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The Debris Risk Evolution And Dispersal (DREAD) tool facilitates the 3D modeling and risk analysis of the fragmentation cloud after a collision or explosion. This tool uses the NASA Standard Breakup Model and other breakup models “under the hood” that are capable of estimating the Probability Density Function (PDF) of induced relative velocity, mass and area of fragments as a function of object size. DREAD can be further enhanced by incorporation of alternate, more detailed hypervelocity simulations that enforce conservation laws (conservation of mass, angular and linear momentum and kinetic energy). We also discuss our recent incorporation of an improved technique to normalize risk by the expansion volume occupied by debris fragments. DREAD is then used to examine the likely debris fragmentation cloud created by the Fengyun 1C (FY1C) antisatellite (ASAT) intercept test conducted by the Chinese in 2007 and the risk it subsequently posed to other spacecraft and the cloud’s evolution and dispersal.

A solar eclipse occurs when the Sun, Moon and Earth are aligned in such a way that shadow of the Moon falls on the Earth. The Moon׳s shadow also falls on the Earth orbiting spacecraft. In this case, the alignment of the Sun, Moon, and spacecraft is similar to that of the Sun, Moon, and Earth but this phenomenon is often referred as a lunar eclipse falling on the spacecraft. Lunar eclipse is not as regular in terms of times of occurrence, duration, and depth as the Earth shadow eclipse and number of its occurrence per orbital location per year ranges from zero to four with an average of two per year; a spacecraft may experience two to three lunar eclipses within a twenty-four hour period [2] . These lunar eclipses can cause severe spacecraft operational problems. This paper describes two lunar shadow eclipse prediction models using a projection map approach and a line of intersection method by extending the Earth shadow eclipse models described by Srivastava et al. [10] , [11] for the Earth orbiting spacecraft. The attractive feature of both models is that they are much easier to implement. Both mathematical models have been simulated for two Indian low Earth orbiting spacecrafts: Oceansat-2, Saral-1, and two geostationary spacecrafts: GSAT-10, INSAT-4CR. Results obtained by the models compare well with lunar shadow model given by Escobal and Robertson [12] , and high fidelity commercial software package, Systems Tool Kit (STK) of AGI.

Relative motion improvements have traditionally focused on inserting additional force models into existing formulations to achieve greater fidelity, or complex expansions to admit eccentric orbits for propagation. A simpler approach may be numerically integrating the two satellite positions and then converting to a modified equidistant cylindrical frame for comparison in a Hill’s-like frame. Recent works have introduced some approaches for this transformation within the Hill’s construct, and examined the accuracy of the transformation. Still others have introduced transformations as they apply to covariance operations. Each of these has some orbital or force model limitations and defines an approximate circular reference dimension. We develop a precise transformation between the Cartesian and curvilinear frame along the actual satellite orbit and test the results for various orbital classes. The transformation has wide applicability.

This paper examines atmospheric drag models and data usage involved with propagating near-Earth satellites. Many studies, and even some International standards try to promote one model over another, rather than identifying the behavior of the numerous parameters necessary to select the best model for a particular mission and application. We briefly summarize existing information, and quantify sources of uncertainty in satellite propagation resulting from several atmospheric models, or from the treatment of input data indices. The goal is for researchers to understand the relative impact of using different models and data indices so they can properly assess which model and data input to use.

Here, observing geosynchronous satellites has numerous applications. Lighting conditions near the equinoxes routinely cause problems for traditional observations of sensors near the equator – the solar exclusion. We investigate using sensors on satellites (in polar and high- altitude orbits) to observe satellites that are in geosynchronous orbit. It is hoped that these satellite configurations will alleviate many of these problems. Assessing the orbit insertion and station-keeping requirements are important to understand. We summarize the literature to understand the relevant perturbing forces and assess the delta-v requirements.

Requirements have existed for several decades for highly accurate satellite orbits. With increased computer power, simplified analytical techniques have lost most of their competitive edge and numerical techniques are experiencing wide-spread popularity. When coupled with increased accuracy requirements from commercial satellites owners and accurate computations for debris and close approach for the International Space Station, a reliable method must be found to form highly-accurate satellite state vectors. This paper explores one approach using dense observational data from short-arcs of geographically distributed sensor sites. In particular, dense observations (consisting of one observation per second for about two minutes) are analyzed to determine the accuracy that can be achieved via high fidelity, numerical, orbit-determination techniques.

The problem of computing Earth satellite entry and exit positions through the Earth’s umbra and penumbra, for satellites in elliptical orbits, is solved without the use of a quartic equation. A condition for existence of a solution in the case of a cylindrical shadow is given. This problem is of interest in case one would like to include perturbation force resulting from solar radiation pressure. Most satellites (including geosynchronous) experience periodic eclipses behind the Earth. Of course when the satellite is eclipsed, it’s not exposed to solar radiation pressure. When we need extreme accuracy, we must develop models that turn the solar radiation calculations “on” and “off,” as appropriate, to account for these periods of inactivity.

Reviews basic statements of the equations of motion, including Kepler's and Newton's laws and the constants of orbital motion. Orbital elements are introduced and the two-body problem is shown along with conic sections. These relations form the basis for astrodynamic applications and permit many useful studies to be accomplished. Perturbation theory and the major forces affecting satellite motion are discussed, along with the variability of those forces. Graphs are included to show the effect of perturbing forces on typical satellite orbits. The distinction is made between mean and osculating elements, fast and slow variables, and periodic forces. Discussion about the main problems in astrodynamics is included – orbit propagation and orbit estimation – along with definitions of analytical, numerical, and semianalytical propagation. The broad concept of orbit determination is introduced. Some relevant problems in astrodynamics are introduced noting the tie to propagation and orbit estimation. A summary concludes the remarks. Keywords: orbital mechanics; fundamentals; two-body motion; perturbations; constants of the motion; perturbation forces; main problems in astrodynamics

A library PASCAL and FORTRAN computer routines to solve various Astrodynamic problems is presented. Diagrams and equations are given for each routine. The main part of the document is the actual code. Rigorous documentation and coding discipline was used during development of these routines. The code contains extensive information for each routine defining Input / Output variables, local variables, constants, coupling, and references. Finally, test cases and answers are presented. References are given, therefore formulas are not derived. THe code presented will run under TURBO PASCAL Ver5.0 +, MICROSOFT FORTRAN Ver 4.0 +, and VAX FORTRAN Ver 4.6. Both langauges have two files, astrodynamic and mathematical. The PASCAL mathematical code includes a number of mathematical operations not inherent to language. The FORTRAN code was developed in LAHEY FORTRAN Ver 3.0 and uses several features of FORTRAN 90. Driver programs are not included since these routines are designed to be a library which one may attach to a main program. These routines were developed for academic use and as such, may not match operational data. Information concerning the latest software version may be obtained from the author.