David A Vallado

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, mas...

Covariance estimates are becoming more widely available as flight dynamics operations work towards greater accuracy. Investigators have looked at how covariance matrices are propagated, to include orbital state formats and coordinate systems. Various equations to convert between orbital state formats and satellite coordinate systems are essential f...

Earth Orientation Parameter (EOP) and Space Weather data are critical data elements for numerical propagation and space operations. Since CSSI first began assembling consolidated files of EOP and space weather data in 2005, we have continually sought to improve the accuracy of that process. A recent effort reexamined all the sources and added addit...

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...

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...

This paper examines diverse approaches to representing gasdynamic drag effects on Low Earth Orbit (LEO) satellites. Although the total drag force on a satellite can be measured, the physics of gasdynamic resistance, dynamics of the orbiting body, and characteristics of the atmosphere are inextricably combined. Investigators must hypothesize physica...

Satellite Laser Ranging (SLR) is an extremely precise method of tracking satellites that is publicly available. The Orbit Determination Toolkit (ODTK) from Analytical Graphics Inc. (AGI) provides precision orbit determination using an extended Kalman-like filter in combination with different methods of smoothing, an approach requiring parameters th...

Orbit determination processing of two-line element (TLE) sets to extract additional orbital accuracy has been studied for several years. Various approaches have claimed success, and full catalog processing is conducted at ESA. We extend the existing analyses and conduct detailed evaluations of alternatives for the OD processing. This includes exami...

Earth Orientation Parameter and Space Weather data are critical data elements for numerical propagation and space operations. Since CSSI first began assembling consolidated files of EOP and space weather data, we have tracked the performance of these data to better understand what operational users can expect. We present detailed analysis and resul...

In practice, Space Situational Awareness (SSA) requires precise knowledge of all objects in orbit. A complete, robust and accurate SSA system is necessary for accurate conjunction analysis (CA) and Radio Frequency Interference (RFI) de-termination. The Space Data Association fuses data from multiple sources to support state-of-the-art CA and RFI op...

Global constellation coverage has been a topic of interest for many years. The Draim four-satellite continuous global coverage constellation offers improvement over traditional coverage constellations. We re-look at this constellation using new analytical search techniques, computational methods to assess the dynamic performance, and graphical depi...

Two-line element sets have been in regular use for decades. As space centers have largely transitioned to numerical operations, the role of TLE's as an initial estimate tool seems only slightly diminished. Use in conjunction and other operations often requires a covariance, which is unavailable. The accuracy can be limited, but advancements have be...

Global Space Situational Awareness (SSA) is the ability to understand and predict the Space domain with quantified ambiguity. SSA relies on complete and accurate space catalogs inferred from a globally distributed suite of disparate sensors via an Orbit Determination (OD) process. All sensor networks have limitations. As diverse and disparate data...

Maintaining a precise catalog of objects in and near the GEO belt is difficult for a variety of reasons. Optical Hosted Payloads (HP) on commercial satellites have been suggested as a solution to provide accurate, persistent catalog updates to augment existing data or even relieve schedule burden on traditional tracking systems. However, significan...

Examines space data that feed SSA analyses and associated metrics which relate SSA to actionability for a variety of orbital regimes, conditions and force mismodeling.

Generating observations for satellites is a difficult process because actual observations are usually withheld and sensor locations and performance are often unknown. While many tools exist, a comprehensive listing of sensor locations and characteristics is difficult to find. When sensor locations are known, the specific tracking frequency is very...

A properly initialized sequential orbit estimator will converge to less certain state estimates whenever the density of the spacecraft tracking is relatively low; nevertheless, these estimates should remain viable as long the estimator's working assumptions are met. However, when tracking data are sparse, violations of certain working assumptions m...

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 theor...

A proof-of-concept analysis is conducted to demonstrate the benefits of combining observations from commercially hosted optical payloads in Geostationary Earth Orbit (GEO) with data from traditional ground-based tracking systems. Several notional combinations of host orbits, ground tracking, hosted sensor scan capability and scheduling patterns are...

Operations in geosynchronous orbit are important for many aspects of commerce. Avoiding conjunctions in an ever increasingly crowded geosynchronous environment is therefore becoming more important especially in light of the Iridium 33 / Cosmos 2251 collision. SOCRATES-GEO has combined owner operator numerical ephemerides with Two-Line Element (TLE)...

The Orbit Determination Tool Kit (ODTK) is a com-mercial software product from Analytical Graphics, Inc., that performs orbit determination and analysis. Its key features include a tracking-data simulator, an ex-tended (Kalman-like) sequential filter, a fixed-interval smoother and a variable lag smoother. There are a vari-ety of custom tools to aid...

Geosynchronous satellites have traditionally been some of the least accurately maintained orbits with existing ground based sensors for several reasons. MIT/LL successfully operated the MSX/SBV sensor to provide additional observations to AFSPC for processing of GEO space objects for many years. Resulting GEO orbits witnessed a large improvement in...

Goodness-of-fit tests – sometimes called consistency tests – are useful for inves-tigating the lack of optimality of an estimator. Statistical hypothesis tests involv-ing observation residuals are often recommended; however, the most common diagnostic tests may have limited applicability to general orbit determination. In this paper, some less-fami...

Covariance information from orbit determination is being relied upon for space operations now more than ever. There have been scattered claims and discus-sions of realistic covariance, but not enough detailed studies to demonstrate the actual performance against independent references using real data. This paper discusses some statistical tests tha...

Operations in geosynchronous orbit are important for many aspects of commerce. Avoiding conjunctions between an ever increasingly crowded geosynchronous environment is therefore becoming more important especially in light of the Iridium 33 – Cosmos 2251 collision. SOCRATES has processed Two-Line Element (TLE) set information for over 5 years. Unfor...

The IAU 2000A precession-nutation theory relates the International Celestial Reference Frame to the International Terrestrial Reference Frame and has been effective since January 2003. In 2006, the IAU moved to adopt a more dynamically consistent precession model to complement the IAU 2000A nutation theory. This update-described as IAU 2006 precess...

With recent events such as the Chinese ASAT test in 2007 and the USA 193 intercept in 2008, many satellite operators are becoming increasingly aware of the potential threat to their satellites as the result of orbital debris or even other satellites. However, to be successful at conjunction monitoring and collision avoidance requires accurate orbit...

We present the space debris operational process in the context of real circumstances that would have required early assessment, prompt warning, and responsive mitigations. We have applied several widely used collision and explosion models to the prompt debris environment, short term moderation of the debris cloud through reentry, mid-term assessmen...

This chapter discusses the perturbed motion. Perturbations are deviations from a normal, idealized, or undisturbed motion. The actual motion will vary from an ideal undisturbed path due to perturbations caused by other bodies and additional forces not considered in Keplerian motion. It is important to know about gradients, accelerations, and functi...

Modern precise navigation services are creating increased applications for numerically generated state vectors for satellite operations. Traditional radar and optical techniques can achieve modest accuracy in orbit determination, but on-board GPS satellite receivers are changing the routine accuracy available. Operational requirements usually invol...

The authors present several spacecraft rendezvous and close proximity maneuvering techniques modeled with a high-precision numerical integrator using full force models and closed loop control with a Fuzzy Logic intelligent controller to command the engines. The authors document and compare the maneuvers, fuel use, and other parameters. This paper p...

Over a quarter century ago, the United States Department of Defense (DoD) released the equations and source code used to predict satellite positions through SpaceTrack Report Number 3 (STR#3). Because the DoD's two-line element sets (TLEs) were the only source of orbital data, widely available through NASA, this code became commonplace among users...

Over a quarter century ago, the United States Department of Defense (DoD) released the equations and source code used to predict satellite positions through SpaceTrack Report Number 3 (STR#3). Because the DoD's two-line element sets (TLEs) were the only source of orbital data, widely available through NASA, this code became commonplace among users...

Since the demonstration of the first numerically generated space catalog by the United States Navy in 1997, a new issue exists of how to transition from the two-line element sets (TLEs) to routine use of numerical vectors in satellite flight dynamics operations. This generates some unique challenges. The historical TLE operations used analytically...

Since the demonstration of the first numerically generated space catalog by the United States Navy in 1997, the issue of how to transition from the two-line element sets (TLEs), to routine use of numerical vectors in satellite flight dynamics operations is generating some unique challenges. Specifically, how will organizations efficiently interact...

This paper is an introduction to astrodynamic standards and the effort of the AIAA Astrodynamics Committee on Standards (ASDCOS). It describes the progress on the AIAA Recommended Practices, including the work on Part II, Methods, Models, and Data formats which has been developed by the AIAA COS. As the new chair of the committee, I felt it was imp...

This chapter reviews fundamental precepts of multisensor data fusion and applies them to predicting the trajectories of Earth orbiting satellites.

Using analytical theories known as General Perturbations (GP), the US Space Command maintains databases of artificial satellite orbital elements known as the Space Object Catalog. The GP Catalog may be more familiar to the general public as NORAD or NASA two-line orbital elements. These elements are referenced to an unconventional reference frame b...

The technological growth in computers over the past decade or two has been un-paralled in history. In fact, we now possess the capability to perform calculations that were only theoretical due to their extreme computational requirements. Much of the work in astrodynamics requires these type of extensive mathematical calculations and the demands pla...

This paper introduces a concept that could support future space surveillance needs, while meeting fiscal constraint during the development. A brief history is included to provide an introduction into the development of some current systems. In particular, we trace the events of the late 20th century that first compelled nations to devote resources...

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 accurat...

Accurate orbit determination relies on dense observational data and numerical processing. As existing analytical methods are replaced with highly accurate numerical techniques, we must use numerical integration methods that efficiently implement reduction calculations. The desirability to integrate and produce state vectors in varying frames requir...

The problem of computing Earth entry and exit position 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 cylindrical shadow is given. this problem is of interest in case one would like to include perturbat...

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...

The estimation of launch vehicle performance parameters was explored through the use of a Bayes filter. The main emphasis was to use an eight state model that would include the vehicle position and velocity vectors, the vehicle exhaust velocity, and the ratio of the mass flow rate to the initial mass. A primary objective was to be able to observe t...

Relative motion studies have traditionally focused on linearized equations, and inserting additional force models into existing formulations to achieve greater fidelity. A simpler approach may be numerically integrating the two satellite positions and then converting to a modified equi-distant cylindrical frame as necessary. Recent works have intro...