Roberts density model, the observed decay in the mean semimajor axis of SME (SMM) over the 4.5-year (5.5-year) predictive period was reproduced to within 1.5 (4.4) percent. The corresponding figure for the Harris-Priester model was 8.6 (20.6) percent. Detailed results and conclusions regarding the importance of accurate drag force modeling for lifetime predictions are presented.

Binebrink, A. L.

X-Ray Detection and Processing Models for Spacecraft Navigation and Timing

The current primary method of deepspace navigation is the NASA Deep Space Network (DSN). High-performance navigation is achieved using Delta Differential One-Way Range techniques that utilize simultaneous observations from multiple DSN sites, and incorporate observations of quasars near the line-of-sight to a spacecraft in order to improve the range and angle measurement accuracies. Over the past four decades, x-ray astronomers have identified a number of xray pulsars with pulsed emissions having stabilities comparable to atomic clocks. The x-ray pulsar-based navigation and time determination (XNAV) system uses phase measurements from these sources to establish autonomously the position of the detector, and thus the spacecraft, relative to a known reference frame, much as the Global Positioning System (GPS) uses phase measurements from radio signals from several satellites to establish the position of the user relative to an Earth-centered fixed frame of reference. While a GPS receiver uses an antenna to detect the radio signals, XNAV uses a detector array to capture the individual xray photons from the x-ray pulsars. The navigation solution relies on detailed xray source models, signal processing, navigation and timing algorithms, and analytical tools that form the basis of an autonomous XNAV system. Through previous XNAV development efforts, some techniques have been established to utilize a pulsar pulse time-of-arrival (TOA) measurement to correct a position estimate. One well-studied approach, based upon Kalman filter methods, optimally adjusts a dynamic orbit propagation solution based upon the offset in measured and predicted pulse TOA. In this delta position estimator scheme, previously estimated values of spacecraft position and velocity are utilized from an onboard orbit propagator. Using these estimated values, the detected arrival times at the spacecraft of pulses from a pulsar are compared to the predicted arrival times defined by the pulsar s pulse timing model. A discrepancy provides an estimate of the spacecraft position offset, since an error in position will relate to the measured time offset of a pulse along the line of sight to the pulsar. XNAV researchers have been developing additional enhanced approaches to process the photon TOAs to arrive at an estimate of spacecraft position, including those using maximum-likelihood estimation, digital phase locked loops, and "single photon processing" schemes that utilize all available time data associated with each photon. Using pulsars from separate, non-coplanar locations provides range and range-rate measurements in each pulsar s direction. Combining these different pulsar measurements solves for offsets in position and velocity in three dimensions, and provides accurate overall navigation for deep space vehicles.

Sheikh, Suneel