King-Hele orbit theory for periodic orbit and attitude variations
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Vishal Ray↗
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GEORB: Release for precise orbit determination of low Earth orbiters and satellite gravity missions
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Thomas Loudis Papanikolaou↗
Variation in Predicted Orbital Lifetime Due to Launch Year
We present trends in predicted orbital lifetimes of CubeSats based not only on orbital parameters, but also launch year and the Area-to-Mass (AtM) ratio of the CubeSat. Determining the orbital lifetime variation of CubeSats in low-Earth orbit (LEO) is an important aspect of mission planning because of two competing factors: (1) the maximum orbital lifetime for orbital debris mitigation requirements, and (2) the minimum orbit duration necessary to accomplish the spacecraft mission requirements. The orbital lifetime is a function of orbital parameters, the AtM ratio of the CubeSat, and date of orbit insertion. Solar flux varies with time, peaking and declining across the 11-year solar cycle and affecting the amount of atmospheric drag on the CubeSat. This results in large variations in orbital lifetime dependent on the mission's launch date. We calculated the variation of orbital lifetime for multiple commonly used 1U to 6U CubeSat mission types across the two upcoming solar cycles. For any given AtM ratio and altitude combination in this analysis, the predicted orbital lifetime varies up to a factor of five due to orbit insertion occurring in a different year. Some examples of orbital lifetime spreads are 5 months to 2 years, and 1.5 to 7.5 years. While orbital lifetimes correlate to the solar cycle, the phasing of the maximum values varies based on a given AtM ratio and altitude combination. Different combinations of these two factors will result in the maximum predicted orbital lifetime occurring at different launch years throughout the solar cycle. Therefore, there is not a specific year within a solar cycle which can be used to calculate the maximum predicted orbital lifetime for all CubeSats. Since CubeSats are typically flown as a rideshare payload on a launch vehicle, mission planners must account for launch date variation in their orbital lifetime predictions. We recommend calculating orbital lifetime for a range of dates to allow for risk planning due to launch date slips, and other mission planning best practices.
CubeSat↗
Cislunar Near Rectilinear Halo Orbit for Human Space Exploration
In order to conduct sustained human exploration beyond Low Earth Orbit (LEO), spacecraft systems are designed to operate in a series of missions of increasing complexity. Regardless of the destination, Moon, Mars, asteroids or beyond, there is a substantial set of common objectives that must be met. Many orbit characterization studies have endeavored to evaluate the potential locations in cislunar space that are favorable for meeting common human exploration objectives in a stepwise approach. Multiple studies, by both NASA and other international space agencies, have indicated that Earth-‐moon libration point orbits are attractive candidates for staging operations in the proving ground and beyond. In particular, the Near Rectilinear Orbit (NRO) has been demonstrated to meet multi-‐mission and multi-‐destination architectural constraints. However, a human mission to a selected NRO presents a variety of new challenges for mission planning. While a growing number of robotic missions have completed successful operations to various specific libration point orbits, human missions have never been conducted to orbits of this class. Human missions have unique challenges that differ significantly from robotic missions, including a lower tolerance for mission risk and additional operational constraints that are associated only with human spacecraft. In addition, neither robotic nor human missions have been operated in the NRO regime specifically, and NROs exhibit dynamical characteristics that can differ significantly as compared to other halo orbits. Finally, multi-‐body orbits, such as libration point orbits, are identified to exist in a simplified orbit model known as the Circular Restricted Three Body Problem (CRTBP) and must then be re-‐solved in the full ephemeris model. As a result, the behavior of multi-‐body orbits cannot be effectively characterized within the classical two-‐body orbit dynamics framework more familiar to the human spaceflight community. In fact, a given NRO is not identified by a set of Keplerian orbit parameters, and a valid epoch specific state vector must be first obtained from a multi-body dynamical model. In this paper, the significant performance and operational challenges of conducting human missions to the NRO are evaluated. First, a systematic process for generating full ephemeris based ballistic NROs of various families is outlined to demonstrate the relative ease in which a multi-‐revolution orbit can be found for any epoch and for various orbit geometries. In the Earth-‐Moon system, NROs, which are halo orbits with close passage over a lunar pole, can exist with respect to libration point 1 (L1) or libration point 2 (L2) and are either from a North or South family orbit class with respect to the ecliptic. Second, the ability to maintain the orbit over the lifetime of a habitat mission by applying a reliable station-keeping strategy is investigated. The NRO, while similar to the quasi-‐halo orbits that the Artemis mission flew, requires an updated station keeping strategy. This is due to several dynamical differences such as the increased relative stability of the NRO compared to other halo orbits and the close passage over the lunar surface as shown in Figure 1. Multiple station-keeping strategies are being investigated to ensure a human spacecraft remains on a predictable path. As the NRO is not described in simple two-‐body parameters, analysis must determine the best strategy for targeting a reference NRO as well as how closely a future state should be constrained. In addition, costs will be minimized by determining maneuver directionality based on an identified pattern in the optimal station-keeping solutions or an analytically derived relationship. The candidate station-keeping algorithm must be stable and robust to environmental and vehicle uncertainties as well to navigation estimation and flight control execution errors. To that end, navigation accuracies, the impact on the station-keeping execution errors as well as other vehicle uncertainties need to be assessed. Starting with Orion, current navigation accuracies are evaluated and then navigation requirements are derived assuming a desired station-keeping propellant budget. Third, the performance requirements to and from the NRO are evaluated. Important parameters for developing expected propellant costs include epoch of operation, size and type of NRO, Earth departure and return constraints, as well as abort or early-‐return capability. Finally, rendezvous and proximity operations are vital aspects of multi-‐mission human exploration endeavors. The ability to conduct rendezvous and the associated propellant costs are assessed as well as the impacts of various profile assumptions including the location within the NRO the rendezvous is performed. The results of these studies will influence plans for international cooperation on both nearer term proving ground missions and beyond.
Whitley, Ryan↗
Polishing the Gold Standard: The Role of Orbital Choice in CCSD(T) Vibrational Frequency Prediction
While CCSD(T) with spin-restricted Hartree-Fock (RHF) orbitals has long been lauded for its ability to accurately describe closed-shell interactions, the performance of CCSD(T) on open-shell species is much more erratic, especially when using a spin-unrestricted HF (UHF) reference. Previous studies have shown improved treatment of open-shell systems when a non-HF set of molecular orbitals, like Brueckner or Kohn-Sham density functional theory (DFT) orbitals, is used as a reference. Inspired by the success of regularized orbital-optimized second-order Møller-Plesset perturbation theory (κ-OOMP2) orbitals as reference orbitals for MP3, we investigate the use of κ-OOMP2 orbitals and various DFT orbitals as reference orbitals for CCSD(T) calculations of the corrected ground-state harmonic vibrational frequencies of a set of 36 closed-shell (29 neutrals, 6 cations, 1 anion) and 59 open-shell diatomic species (38 neutrals, 15 cations, 6 anions). The aug-cc-pwCVTZ basis set is used for all calculations. The use of κ-OOMP2 orbitals in this context alleviates difficult cases observed for both UHF orbitals and OOMP2 orbitals. Removing two multireference systems and 12 systems with ambiguous experimental data leaves a pruned data set. Overall performance on the pruned data set highlights CCSD(T) with a B97 orbital reference (CCSD(T):B97), CCSD(T) with a κ-OOMP2 orbital reference (CCSD(T):κ-OOMP2), and CCSD(T) with a B97M-rV orbital reference (CCSD(T):B97M-rV) with RMSDs of 8.48 cm -1 , and 8.50 cm -1 , and 8.75 cm -1 respectively, outperforming CCSD(T):UHF by nearly a factor of 5. Moreover, the performance on the closed- and open-shell subsets shows these methods are able to treat open-shell and closed-shell systems with comparable accuracy and robustness. CCSD(T) with RHF orbitals is seen to improve upon UHF for the closed-shell species, while spatial symmetry breaking in a number of restricted open-shell HF (ROHF) references leads CCSD(T) with ROHF reference orbitals to exhibit the poorest statistical performance of all methods surveyed for open-shell species. The use of κ-OOMP2 orbitals has also proven useful in diagnosing multireference character that can hinder the reliability of CCSD(T).
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
f-Orbital Mixing in the Octahedral f 2 Compounds UX 6 2– [X = F, Br, Cl, I] and PrCl 6 3–
Understanding how interactions between the f orbitals and ligand orbitals in lanthanide and actinide systems affect their physical properties is the central issue in f-element chemistry. A wide variety of approaches including both theoretical and experimental tools have been used to study these relationships. Among the most widely used tools has been crystal field theory (CFT), which bridges theory and experiment in that it is a model based largely on atomic theory that is parametrized using experimental data. Crystal field theory is quite accurate for the lanthanides, due in part to the highly contracted nature of the 4f orbitals. For actinides, crystal field theory is less accurate, potentially due to the treatment of orbital mixing. In CFT, orbital mixing is handled implicitly by allowing the electron repulsion parameters (Slater F k parameters) and the spin–orbit coupling constant to vary. As a result, orbital mixing in CFT is isotropic in that the F k parameters and the spin–orbit coupling constant affect all f orbitals equally. This approximation works well for the lanthanides due to the limited degree of orbital mixing in these complexes. In actinide complexes, the 5f orbitals have greater overlap with the ligand orbitals, and this approximation is less accurate than in the lanthanides. In this work, we report a modification of CFT that includes the effect of orbital mixing on electron repulsion and spin–orbit coupling for each f orbital. The model is applied to the tetravalent uranium hexahalide dianions and PrCl 6 3– for which the energies of many low-lying excited states are known. The new model generally fits the data as well the traditional CFT although with fewer parameters. However, the new model does not fit the data better than the more complex CFT models of Faucher and co-workers. The results of the model show in detail how changes in overlap and orbital energies influence the energies of the bonding and antibonding orbitals.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
JSC Orbital Debris Website Description
Purpose: The website provides information about the NASA Orbital Debris Program Office at JSC, which is the lead NASA center for orbital debris research. It is recognized world-wide for its leadership in addressing orbital debris issues. The NASA Orbital Debris Program Office has taken the international lead in conducting measurements of the environment and in developing the technical consensus for adopting mitigation measures to protect users of the orbital environment. Work at the center continues with developing an improved understanding of the orbital debris environment and measures that can be taken to control its growth. Major Contents: Orbital Debris research is divided into the following five broad efforts. Each area of research contains specific information as follows: 1) Modeling - NASA scientists continue to develop and upgrade orbital debris models to describe and characterize the current and future debris environment. Evolutionary and engineering models are described in detail. Downloadable items include a document in PDF format and executable software. 2) Measurements - Measurements of near-Earth orbital debris are accomplished by conducting ground-based and space-based observations of the orbital debris environment. The data from these sources provide validation of the environment models and identify the presence of new sources. Radar, optical and surface examinations are described. External links to related topics are provided. 3) Protection - Orbital debris protection involves conducting hypervelocity impact measurements to assess the risk presented by orbital debris to operating spacecraft and developing new materials and new designs to provide better protection from the environment with less weight penalty. The data from this work provides the link between the environment defined by the models and the risk presented by that environment to operating spacecraft and provides recommendations on design and operations procedures to reduce the risk as required. These data also help in the analysis and interpretation of impact features on returned spacecraft surfaces. 4) Mitigation - Controlling the growth of the orbital debris population is a high priority for NASA, the United States, and the major space-faring nations of the world to preserve near-Earth space for future generations. Mitigation measures can take the form of curtailing or preventing the creation of new debris, designing satellites to withstand impacts by small debris, and implementing operational procedures ranging from utilizing orbital regimes with less debris, adopting specific spacecraft attitudes, and even maneuvering to avoid collisions with debris. Downloadable items include several documents in PDF format and executable software.and 5) Reentry - Because of the increasing number of objects in space, NASA has adopted guidelines and assessment procedures to reduce the number of non-operational spacecraft and spent rocket upper stages orbiting the Earth. One method of postmission disposal is to allow reentry of these spacecraft, either from orbital decay (uncontrolled entry) or with a controlled entry. Orbital decay may be achieved by firing engines to lower the perigee altitude so that atmospheric drag will eventually cause the spacecraft to enter. However, the surviving debris impact footprint cannot be guaranteed to avoid inhabited landmasses. Controlled entry normally occurs by using a larger amount of propellant with a larger propulsion system to drive the spacecraft to enter the atmosphere at a steeper flight path angle. It will then enter at a more precise latitude, longitude, and footprint in a nearly uninhabited impact region, generally located in the ocean.
Johnson, Nicholas L.↗
Small Aerostationary Telecommunications Orbiter Concept for Mars in the 2020s
Current Mars science orbiters carry UHF proximity payloads to provide limited access and data services to landers and rovers on Mars surface. In the era of human spaceflight to Mars, very high rate and reliable relay services will be needed to serve a large number of supporting vehicles, habitats, and orbiters, as well as astronaut EVAs. These will likely be provided by a robust network of orbiting assets in very high orbits, such as areostationary orbits. In the decade leading to that era, telecommunications orbits can be operated at areostationary orbit that can support a significant population of robotic precursor missions and build the network capabilities needed for the human spaceflight era. Telecommunications orbiters of modest size and cost, delivered by Solar Electric Propulsion to areostationary orbit, can provide continuous access at very high data rates to users on the surface and in Mars orbit.In the era of human spaceflight to Mars very high rate andreliable relay services will be needed to serve a largenumber of supporting vehicles, habitats, and orbiters, aswell as astronaut EVAs. These could be provided by arobust network of orbiting assets in very high orbits. In thedecade leading to that era, telecommunications orbiterscould be operated at areostationary orbit that could support asignificant population of robotic precursor missions andbuild the network capabilities needed for the humanspaceflight era. These orbiters could demonstrate thecapabilities and services needed for the future but withoutthe high bandwidth and high reliability requirements neededfor human spaceflight.Telecommunications orbiters of modest size and cost,delivered by Solar Electric Propulsion to areostationaryorbit, could provide continuous access at very high datarates to users on the surface and in Mars orbit. Twoexamples highlighting the wide variety of orbiter deliveryand configuration options were shown that could providehigh-performance service to users.
Lock, Robert E.↗
Recent Radar Observations of the Sub-Centimeter Orbital Debris Environment
The NASA Orbital Debris Program Office (ODPO) has conducted radar observations of the orbital debris environment since the early 1990’s to provide measurement data that supports orbital debris models and risk mitigation activities in support of NASA mission objectives. Orbital debris radar observations are a unique mode for radar operation, employing a fixed beam configuration to statistically sample the environment. An advantage of conducting operations in this fashion is that it enables observations of smaller classes of orbital debris than would otherwise be available from the same sensor operating in a traditional tracking mode. Orbital debris-mode radar observations are used to fill in the gaps, which exist in the currently available data from the Space Surveillance Network (SSN), on small size orbital debris populations that represent significant risk to NASA programs. These gaps have typically covered orbital debris with characteristic sizes less than approximately 10 cm down to approximately 3 mm in low Earth orbit (LEO) – depending upon the altitude and sensor configuration. The value of orbital debris radar measurements lies in the ability to extract partial orbital element information about orbital debris in the centimeter to several millimeter size regimes in low Earth orbit – which are not available from other measurement sources. This paper will discuss observations of this smaller class of orbital debris observed in recent years from the radars at the MIT Haystack Observatory in Westford, Massachusetts, and the Goldstone Solar System Radar near Barstow, California. The former radar is able to observe orbital debris down to approximately 5 mm, and the latter, orbital debris with characteristic sizes near 3 mm – at altitudes less than 1000 km. The characteristics and inferences about the current LEO orbital debris environment, and the different subpopulations that are identifiable in the observations are highlighted.
Kennedy, Timothy↗
Origin of orbital debris impacts on Long Duration Exposure Facility's (LDEF) trailing surfaces
Orbital debris tracked by the US Space Command is mostly in near circular orbit around the Earth. If small debris were in the same types of orbits, there would be very few orbital debris impacts on the Long Duration Exposure Facility's (LDEF's) trailing surfaces. However, at least 15 percent of the impacts found on the trailing A03 gold surface was found to be orbital debris impacts. This measurement suggests that the orbital distribution of small debris is not the same as that of larger debris. Although this is not a total surprise, since modelling of satellite breakups has predicted different distributions, it does raise questions as to what types of orbits could be responsible for these impacts. A model was developed to explain these LDEF results. The model calculates the expected debris impact crater distribution around LDEF, as a function of debris orbital parameters. The results show that only low inclination and highly elliptical orbits could be responsible for these impacts. The most common object left in this type of orbit is an orbital transfer stage, used by the US and ESA to place objects into geosynchronous orbit, and inclinations near 28 and 7 degrees for the US and ESA, respectively. Even large fragments from satellites, which break up in these types of orbits, are difficult to observe from the ground; consequently, little is known about the number and characteristics of breakups in these orbits. The LDEF data suggest that these objects are breaking up. The LDEF data also suggest that the ratio of the contribution of small debris from this type of orbit to the contribution from circular orbits is about an order of magnitude larger than the same ratio for debris tracked by the US Space Command.
Kessler, Donald J.↗
Nozomi Cis-Lunar Phase Orbit Determination
Japan's Institute of Space and Astronautical Science (ISAS) launched Nozomi, its first mission to the planet Mars using the newly developed M-V launch vehicle on July 3, 1998. Scientific objectives of the mission are to study the structure and dynamics of the Martian upper atmosphere and its interaction with the solar wind. Nozomi is a cooperative mission between ISAS and the National Aeronautics and Space Administration (NASA). The NASA contribution includes navigation and tracking services provided by the Jet Propulsion Laboratory (JPL). The spacecraft also serves as an engineering demonstration of basic technology for planetary exploration. One of the new technologies was a unique trajectory, developed by ISAS, which used solar gravitational perturbations at the weak stability boundary as an aid to achieve an Earth-Mars transfer orbit. This trajectory saves approximately 120 m/s of Delta V compared to direct hyperbolic insertion and is considered an enabling technology for the mission. Nozomi was the first spacecraft to employ this trajectory and provided on-orbit validation of the technique. The trajectory was achieved by initially placing the spacecraft in a highly elliptical cis-lunar phasing orbit. Six maneuvers were performed during this period to correct injection errors and target an outbound lunar swingby in September 1998. The gravity assist from the lunar swingby raised apogee to the vicinity of the weak stability boundary. After three more targeting maneuvers, Nozomi performed an inbound lunar swingby followed immediately by a powered Earth swingby in late December 1998. A 420 m/s Trans Mars Insertion (TMI) burn at the final Earth periapsis was intended to place the spacecraft on a heliocentric trajectory leading to Mars orbit insertion in October 1999. Orbit determination for Nozomi is performed in parallel by both ISAS and the Multi-Mission Navigation (MMNAV) group at JPL. This was an advantage for the mission because each group would generate solutions based on data collected from their respective tracking networks. Spacecraft events, such as sequence uplinks and maneuvers, were generally scheduled during passes at the Usuda tracking station in Japan. As a result, maneuver design and reconstruction was derived from MMNAV solutions based on JPL tracking data obtained immediately prior to or following maneuvers. Data was also exchanged between ISAS and MMNAV so orbit determination could be performed on joint data sets in support of critical targeting late in the cis-lunar phase. In this paper, information regarding the MMNAV orbit determination effort for the first six months of the mission is presented. The spacecraft trajectory is characterized first, followed by a discussion of the orbit determination estimation procedure and models. Results from selected orbit solutions are presented and compared against reconstructed trajectories. One area of emphasis in this paper is orbit determination in the vicinity of the weak stability boundary. Precise navigation was necessary to target the second lunar swingby and the powered Earth swingby. Delivery accuracy of 150 m was required for these critical encounters, but a number of factors contributed to the general degradation of orbit determination accuracy. This included the fact that the spacecraft was at apogee, at a range of 1.7 million km and moving at less than I km/sec perpendicular to the line of sight. Nozomi was also close to zero degrees declination where there are known limitations on orbit determination performance. Finally, S-band tracking data was acquired through the Nozomi backup low gain antenna. This antenna is offset from the axis of this spin stabilized spacecraft and superimposed large signatures in the Doppler and range data. These difficulties were overcome by combining long data arcs, spanning several maneuvers, with a high fidelity solar pressure model. The model included a physically accurate representation of the spacecraft structure and a high time resolution orientation model. Observation modeling included the removal of the spin induced Doppler bias, spin signature and per pass correction of range calibration errors applied for data leading up to critical events. As a result, all orbit determination goals were met. A second area of emphasis in this paper is the JPL tracking and orbit determination effort in support of the TMI maneuver. TMI occurred out of contact with ground stations and the JPL Goldstone tracking complex had the first pass following the bum. As a result, MMNAV had the responsibility to make a rapid assessment of the maneuver performance. MMNAV made the determination that a 100 m/s under bum had occurred and promptly informed ISAS via voice lines. ISAS immediately began preparations for a correction maneuver (TMIc), which had to be performed during the next Usuda pass. The near real time assessment by MMNAV provided accurate antenna frequency and pointing updates for the spacecraft acquisition at Usuda and the close coordination between the two agencies enabled the design and successful execution of the TMc maneuver. Propellant consumption during the correction burn dictated that the mission be redesigned. ISAS developed a new plan which adds 3 full solar orbits, two Earth swingbys and one lunar swingby with arrival at Mars in January 2004. The final Mars orbit will still enable the mission to achieve all of its science objectives.
Ryne, Mark↗
In-Flight Operation of the Dawn Ion Propulsion System Through Completion of the Final Orbit Around Dwarf Planet Ceres
The Dawn mission, part of NASA’s Discovery Program, has as its goal the scientific exploration of the two most massive main-belt objects, Vesta and Ceres. The Dawn spacecraft was launched from the Cape Canaveral Air Force Station on September 27, 2007 on a Delta-II 7925H- 9.5 (Delta-II Heavy) rocket that placed the 1218-kg spacecraft onto an Earth-escape trajectory. On-board the spacecraft is an ion propulsion system (IPS) developed at the Jet Propulsion Laboratory for the heliocentric transfer to Vesta, orbit capture at Vesta, transfer between Vesta science orbits, departure and escape from Vesta, heliocentric transfer to Ceres, orbit capture at Ceres, transfer between Ceres science orbits, and orbit maintenance maneuvers. Full-power thrusting from December 2007 through October 2008 was used to successfully target a Mars gravity assist flyby in February 2009 that provided an additional DV of 2.6 km/s. Deterministic thrusting for the heliocentric transfer to Vesta resumed in June 2009 and concluded with orbit capture at Vesta on July 16, 2011. From July 2011 through September 2012 the IPS was used to transfer to all the different science orbits at Vesta and to escape from Vesta orbit. Cruise for a rendezvous with Ceres began in August 2012 and completed in late December 2014. From December 2014 through June 2016 the IPS was used for transiting the spacecraft to all science orbits at Ceres including the final orbit for Dawn’s primary mission, called the low altitude mapping orbit (LAMO), a circular orbit at a mean altitude above Ceres of approximately 385 km. Dawn met or exceeded all pre-launch science requirements and Dawn's prime mission concluded on June 30, 2016. Dawn subsequently received NASA approval for two extended missions at Ceres, called XM1 and XM2. During XM1 IPS was used for orbit maintenance and to transit the spacecraft to several new, higher-altitude science orbits, ending in an elliptical orbit at a maximum altitude of approximately 38,000 km. In XM2, IPS operations included transiting the Dawn spacecraft to its final, highly elliptical orbit at Ceres ranging from 35 km perigee to 4,800 km apogee. Science data acquisition will continue in XM2 until the hydrazine is exhausted, which is expected to occur between August and October 2018. Dawn has successfully completed all science goals for both the primary and XM1 extended missions. To date the IPS has been operated for approximately 51,250 hours, consumed approximately 416 kg of xenon, and provided a delta-V of almost 11.5 km/s, a record for an on-board propulsion system. The IPS performance characteristics are close to the expected performance based on analysis and testing performed pre-launch. Dawn’s IPS continues to be fully operational as of June 2018. This paper provides an overview of Dawn’s mission objectives and the results of Dawn IPS mission operations for XM1, and XM2 through June 2018.
Rayman, Marc D.↗
GOES-T Goddard Magnetometer Sensor Unit Flight Thermal Predictions and On-Orbit Thermal Performance
The GOES-T Goddard Magnetometer (GMAG) sensor unit (SU) thermal design was validated by SU level thermal balance (TB) testing. The correlated SU thermal model was integrated to the observatory thermal model to predict the outboard SU temperatures and operating heater duty cycles in the worst cold case and worst hot case orbits. An orbit with the highest solar beta angle (23.5°) and an orbit with the lowest solar beta angle (0°) were run for each case. A comparison in the SU temperature predictions and heater duty cycles were made. The Autumnal Equinox (AE) cold case orbit is slightly colder than the Winter Solstice (WS) cold case orbit. The WS hot case orbit is slightly warmer than the March Equinox (VE) hot case orbit. Additionally, the lunar eclipse cold case orbit was run. It is the coldest environment. Using a 23°C set point for the SU cover heater controller, there is positive heater control for all the orbits. The heater duty cycle predictions for the AE worst cold case orbit and WS worst hot case orbit were 44.4% and 33% respectively. During the lunar eclipse, the heater cycle increases to 68.8% at the end of the eclipse. The temperature predictions for the bobbins are in the 21.9°C to 22.8°C range in the AE worst cold case orbit and in the 21.8°C to 23.0°C range in the WS worst hot case orbit. The SU temperatures during nominal operation on orbit were expected to be within the design goal, despite seasonal variations in solar beta angle and solar irradiance, and no solar flux in a lunar eclipse. The maximum operating SU cover flight heater duty cycle was expected to comply with GOLD Rule 4.25. The SU thermal design is now flight proven based on its long-term (>1 year) thermal performance on orbit.
GOES-T↗
Spectral characteristics of time-dependent orbit errors in altimeter height measurements
A mean reference surface and time-dependent orbit errors are estimated simultaneously for each exact-repeat ground track from the first two years of Geosat sea level estimates based on the Goddard Earth model (GEM)-T2 orbits. Motivated by orbit theory and empirical analysis of Geosat data, the time-dependent orbit errors are modeled as 1 cycle per revolution (cpr) sinusoids with slowly varying amplitude and phase. The method recovers the known 'bow tie effect' introduced by the existence of force model errors within the precision orbit determination (POD) procedure used to generate the GEM-T2 orbits. The bow tie pattern of 1-cpr orbit errors is characterized by small amplitudes near the middle and larger amplitudes (up to 160 cm in the 2 yr of data considered here) near the ends of each 5- to 6-day orbit arc over which the POD force model is integrated. A detailed examination of these bow tie patterns reveals the existence of daily modulations of the amplitudes of the 1-cpr sinusoid orbit errors with typical and maximum peak-to-peak ranges of about 14 cm and 30 cm, respectively. The method also identifies a daily variation in the mean orbit error with typical and maximum peak-to-peak ranges of about 6 and 30 cm, respectively, that is unrelated to the predominant 1-cpr orbit error. Application of the simultaneous solution method to the much less accurate Geosat height estimates based on the Naval Astronautics Group orbits concludes that the accuracy of POD is not important for collinear altimetric studies of time-dependent mesoscale variability (wavelengths shorter than 1000 km), as long as the time-dependent orbit errors are dominated by 1-cpr variability and a long-arc (several orbital periods) orbit error estimation scheme such as that presented here is used.
Chelton, Dudley B.↗
Determination of Eros Physical Parameters for Near Earth Asteroid Rendezvous Orbit Phase Navigation
Navigation of the orbit phase of the Near Earth steroid Rendezvous (NEAR) mission will re,quire determination of certain physical parameters describing the size, shape, gravity field, attitude and inertial properties of Eros. Prior to launch, little was known about Eros except for its orbit which could be determined with high precision from ground based telescope observations. Radar bounce and light curve data provided a rough estimate of Eros shape and a fairly good estimate of the pole, prime meridian and spin rate. However, the determination of the NEAR spacecraft orbit requires a high precision model of Eros's physical parameters and the ground based data provides only marginal a priori information. Eros is the principal source of perturbations of the spacecraft's trajectory and the principal source of data for determining the orbit. The initial orbit determination strategy is therefore concerned with developing a precise model of Eros. The original plan for Eros orbital operations was to execute a series of rendezvous burns beginning on December 20,1998 and insert into a close Eros orbit in January 1999. As a result of an unplanned termination of the rendezvous burn on December 20, 1998, the NEAR spacecraft continued on its high velocity approach trajectory and passed within 3900 km of Eros on December 23, 1998. The planned rendezvous burn was delayed until January 3, 1999 which resulted in the spacecraft being placed on a trajectory that slowly returns to Eros with a subsequent delay of close Eros orbital operations until February 2001. The flyby of Eros provided a brief glimpse and allowed for a crude estimate of the pole, prime meridian and mass of Eros. More importantly for navigation, orbit determination software was executed in the landmark tracking mode to determine the spacecraft orbit and a preliminary shape and landmark data base has been obtained. The flyby also provided an opportunity to test orbit determination operational procedures that will be used in February of 2001. The initial attitude and spin rate of Eros, as well as estimates of reference landmark locations, are obtained from images of the asteroid. These initial estimates are used as a priori values for a more precise refinement of these parameters by the orbit determination software which combines optical measurements with Doppler tracking data to obtain solutions for the required parameters. As the spacecraft is maneuvered; closer to the asteroid, estimates of spacecraft state, asteroid attitude, solar pressure, landmark locations and Eros physical parameters including mass, moments of inertia and gravity harmonics are determined with increasing precision. The determination of the elements of the inertia tensor of the asteroid is critical to spacecraft orbit determination and prediction of the asteroid attitude. The moments of inertia about the principal axes are also of scientific interest since they provide some insight into the internal mass distribution. Determination of the principal axes moments of inertia will depend on observing free precession in the asteroid's attitude dynamics. Gravity harmonics are in themselves of interest to science. When compared with the asteroid shape, some insight may be obtained into Eros' internal structure. The location of the center of mass derived from the first degree harmonic coefficients give a direct indication of overall mass distribution. The second degree harmonic coefficients relate to the radial distribution of mass. Higher degree harmonics may be compared with surface features to gain additional insight into mass distribution. In this paper, estimates of Eros physical parameters obtained from the December 23,1998 flyby will be presented. This new knowledge will be applied to simplification of Eros orbital operations in February of 2001. The resulting revision to the orbit determination strategy will also be discussed.
Miller, J. K.↗
Experimental Space Shuttle Orbiter Studies to Acquire Data for Code and Flight Heating Model Validation
In an experimental study to obtain detailed heating data over the Space Shuttle Orbiter, CUBRC has completed an extensive matrix of experiments using three distinct models and two unique hypervelocity wind tunnel facilities. This detailed data will be employed to assess heating augmentation due to boundary layer transition on the Orbiter wing leading edge and wind side acreage with comparisons to computational methods and flight data obtained during the Orbiter Entry Boundary Layer Flight Experiment and HYTHIRM during STS-119 reentry. These comparisons will facilitate critical updates to be made to the engineering tools employed to make assessments about natural and tripped boundary layer transition during Orbiter reentry. To achieve the goals of this study data was obtained over a range of Mach numbers from 10 to 18, with flight scaled Reynolds numbers and model attitudes representing key points on the Orbiter reentry trajectory. The first of these studies were performed as an integral part of Return to Flight activities following the accident that occurred during the reentry of the Space Shuttle Columbia (STS-107) in February of 2003. This accident was caused by debris, which originated from the foam covering the external tank bipod fitting ramps, striking and damaging critical wing leading edge heating tiles that reside in the Orbiter bow shock/wing interaction region. During investigation of the accident aeroheating team members discovered that only a limited amount of experimental wing leading edge data existed in this critical peak heating area and a need arose to acquire a detailed dataset of heating in this region. This new dataset was acquired in three phases consisting of a risk mitigation phase employing a 1.8% scale Orbiter model with special temperature sensitive paint covering the wing leading edge, a 0.9% scale Orbiter model with high resolution thin-film instrumentation in the span direction, and the primary 1.8% scale Orbiter model with detailed thin-film resolution in both the span and chord direction in the area of peak heating. Additional objectives of this first study included: obtaining natural or tripped turbulent wing leading edge heating levels, assessing the effectiveness of protuberances and cavities placed at specified locations on the orbiter over a range of Mach numbers and Reynolds numbers to evaluate and compare to existing engineering and computational tools, obtaining cavity floor heating to aid in the verification of cavity heating correlations, acquiring control surface deflection heating data on both the main body flap and elevons, and obtain high speed schlieren videos of the interaction of the orbiter nose bow shock with the wing leading edge. To support these objectives, the stainless steel 1.8% scale orbiter model in addition to the sensors on the wing leading edge was instrumented down the windward centerline, over the wing acreage on the port side, and painted with temperature sensitive paint on the starboard side wing acreage. In all, the stainless steel 1.8% scale Orbiter model was instrumented with over three-hundred highly sensitive thin-film heating sensors, two-hundred of which were located in the wing leading edge shock interaction region. Further experimental studies will also be performed following the successful acquisition of flight data during the Orbiter Entry Boundary Layer Flight Experiment and HYTHIRM on STS-119 at specific data points simulating flight conditions and geometries. Additional instrumentation and a protuberance matching the layout present during the STS-119 boundary layer transition flight experiment were added with testing performed at Mach number and Reynolds number conditions simulating conditions experienced in flight. In addition to the experimental studies, CUBRC also performed a large amount of CFD analysis to confirm and validate not only the tunnel freestream conditions, but also 3D flows over the orbiter acreage, wing leading edge, and controlurfaces to assess data quality, shock interaction locations, and control surface separation regions. This analysis is a standard part of any experimental program at CUBRC, and this information was of key importance for post-test data quality analysis and understanding particular phenomena seen in the data. All work during this effort was sponsored and paid for by the NASA Space Shuttle Program Office at the Johnson Space Center in Houston, Texas.
Wadhams, T. P.↗
ARTEMIS: The First Mission to the Lunar Libration Orbits
The ARTEMIS mission will be the first to navigate to and perform stationkeeping operations around the Earth-Moon L1 and L2 Lagrangian points. The NASA Goddard Space Flight Center (GSFC) has previous mission experience flying in the Sun-Earth L1 (SOHO, ACE, WIND, ISEE-3) and L2 regimes (WMAP) and have maintained these spacecraft in libration point orbits by performing regular orbit stationkeeping maneuvers. The ARTEMIS mission will build on these experiences, but stationkeeping in Earth-Moon libration orbits presents new challenges since the libration point orbit period is on the order of two weeks rather than six months. As a result, stationkeeping maneuvers to maintain the Lissajous orbit will need to be performed frequently, and the orbit determination solutions between maneuvers will need to be quite accurate. The ARTEMIS mission is a collaborative effort between NASA GSFC, the University of California at Berkeley (UCB), and the Jet Propulsion Laboratory (JPL). The ARTEMIS mission is part of the THEMIS extended mission. ARTEMIS comprises two of the five THEMIS spacecraft that will be maneuvered from near-Earth orbits into lunar libration orbits using a sequence of designed orbital maneuvers and Moon & Earth gravity assists. In July 2009, a series of orbit-raising maneuvers began the proper orbit phasing of the two spacecraft for the first lunar flybys. Over subsequent months, additional propulsive maneuvers and gravity assists will be performed to move each spacecraft though the Sun-Earth weak stability regions and eventually into Earth-Moon libration point orbits. We will present the overall orbit designs for the two ARTEMIS spacecraft and provide analysis results of the 3/4-body dynamics, and the sensitivities of the trajectory design to both · maneuver errors and orbit determination errors. We will present results from the. initial orbit-raising maneuvers.
Woodward, Mark↗
Radar Measurements of the LEO Orbital Debris Environment
Access to space and the preservation of the near-Earth space environment is of critical significance. Increased interest in issues surrounding space traffic management and the continued assessment and discussion of orbital debris at the United Nations Committee on the Peaceful Uses of Outer Space (COPUOS) illustrates the significance of the topic of orbital debris. There are currently over 20,000 tracked objects in the publicly available satellite catalog on Space-Track.org. The catalog is maintained by the US Air Force Space Command using a network of optical and radar ground-based sensors and is believed to be complete for a characteristic size of 10 cm or larger in low Earth orbit (LEO). Based on the work of the NASA Orbital Debris Program Office (ODPO) over approximately the past 40 years it is understood that the small debris population (< 10 cm) increases by orders of magnitude as characteristic size decreases. With population estimates ranging from 500,000 to 1,000,000 small debris objects (> 5 mm) in orbit, it is currently not practical to track and maintain precision orbits on every object. Instead the NASA ODPO uses powerful ground-based radars to sample the low Earth Orbit (LEO) environment and assign approximate orbits to each detection. This poses an interesting signal processing challenge as we are trying to detect the smallest objects possible on the edge of the radar's sensitivity. For approximately the last 30 years, NASA ODPO has partnered with the Massachusetts Institute of Technology Lincoln Laboratory (MIT/LL) to utilize the Haystack Ultra-wideband Satellite Imaging Radar (HUSIR - formerly the Long-Range Imaging Radar or simply Haystack) and the Haystack Auxiliary (HAX) radar to collect orbital debris radar data. Additionally, the ODPO collaborates with the NASA Jet Propulsion Laboratory (JPL) to use the Goldstone Solar System Radar. The orbital debris detections from these radars serve as inputs for statistical risk models used by the human spaceflight and satellite communities to assess risk to spacecraft posed by orbital debris. In this paper, we will describe the history of orbital debris radar measurements conducted by NASA, provide an overview of current radar measurements techniques and facilities, discuss the signal processing software used for orbital debris measurements and the inference of debris size and orbital parameters from these measurements, and discuss how orbital debris radar measurements are validated for use in models that are used throughout the aerospace industry.
Blackwell, Chris↗