Jay W. McMahon

New Solar Radiation Pressure Force Model for Navigation

This paper presents a new force model for solar radiation pressure acting on a satellite. The model is based on a Fourier series representation of the satellite properties and the position of the sun with respect to the body. The perturbative effects on the satellites orbit due to the solar radiation pressure are derived in full and subsequently averaged to determine the secular change in the orbit due to solar radiation pressure, as well as the short-period dynamics. The theory presented includes a methodology for analyzing the changes to the secular and short-period dynamics due to the spacecraft passing through the Earths shadow. This preliminary study shows that for a spacecraft in a circular orbit with synchronous rotation, the secular effects of solar radiation can be described with only seven Fourier coefficients. The benefits of using this theory for navigation applications are discussed. Finally, an example based on the Gravity Recovery and Climate Experiment satellite illustrates the applicability of the theory presented.

OSIRIS-REx: Sample Return from Asteroid (101955) Bennu

In May of 2011, NASA selected the Origins, Spectral Interpretation, Resource Identification, and Security–Regolith Explorer (OSIRIS-REx) asteroid sample return mission as the third mission in the New Frontiers program. The other two New Frontiers missions are New Horizons, which explored Pluto during a flyby in July 2015 and is on its way for a flyby of Kuiper Belt object 2014 MU69 on January 1, 2019, and Juno, an orbiting mission that is studying the origin, evolution, and internal structure of Jupiter. The spacecraft departed for near-Earth asteroid (101955) Bennu aboard an United Launch Alliance Atlas V 411 evolved expendable launch vehicle at 7:05 p.m. EDT on September 8, 2016, on a seven-year journey to return samples from Bennu. The spacecraft is on an outbound-cruise trajectory that will result in a rendezvous with Bennu in November 2018. The science instruments on the spacecraft will survey Bennu to measure its physical, geological, and chemical properties, and the team will use these data to select a site on the surface to collect at least 60 g of asteroid regolith. The team will also analyze the remote-sensing data to perform a detailed study of the sample site for context, assess Bennu’s resource potential, refine estimates of its impact probability with Earth, and provide ground-truth data for the extensive astronomical data set collected on this asteroid. The spacecraft will leave Bennu in 2021 and return the sample to the Utah Test and Training Range (UTTR) on September 24, 2023.

Fission and reconfiguration of bilobate comets as revealed by 67P/Churyumov–Gerasimenko

The solid, central part of a comet--its nucleus--is subject to destructive processes, which cause nuclei to split at a rate of about 0.01 per year per comet. These destructive events are due to a range of possible thermophysical effects; however, the geophysical expressions of these effects are unknown. Separately, over two-thirds of comet nuclei that have been imaged at high resolution show bilobate shapes, including the nucleus of comet 67P/Churyumov-Gerasimenko (67P), visited by the Rosetta spacecraft. Analysis of the Rosetta observations suggests that 67Ps components were brought together at low speed after their separate formation. Here, we study the structure and dynamics of 67Ps nucleus. We find that sublimation torques have caused the nucleus to spin up in the past to form the large cracks observed on its neck. However, the chaotic evolution of its spin state has so far forestalled its splitting, although it should eventually reach a rapid enough spin rate to do so. Once this occurs, the separated components will be unable to escape each other; they will orbit each other for a time, ultimately undergoing a low-speed merger that will result in a new bilobate configuration. The components of four other imaged bilobate nuclei have volume ratios that are consistent with a similar reconfiguration cycle, pointing to such cycles as a fundamental process in the evolution of short-period comet nuclei. It has been shown that comets were not strong contributors to the so-called late heavy bombardment about 4 billion years ago. The reconfiguration process suggested here would preferentially decimate comet nuclei during migration to the inner solar system, perhaps explaining this lack of a substantial cometary flux.

Improving Space Object Catalog Maintenance Through Advances in Solar Radiation Pressure Modeling

This paper investigates the weaknesses of using the cannonball model to represent the solar radiation pressure force on an object in an orbit determination process, and it presents a number of alternative models that greatly improve the orbit determination performance. These weaknesses are rooted in the fact that the cannonball model is not a good representation of the true solar radiation pressure force acting on an arbitrary object. Using an erroneous force model results in poor estimates, inaccurate trajectory propagation, unrealistic covariances, and the inability to fit long and/or dense arcs of data. The alternative models presented are derived from a Fourier series representation of the solar radiation pressure force. The simplest instantiation of this model requires only two more parameters to be estimated, however, this results in orders of magnitude improvements in tracking accuracy. This improvement is illustrated through numerical examples of a discarded upper stage in a geosynchronous transfe...

Variation of delivered impulse as a function of asteroid shape

This paper will review recent research results focused on the effect of realistic asteroid shapes on the linear momentum delivered to an asteroid during a mitigation attempt. We use simple models for the effect of kinetic impactors and convolve these with a realistic asteroid shape model. For the asteroid shape we use a radar-derived shape model for the asteroid Golevka that captures global topography. For a given impact site we use realistic error distributions and determine how variable the delivered linear and angular momentum impulse is. We find strongly non-Gaussian deviations in delivered momentum, indicating that it may be difficult to achieve a desired level of precision in a deflection attempt.

General Solar Radiation Pressure Model for Global Positioning System Orbit Determination

T HERE are a wide variety of solar radiation pressure (SRP) models used for the GPS satellites. The most complicated numerical methods use ray-tracing methods [1] to attempt to predict the details of the physical interactions that cause the SRP accelerations. Simpler models, such as those by Fliegel and Gallini [2], use geometric primitives to try and capture the main effects at a much smaller computational cost. Thesemodels suffer from the same weakness for orbit determination in that these models are based on ground-measured data of the spacecraft. Once the spacecraft enters the space environment, however, many of the assumptions that go into these models will change in an unpredictable fashion, whichwill change the accelerations caused by the solar radiation pressure. Due to the manner in which these models are developed and used, it is nearly impossible to separate how errors in model parameters impact the spacecraft’s orbit. The most common method to improve the model solution is to apply an estimated correction factor to all parts of the spacecraft equally; however, this method cannot capture all possible model errors, as it changes the accelerations in all directions proportionally. A different type of SRP model was developed independently by Springer et al. [3] at theUniversity of Bern and byBar-Sever [4] at the Jet Propulsion Laboratory, California Institute of Technology (JPL) to model the SRP effect on the orbits of GPS satellites. Both of these models are truncated Fourier series expressed in body-fixed coordinates, for which the coefficients can vary over the course of a year depending on the orbit plane tilt with respect to the sun–Earth line. The University of Bern model uses the difference between the spacecraft and sun’s respective arguments of latitude as the Fourier series argument, while the JPL model uses the sun–spacecraft–Earth angle (see Sec. IV.A for a full explanation of the JPLmodel). In either case, the coefficients were determined byminimizing the residuals of a large number of orbit fits. In other words, the SRP model was determined by observing the orbital effects of SRP without focusing on the physical process that is causing these effects. The model previously derived by the authors [5,6] is similar to the preceding models [2–4], in that it uses a Fourier series expression for the SRP force. The main difference is that the authors’ model is expressed in terms of mean anomaly in the rotating (or local-vertical/ local-horizontal) frame, which allows for an analytical determination of the secular effects on the orbit in terms of the Fourier coefficients. Using the authors’ SRP model has three main advantages over the existingmodels. First, the authors’model is derived in such away that the Fourier series coefficients can be tied to the physics of the SRP interaction with the spacecraft model. Second, an analytical framework has been developed that gives the periodic and secular orbital effects of the rotating frame coefficients. Finally, the authors’ model has a generic formulation that can be applied to any spacecraft, and not only GPS. In this Note, our model [5,6] is applied to the GPS Block IIR-M spacecraft. The model is reviewed in Sec. II. Section III reviews the previous expression for the secular changes to an orbit due to SRP. Section IV explains how the rotating frame coefficients can be determined from the JPL model [4]. In this Note, we show the values of the rotating coefficients computed from the JPL model. These coefficients were used in several estimation schemes, which are discussed in Sec.V. The results of these estimation tests are compared to the performance of the JPL model, and they are shown to be equivalent.

Decentralized Mean Orbit-Element Formation Guidance, Navigation, and Control: Part 1

ight about an estimated weighted mean orbit element formation barycenter is investigated. Consensus over random directed graphs in the presence of time delays is reviewed and applied to the problem. On-orbit spacecraft formations are considered random directed graphs with time delays and agreement over formation parameters is shown. Consensus of formation state estimates and formation barycenter using a distributed formation sensor network is proven. A simulation is described, demonstrating the functionality and applicability of the approach. Conclusions and future work are discussed.

Linearized Lambert’s Problem Solution

Lambert’s problem is the well-known problem to determine the orbit that allows an object to travel between two given position vectors in a given time of flight under Keplerian dynamics. One drawback of solving this problem is that it requires solving a transcendental equation, which involves commonly using an iterative method that can be undesirable for autonomous onboard applications. In this paper, we present a linearization to the solution of Lamberts problem using Lagrange parameters. It is shown that, around a wide variety of nominal transfer trajectories, high-accuracy solutions to the neighboring transfers can be rapidly determined using this linearized solution. Sensitivity studies are presented that show that errors in the terminal velocities are typically well below 1% for cases with 5% perturbations in the terminal positions and time of transfer. Unlike many similar solutions for the relative Lambert’s problem, the linearized results presented here do not suffer in general when the nominal tra...

Decentralized mean orbit element formation stability for uncoordinated maneuvers

Sufficient stability conditions are derived for simultaneous uncoordinated impulsive maneuvers in distributed mean orbit element spacecraft formations. Lyapunov stability formalisms are used in conjunction with distributed mean orbit element spacecraft formation definitions. Special cases of the sufficient stability conditions are examined. Simulated results demonstrate the efficacy of the approach, and conclusions and future work are discussed.

Precise Solar Radiation Pressure Models for Small-Body Orbiters: Applications to OSIRIS-REx Spacecraft

This paper presents a framework for the precise representation of solar radiation pressure effects on spacecraft orbiting around small bodies. It uses a Fourier-series expansion to model the solar ...