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NASA NTRSDate not supplied

A New Statistical Estimate of the Radar Coverage of the Low Earth Orbit Debris Environment

For over three decades, the NASA Orbital Debris Program Office (ODPO) has used the Goldstone Orbital Debris Radar, Haystack Ultrawideband Satellite Imaging Radar (HUSIR), and Haystack Auxiliary (HAX) radar assets to collect data on the low Earth orbit (LEO) debris environment. Each radar, with its unique beamwidth, altitude and inclination coverage, and limiting size threshold, operates in a beam park mode to statistically sample the orbital debris population in LEO. Provided that these assets are shared with other users, the orbital debris data collection is not continuous; rather, intermittent data collects are acquired and sent to the NASA ODPO. To understand the sampling process conducted by each radar over time and any related observational biases, a Statistical Confirmation of Radar Uniformity or Bias (SCRUB) code has been implemented to model the coverage of these assets for informing future operations, as well as usage of the data collected from these ground-based sensors. For this analysis, Right Ascension of the Ascending Node (RAAN) is used as a metric to measure statistical coverage. A complete survey of the LEO environment is understood to be measurements that sufficiently sample all values of RAAN for each altitude-inclination pair visible from the radar asset. Regions of incompleteness or statistical bias can help inform future observation campaigns. The SCRUB tool evaluates the coverage of the LEO environment, not by examining individual objects that may pass through a sensor’s field of view (FOV), but by determining which orbit planes pass through the FOV. Once a pointing geometry for a radar site, observation time, and range extent are configured by the user, SCRUB computes the inclinations and altitudes that are visible by the sensor. For each inclination-altitude pair, there is a distinct pair of possible RAAN values, corresponding to the ascending and descending orbit passing through that point in the sensor cone. Repeating this process for all points in the beam, and for multiple time periods during an observation window, creates a matrix of all inclination-altitude-RAAN combinations that are visible during a sensor run. This process can then be repeated for all observations within a year (for an annual survey), propagating all the RAAN values to a common epoch, typically the start of a calendar year, and combining the observations to assemble a full estimate of the RAAN coverage of the LEO environment. This RAAN coverage can then be analyzed for uniformity of sampling, within a certain inclination-altitude pair, or between larger regions of the space environment. This paper provides a general overview of the radar assets utilized by ODPO, typical analysis data products assuming circular orbits, and a discussion of the algorithms that feed between modeling and measurement operations. Following the description of the algorithm, estimates of coverage using HUSIR radar data collected from multiple years are developed and compared.

Chris L Ostrom↗

NASA NTRS2023

Orbital Debris Shape Effect Investigations for Mitigating Risk

NASA’s Orbital Debris Program Office (ODPO) and Hypervelocity Impact Technology (HVIT) team have coordinated to better understand the risks to upper stages and spacecraft from non-spherical orbital debris. It is well understood that fragmentation (collision or explosion) events in orbit produce fragments of various materials, sizes, and shapes. To further characterize these parameters, the ODPO is developing the next-generation Orbital Debris Engineering Model (ORDEM) version 4.0 to include orbital debris shape distributions. Ground-based assets, such as radar and optical sensors, can provide size estimates and some insight into material based on radar return or optical filter photometry/spectroscopy, respectively. Characterizing an object’s shape requires more laboratory analyses to infer how shape affects these measurements. More importantly, in addition to size and material/density, the shape of fragments in orbit will alter the ballistic limit equations used in orbital debris risk assessments with NASA’s Bumper Code. The ODPO plans to release ORDEM 4.0 in the coming years. Performing ground-based laboratory impact tests on high-fidelity spacecraft mockups provides the means to directly measure size, mass, material/density, and shape of fragments, all key parameters needed to characterize real-world break up events. The DebriSat test, the results of which are provided, showcases the details of this type of experiment. The goal of this collaborative research between the ODPO and the HVIT team is to include a shape parameter in the environmental and breakup models used to assess risk for various space structures. This paper examines ground-based laboratory impact tests and the associated fragment shape categories. Provided these defined shapes, the approach is simplified by assuming a right circular cylinder (RCC) approximation with varying length-to-diameter ratios. Highlights of impact tests conducted by the HVIT team using non-spherical projectiles based on the RCC approximation are presented. Hydrocode simulations have also been performed to expand on the complexity of variations with non-spherical projectiles. Lastly, ray-tracing simulations of various RCCs of known material are provided to support the ongoing research on optical reflectance distributions with known shapes and to highlight how this may modify the current optical size estimation model. The status and plan forward are outlined for NASA's orbital debris shape effect investigation using a multidisciplinary approach by the ODPO and the HVIT team.

Heather Cowardin↗

NASA NTRSDate not supplied

Aerocapture Trajectory Design for Uranus Orbiter

Introduction: The recently released National Academies Planetary Science and Astrobiology Decadal Survey 2023-2032 [1] identified the Ice Giants as the top priority science destination. While the survey acknowledged the potential for either a Uranus Orbiter and Probe (UOP) mission or a Neptune-Triton Odyssey mission, it ultimately identified the former as the highest priority new flagship mission. UOP missions calls for a launch window of opportunity between 2031-2038 with 12-15 year interplanetary cruise time along with a fully-propulsive Uranus Orbit Insertion burn on the order of a few km/s. However, a mission to Uranus with the same science payload could utilize aerocapture for orbit insertion to achieve both a significant reduction in the interplanetary cruise time and reduction in propulsive burn costs. Why Aerocapture: Aerocapture is a promising propellant and time-saving orbital insertion technique for planetary destinations with an atmosphere. Although not flight-proven, previous aerocapture systems studies in the literature have demonstrated both the validity and robustness of the technique at various planetary destinations. With respect to the Ice Giant planets, Neptune has seen more of the analysis in the literature. For science missions at Neptune, aerocapture can enable 1.4 times more delivered mass to orbit than an all-propulsive mission for the same launch vehicle while reducing interplanetary cruise times by more than 3 years [2] Additionally with modern guidance and control, Neptune aerocapture with blunt-body aeroshells is realizable [3][4]. There are limited papers in the literature investigating Uranus aerocapture with those available providing a preliminary feasibility assessment [5]. Consequently, the two-year funded NASA Space Technology Mission Directorate (STMD)-funded project, titled Aerocapture System as an Enabling Technology for Ice Giants Missions, aims to mature the analysis and technology state of Uranus aerocapture. Trajectory Design: This paper presents the current state of the trajectory design in support of the new aerocapture project. The project design philosophy is inspired from recent Neptune aerocapture studies, which employed modern guidance and control, in the sense that blunt-body aeroshells are analyzed. An assessment of the theoretical flight path angle corridor width is conducted for a range of ballistic coefficients and lift-to-drag ratios for both Space Launch System and Falcon Heavy Launch Vehicle interplanetary trajectory solutions. The results from the corridor width assessment provide an assessment of the aerocapture design-space and qualitative metrics on trajectory design considerations. The Program to Optimize Simulated Trajectories II (POST2) is utilized to run Monte Carlo simulations of Uranus aerocapture three-degree-of-freedom bank angle modulated trajectories using a closed-loop numerical-predictor corrector guidance algorithm. UranusGRAM 2021 is utilized as the atmospheric model [6]. A Uranus-developed aerodatabase, originally derived from Mars Science Laboratory (MSL), is utilized to provide vehicle aerodynamics over a wide range of hypersonic flow regimes. A MSL-derived 70 deg 4.5m diameter sphere-cone aeroshell that houses the UOP payload mass is assumed. Robustness testing and performance analysis is conducted, including the assessment of entry state errors, atmosphere density variations, and aerodynamic dispersions. Post-aerocapture Delta-V and aerothermal statistics are formulated into propellant mass and TPS requirements. The results presented in the paper will demonstrate the trajectory viability of Uranus aerocapture. Preliminary Results: Preliminary trajectory design results indicates successful Uranus aerocapture with a blunt-body aeroshell housing the same payload mass as the UOP mission from an Earth-to-Uranus interplanetary trajectory arriving in less than 7 years. From this interplanetary trajectory, aerocapture provides an orbit insertion Delta-V capability of 6.9 km/s requiring less than 300 m/s for post-aerocapture correction burns (15% of wet mass allocated to propellant). To put this into perspective, the UOP study utilized an Earth-to-Uranus trajectory that arrives in 13 years and requires more than 1000 m/s for fully-propulsive orbit insertion (40% of wet mass allocated to propellant). Achieving the same 6.9 km/s Delta-V capability fully-propulsively is mass prohibitive (97% of wet mass allocated to propellant). Nevertheless, aerocapture has the potential to reduce interplanetary transit times to Uranus by half while delivering the same payload mass to orbit in a reduced propellant mass footprint.

Rohan Deshmukh↗

NASA NTRS2023

Orbital Debris Shape Effect Investigations for Mitigating Risk

Heather Cowardin↗

NASA NTRS2024

Impacts of an Early Morning Low Earth Orbit Observing Platform in A Future Global Observing Network Scenario

Significant changes to the global observing network are expected in the coming decades including the launch of a global ring of geostationary satellites and a reduction in the number of low earth orbit (LEO) platforms. It is anticipated that there may be a gap in the LEO coverage between the planned mid-morning and early afternoon orbits. Here, the utility of an early morning LEO orbit for numerical weather prediction is considered using an observing system simulation experiment (OSSE). A global observing network with two LEO platforms including microwave and hyperspectral infrared instruments and three geostationary hyperspectral infrared platforms is considered for a future baseline scenario. Two instruments, a microwave radiometer modeled on the Advanced Technology Microwave Sounder (ATMS) and a hyperspectral infrared radiometer modeled on the Cross-track Infrared Sounder (CrIS), are tested both individually and in conjunction on a new early morning orbit in addition to the future baseline scenario. The microwave instrument is found to have beneficial impacts for up to 4–7 days in the medium range forecast period with beneficial impacts for the infrared instrument for up to 3–5 days. Short-range forecast impacts estimated with Forecast Sensitivity Observation Impacts (FSOI) over the conterminous United States for the early morning orbit are somewhat weaker than for the same instruments in the early afternoon orbit due to the orbital passage being coincident with rawinsondes while the afternoon orbit is coincident with the minima of both rawinsondes and aircraft.

Nikki C Prive↗

NASA NTRS2003

Simple control laws for low-thrust orbit transfers

Two methods are presented by which to determine both a thrust direction and when to apply thrust to effect specified changes in any of the orbit elements except for true anomaly, which is assumed free. The central body is assumed to be a point mass, and the initial and final orbits are assumed closed. Thrust, when on, is of a constant value, and specific impulse is constant. The thrust profiles derived from the two methods are not propellant-optimal, but are based firstly on the optimal thrust directions and location on the osculating orbit for changing each of the orbit elements and secondly on the desired changes in the orbit elements. Two examples of transfers are presented, one in semimajor axis and inclination, and one in semimajor axis and eccentricity. The latter compares favourably with a propellant-optimized transfer between the same orbits. The control laws have few input parameters, but can still capture the complexity of a wide variety of orbit transfers.

orbit transfer control algorithm↗

NASA NTRS1995

Orbital and Landing Operations at Near-Earth

Orbital and landing operations about near-Earth asteroids are different than classical orbital operations about large bodies. The major differences lie with the small mass of the asteroid, the lower orbital velocities, the larger Solar tide and radiation pressure perturbations, the irregular shape of the asteroid and the potential for non-uniform rotation of the asteroid. These differences change the nature of orbits about an asteroid to where it is often common to find trajectories that evolve from stable, near-circular orbits to crashing or escaping orbits in a matter of days. The understanding and control of such orbits is important if a human or robotic presence at asteroids is to be commonplace in the future.

Orbital Near-Earth↗

NASA NTRS2006

Designing capture trajectories to unstable periodic orbits around Europa

The hostile environment of third body perturbations restricts a mission designer's ability to find well-behaved reproducible capture trajectories when dealing with limited control authority as is typical with low-thrust missions. The approach outlined in this paper confronts this shortcoming by utilizing dynamical systems theory and an extensive preexisting database of Restricted Three Body Problem (RTBP) periodic orbits. The stable manifolds of unstable periodic orbits are utilized to attract a spacecraft towards Europa. By selecting an appropriate periodic orbit, a mission designer can control important characteristics of the captured state including stability, minimum altitudes, characteristic inclinations, and characteristic radii among others. Several free parameters are optimized in the non-trivial mapping from the RTBP to a more realistic model. Although the ephemeris capture orbit is ballistic by design, low-thrust is used to target the state that leads to the capture orbit, control the spacecraft after arriving on the unstable quasi-periodic orbit, and begin the spiral down towards the science orbit. The approach allows a mission designer to directly target fuel efficient captures at Europa in an ephemeris model. Furthermore, it provides structure and controllability to the design of capture trajectories that reside in a chaotic environment.

low-thrust↗

NASA NTRS2008

Subregions of Motion and Elliptic Halo Orbits in the Elliptic Restricted Three-Body Problem

In this paper we present regions of motion and periodic orbits in the spatial elliptic restricted three body problem (ER3BP). Periodic orbits and regions of motion are fundamental keys to understand any dynamical system; for this reason the Hill's surfaces or the families of halo orbits have been extensively studied in the frame of the circular restricted three body problem. It is our opinion that their natural extensions to the ER3BP have not been studied enough. We divide the position space into forbidden subregions, subregions of motion and low-velocity subregions.We use these notions to define necessary condition for a transfer trajectory in the ER3BP. Also we compute branches of elliptic halo orbits bifurcating from halo orbits in the circular restricted three body problem. The new periodic orbits have principal periods and stability properties different from those of the originating halo orbit.

mission design↗

NASA NTRS2012

Earth Orbit Raise Design for the ARTEMIS Mission

ARTEMIS is a mission to send two spacecraft from Earth orbit to libration orbits around the Moon Lagrange points and then into lunar orbit. Lunar flybys were used early in the mission to send the spacecraft into low-energy lunar transfers which were designed libration orbits for minimal deltaV. ARTEMIS began by raising the Earth orbits of each spacecraft to achieve the planned lunar flybys. Spacecraft conguration and operation constraints made the Earth orbit raise phase of the mission a signicant mission design challenge by itself. This paper describes the process used to and trajectories that achieved mission goals and the resulting series of Earth orbits that culminated in successful lunar flybys.

lunar transfer↗

NASA NTRS2013

The Thermal Expansion of Ring Particles and the Secular Orbital Evolution of Rings Around Planets and Asteroids

The thermal expansion and contraction of ring particles orbiting a planet or asteroid can cause secular orbit evolution. This effect, called here the thermal expansion effect, depends on ring particles entering and exiting the shadow of the body they orbit. A particle cools off in the shadow and heats up again in the sunshine, suffering thermal contraction and expansion. The changing cross-section it presents to solar radiation pressure plus time lags due to thermal inertia lead to a net along-track force. The effect causes outward drift for rocky particles. For the equatorial orbits considered here, the thermal expansion effect is larger than Poynting-Robertson drag in the inner solar system for particles in the size range approx. 0.001 - 0.02 m. This leads to a net increase in the semimajor axis from the two opposing effects at rates ranging from approx. 0.1 R per million years for Mars to approx. 1 R per million years for Mercury, for distances approx. 2R from the body, where R is the body's radius. Asteroid 243 Ida has approx. 10 R per million years, while a hypothetical Near-Earth Asteroid (NEA) can have faster rates of approx. 0.5 R per thousand years, due chiefly to its small radius compared to the planets. The thermal expansion effect weakens greatly at Jupiter and is overwhelmed by Poynting-Robertson for icy particles orbiting Saturn. Meteoroids in eccentric orbits about the Sun also suffer the thermal expansion effect, but with only approx. 0.0003e2 AU change in semimajor axis over a million years for a 2 m meteoroid orbiting between Mercury and Earth.

Ring particles↗

NASA NTRS2016

Alternative Method of On-Orbit Response-Versus-Scan-Angle Characterization for MODIS Reflective Solar Bands

The moderate resolution imaging spectroradiometer (MODIS) has 20 reflective solar bands (RSB), covering a spectral range from 0.41 to 2.2 microns, which are calibrated on-orbit using its onboard calibrators, which include a solar diffuser, a solar diffuser stability monitor, and a spectroradiometric calibration assembly. A space view (SV) port is used to provide a background reference and also facilitates near-monthly lunar observations through a spacecraft roll. In every scan, the Earth's surface, SV, and onboard calibrators are viewed via a two-sided scan mirror, the reflectance of which depends on the angle of incidence (AOI) as well as the wavelength of the incident light. Response-versus-scan-angle (RVS) is defined as a dependence function of the scan mirror's reflectance over AOI. An initial RVS for each RSB was measured prelaunch for both Terra and Aqua MODIS. Algorithms have been developed to track the on-orbit RVS variation using the measurements from the onboard calibrators, supplemented with the earth view (EV) trends from pseudoinvariant desert targets obtained at different AOI. Since the mission beginning, the MODIS characterization support team (MCST) has dedicated efforts in evaluating approaches of characterizing the on-orbit RVS. A majority of the approaches focused on fitting the data at each AOI over time and then deriving the relative change at different AOI. The current version of the on-orbit RVS algorithm, as implemented in the collection 6 (C6) level-1B (L1B), is also based on the above rationale. It utilizes the EV response trends from the pseudoinvariant Libyan desert targets to supplement the gain derived from the onboard calibrators. The primary limitation of this approach is the assumption of the temporal stability of these desert sites. Consequently, MCST developed an approach that derives the on-orbit RVS change using measurements from a single desert site, combined with the on-orbit lunar measurements. In addition, the EV and onboard responses are fit first as a function of AOI before fitting temporally in order to eliminate the dependence on the stability of the desert site. Comprehensive comparisons are performed with current C6 RVS results for both Terra and Aqua MODIS. Results demonstrate that this alternative method provides a supplemental means to monitor the on-orbit RVS for MODIS RSB.

solar bands↗

NASA NTRS2017

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↗

NASA NTRS1972

A Monte Carlo error analysis program for near-Mars, finite-burn, orbital transfer maneuvers

A computer program was developed which performs an error analysis of a minimum-fuel, finite-thrust, transfer maneuver between two Keplerian orbits in the vicinity of Mars. The method of analysis is the Monte Carlo approach where each off-nominal initial orbit is targeted to the desired final orbit. The errors in the initial orbit are described by two covariance matrices of state deviations and tracking errors. The function of the program is to relate these errors to the resulting errors in the final orbit. The equations of motion for the transfer trajectory are those of a spacecraft maneuvering with constant thrust and mass-flow rate in the neighborhood of a single body. The thrust vector is allowed to rotate in a plane with a constant pitch rate. The transfer trajectory is characterized by six control parameters and the final orbit is defined, or partially defined, by the desired target parameters. The program is applicable to the deboost maneuver (hyperbola to ellipse), orbital trim maneuver (ellipse to ellipse), fly-by maneuver (hyperbola to hyperbola), escape maneuvers (ellipse to hyperbola), and deorbit maneuver.

Green, R. N.↗

NASA NTRS1972

Some higher order analyses of earth and lunar orbiters

The accurate modelling of the translational behavior of a drag-free satellite in an almost circular near-earth orbit is investigated. All short and long period position fluctuations in the satellite's coordinates down to 1 m are determined. The general zonal and tesseral harmonic effects are considered as well as lunar and solar effects. A noncanonical approach is followed. A mean orbital plane is chosen so that no short period out-of-plane fluctuations greater than second order occur. Short period radial and cross-track fluctuations and in-track fluctuations are computed. Long period and secular rates of the mean elements which define the slowly varying plane of reference are determined to third order in the small quantities. The equations of motion are integrated analytically away from critical inclination and tesseral resonance. The resonant situation of a sun-synchronous orbit is discussed as a special case. The long-period behavior of a lunar orbiter is also considered, including the effects due to the inclination of the earth's apparent orbit about the moon and those described by Cassini laws on the equations of motion. Both resonant and nonresonant low orbits, and high orbits are discussed.

Dasenbrock, R. R.↗

NASA NTRS1973

The tidal loss of satellite-orbiting objects and its implications for the lunar surface

The solar system is composed of numerous bodies orbiting the sun, and numerous satellites orbiting planets. However, no objects greater than a kilometer in diameter are known to orbit satellites. Theoretical arguments are used to show that most objects orbiting satellites ultimately would be destroyed by tidal interactions. This may explain why such objects have not been observed. These arguments are applied to objects orbiting the moon. The ages and sizes of most of the circular mare basins are compatible with the lifetimes and crater sizes expected for impacts by objects caught in decaying lunar orbits. The morphology of a few circular mare basins (Crisium, Serenitatis, and possibly Imbrium) indicates that they could have been formed by such impacts. Thus, the lunar surface may provide a record of impacts due to objects caught in tidally decaying lunar orbits.

Reid, M. J.↗

NASA NTRS1974

Calculation of precision satellite orbits with nonsingular elements /VOP formulation/

Review of some results obtained in an effort to develop efficient, high-precision trajectory computation processes for artificial satellites by optimum selection of the form of the equations of motion of the satellite and the numerical integration method. In particular, the matching of a Gaussian variation-of-parameter (VOP) formulation is considered which is expressed in terms of equinoctial orbital elements and partially decouples the motion of the orbital frame from motion within the orbital frame. The performance of the resulting orbit generators is then compared with the popular classical Cowell/Gauss-Jackson formulation/integrator pair for two distinctly different orbit types - namely, the orbit of the ATS satellite at near-geosynchronous conditions and the near-circular orbit of the GEOS-C satellite at 1000 km.

Velez, C. E.↗

NASA NTRS1975

Pioneer probe mission with orbiter option

A spacecraft is described which is based on Pioneer 10 and 11, and existing propulsion technology; it can transport and release a probe for entry into Jupiter's atmosphere, and subsequently maneuver to place the spacecraft in orbit about Jupiter. Orbital operations last 3 years and include maneuvers to provide multiple close satellite encounters which allow the orbit to be significantly changed to explore different parts of the magnetosphere. A mission summary, a guide to related documents, and background information about Jupiter are presented along with mission analysis over the complete mission profile. Other topics discussed include the launch, interplanetary flight, probe release and orbit deflection, probe entry, orbit selection, orbit insertion, periapsis raising, spacecraft description, and the effects of Jupiter's radiation belt on both orbiter and the probe.

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