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Effect of resonance-oblateness coupling on a satellite orbit

Second-order effects of the coupling between geopotential resonance and oblateness on a satellite orbit are calculated. These effects arise from the interaction of resonance with the secular changes of the orbit's node, perigee, and mean anomaly. They have the same period and phase as first-order resonance perturbations. But their amplitudes are proportional to the square of the period and dominate the first-order effects as the orbit becomes commensurate. A striking example of this coupling is seen in the 18-day resonance variation of the node of the orbit of the first earth resources technology satellite. Analysis of this 1 arc sec (31 m) variation yields a strong fourteenth-order constraint to the geopotential field for odd degree terms. This constraint (lumped coefficient) is poorly predicted by most current models.

Wagner, C. A.↗

The Precise Orbit and the Challenge of Long Term Stability

The computation of a precise orbit reference is a fundamental component of the altimetric measurement. Since the dawn of the modern altimeter age, orbit accuracy has been determined by the quality of the GPS, SLR, and DORIS tracking systems, the fidelity of the measurement and force models, and the choice of parameterization for the orbit solutions, and whether a dynamic or a reduced-dynamic strategy is used to calculate the orbits. At the start of the TOPEX mission, the inaccuracies in the modeling of static gravity, dynamic ocean tides, and the nonconservative forces dominated the orbit error budget. Much of the error due to dynamic mismodeling can be compensated by reduced-dynamic tracking techniques depending on the measurement system strength. In the last decade, the launch of the GRACE mission has eliminated the static gravity field as a concern, and the background force models and the terrestrial reference frame have been systematically refined. GPS systems have realized many improvements, including better modeling of the forces on the GPS spacecraft, large increases in the ground tracking network, and improved modeling of the GPS measurements. DORIS systems have achieved improvements through the use of new antennae, more stable monumentation, and of satellite receivers that can track multiple beacons, and as well as through improved modeling of the nonconservative forces. Many of these improvements have been applied in the new reprocessed time series of orbits produced for the ERS satellites, Envisat, TOPEX/Poseidon and the Jason satellites, and as well as for the most recent Cryosat-2 and HY2A. We now face the challenge of maintaining a stable orbit reference for these altimetric satellites. Changes in the time-variable gravity field of the Earth and how these are modelled have been shown to affect the orbit evolution, and the calibration of the altimetric data with tide gauges. The accuracy of the reference frame realizations, and their projection into the future remains a source of error. Other sources of omission error include the geocenter for which no consensus model is as of yet applied. Although progress has been made in nonconservative force modeling through the use of detailed satellite-specific models, radiation pressure modeling, and atmospheric density modeling remain a potential source of orbit error. The longer term influence of variations in the solar and terrestrial radiation fields over annual and solar cycles remains principally untested. Also the long term variation in optical and thermal properties of the space vehicle surfaces would contribute to biases in the orbital frame if ignored. We review the status of altimetric precision orbit determination as exemplified by the recent computations undertaken by the different analysis centers for ERS, Envisat, TOPEX/Poseidon, Jason, Cryosat2 and HY2A, and we provide a perspective on the challenges for future missions such as the Jason-3, SENTINEL-3 and SWOT.

Lemoine, Frank G.↗

The Geosynchrous Environment for ORDEM2010

The new version of the NASA Orbital Debris Engineering Model (ORDEM2010) requires accurate populations as input files to be used in the calculation of orbital debris fluxes on chosen spacecraft or within telescope/radar fields-of-view. Populations in ORDEM2010 are derived from an amalgam of data and modeling. Geosynchronous orbit (GEO) satellites and debris form a distinct ORDEM2010 population that is applied to the distinct analysis of GEO fluxes. Low Earth orbit (LEO) populations are derived by combining modeling results with ground-based data, primarily from radar systems, and in-situ data. In contrast, the GEO region has not been as well observed. The distance between orbiting objects and ground-based instruments precludes the wide usage of radar as a means of observation. Instead, optical instruments dominate in the study of GEO. Of these, the NASA sponsored Michigan Orbital Debris Survey Telescope (MODEST) has provided 3 years of surveys of the region detecting cataloged objects (correlated targets) and non-cataloged objects (uncorrelated targets) to an estimated minimum size of 30 cm. This paper describes the methods of combining NASA launch database and satellite breakup and orbital propagation modeling with MODEST 2004-to-2006 uncorrelated target data to attain a GEO environment to 10 cm. Assuming that MODEST uncorrelated targets are breakup debris allows for the extension of the debris survey data to smaller sizes using the NASA Standard Breakup Model. Each orbit within the total resulting GEO population is marked by a random argument of perigee and nearly constant mean motion, eccentricity, inclination, and right ascension of ascending node (RAAN) over the nearly 3 years of observation. Lack of published references of past breakups in GEO is mitigated by the orbital propagation of MODEST extended data to 1995 (the beginning epoch of ORDEM2010).

Krisko, Paula H.↗

Geosynchronous Environment for ORDEM2008

The new version of the NASA Orbital Debris Engineering Model (ORDEM2008) requires accurate populations as input template files to be used in the calculation of orbital debris fluxes on chosen spacecraft or within telescope/radar fields-of-view. Populations in ORDEM2008 are derived from a consortium of data and modeling. Geosynchronous (GEO) satellites and debris form a distinct ORDEM2008 population that is applied to the distinct analysis of GEO fluxes. Low Earth orbit (LEO) populations are derived by combining modeling results with ground-based data, primarily from radar systems and in-situ data. In contrast, the GEO region has not been as well observed. The distance between orbiting objects and ground-based instruments precludes the wide usage of radar as a means of observation. Instead, optical instruments dominate in the study of GEO. Of these, the NASA sponsored Michigan Orbital Debris Survey Telescope (MODEST) has provided 4 years of surveys of the region detecting cataloged objects (correlated targets) and non-cataloged objects (uncorrelated targets) to an estimated minimum size of 30 cm. This paper describes the methods of combining NASA launch database and satellite breakup and orbital propagation modeling with MODEST 2004-to-2006 uncorrelated target data to attain a GEO environment to 10 cm. Assuming that MODEST uncorrelated targets are breakup debris allows for the extension of the debris survey data to smaller sizes with the NASA Standard Breakup model. Each orbit within the total resulting GEO population is marked by a random argument of perigee and nearly constant mean motion, eccentricity, inclination, and node over the nearly 3 years of observation. Lack of published references of past breakups in GEO is mitigated by the orbital propagation of MODEST extended data to 1995 (the beginning epoch of ORDEM2008).

Krisko, Paula H.↗

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↗

Effect of resonance-oblateness coupling on a satellite orbit

Second order effects of the coupling between geopotential resonance and oblateness on a satellite orbit are calculated. Results show that: (1) these effects arise from the interaction of resonance with the secular changes of the orbit's node, perigee, and mean anomaly; (2) they have the same period and phase as first order resonance perturbations; and (3) their amplitudes are proportional to the square of the period and dominate the first order effects as the orbit becomes commensurate. A striking example of this coupling is seen in the 18 day resonance variation of the node of the orbit of the first earth resources technology satellite. Analysis of this one arc second (31m) variation yielded a strong 14th order constraint to the geopotential for odd degree terms. This constraint is poorly predicted by current models.

Wagner, C. A.↗

On the 'edge-on' configuration of the nuclei of comet West /1975n/

Observations made when earth crossed the orbital plane of comet West in 1976, providing an 'edge-on' view of the multiple nucleus, are used to calculate improved orbital elements for nucleus A at the time of crossing, for nucleus B relative to A and to D, and for nucleus D relative to A. The results appear to confirm that the motions of the fragments normal to the orbital plane were rather insignificant. Difficulties created by this finding for the solar-attraction theory on the rate of separation of split-comet fragments are discussed. The motion of a comet fragment off the orbital plane of the principal nucleus is analyzed in terms of both the initial-impulse and the nongravitational-acceleration hypotheses. Prospects for observing the nuclei of this comet at the next favorable edge-on projection (July 21, 1977) are evaluated.

Sekanina, Z.↗

Communications satellite systems capacity analysis

Analog and digital modulation techniques are compared with regard to efficient use of the geostationary orbit by communications satellites. Included is the definition of the baseline systems (both space and ground segments), determination of interference susceptibility, calculation of orbit spacing, and evaluation of relative costs. It is assumed that voice or TV is communicated at 14/11 GHz using either FM or QPSK modulation. Both the Fixed-Satellite Service and the Broadcasting-Satellite Service are considered. For most of the cases examined the digital approach requires a satellite spacing less than or equal to that required by the analog approach.

Browne, L.↗

Solar particle events observed at Mars: dosimetry measurements and model calculations

During the period from March 13, 2002 to mid-September, 2002, six solar particle events (SPE) were observed by the MARIE instrument onboard the Odyssey Spacecraft in Martian Orbit. These events were observed also by the GOES 8 satellite in Earth orbit, and thus represent the first time that the same SPE have been observed at these separate locations. The characteristics of these SPE are examined, given that the active regions of the solar disc from which the event originated can usually be identified. The dose rates at Martian orbit are calculated, both for the galactic and solar components of the ionizing particle radiation environment. The dose rates due to galactic cosmic rays (GCR) agree well with the HZETRN model calculations. Published by Elsevier Ltd on behalf of COSPAR.

Non-NASA Center↗

Space shuttle engineering and operations support. Isolation between the S-band quad antenna and the S-band payload antenna. Engineering systems analysis

The isolation between the upper S-band quad antenna and the S-band payload antenna on the shuttle orbiter is calculated using a combination of plane surface and curved surface theories along with worst case values. A minimum value of 60 db isolation is predicted based on recent antenna pattern data, antenna locations on the orbiter, curvature effects, dielectric covering effects and edge effects of the payload bay. The calculated value of 60 db is significantly greater than the baseline value of 40 db. Use of the new value will result in the design of smaller, lighter weight and less expensive filters for S-band transponder and the S-band payload interrogator.

Lindsey, J. F.↗

Earth Observing System Covariance Realism

The purpose of covariance realism is to properly size a primary object's covariance in order to add validity to the calculation of the probability of collision. The covariance realism technique in this paper consists of three parts: collection/calculation of definitive state estimates through orbit determination, calculation of covariance realism test statistics at each covariance propagation point, and proper assessment of those test statistics. An empirical cumulative distribution function (ECDF) Goodness-of-Fit (GOF) method is employed to determine if a covariance is properly sized by comparing the empirical distribution of Mahalanobis distance calculations to the hypothesized parent 3-DoF chi-squared distribution. To realistically size a covariance for collision probability calculations, this study uses a state noise compensation algorithm that adds process noise to the definitive epoch covariance to account for uncertainty in the force model. Process noise is added until the GOF tests pass a group significance level threshold. The results of this study indicate that when outliers attributed to persistently high or extreme levels of solar activity are removed, the aforementioned covariance realism compensation method produces a tuned covariance with up to 80 to 90% of the covariance propagation timespan passing (against a 60% minimum passing threshold) the GOF tests-a quite satisfactory and useful result.

Realism↗

Method for constructing periodic orbits in nonlinear dynamic systems

Method is modification of generalized Newton-Ralphson algorithm for analyzing two-point boundary problems. It constructs sequence of solutions that converge to precise dynamic solution in the sequence limit. Program calculates periodic orbits in either circular or elliptical restricted three-body problems.

Bennett, A. G.↗

A new approach to the linear theory of single-species tearing in two-dimensional quasi-neutral sheets

We have developed the linear theory of collisionless ion tearing in a two-dimensional magnetotail equilibrium for a single resonant species. We have solved the normal mode problem for tearing instability by an algorithm that employs particle-in-cell simulation to calculate the orbit integrals in the Maxwell-Vlasov eigenmode equation. The results of our single-species tearing analysis can be applied to ion tearing where electron effects are not included. We have calculated the tearing growth rate as a function of the magnetic field component B(sub n) normal to the current sheet for thick and thin current sheets, and we show that marginal stability occurs when the normal gyrofrequency Omega(sub n) is comparable to the Harris neutral sheet growth rate. A cross-tail B(sub y) component has little effect on the growth rate for B(sub y) approximately = B(sub n). Even in the limit B(sub y) much greater than B(sub n), the mode is strongly stabilized by B(sub n). We report than random pitch angle scattering can overcome the stabilizing effect of B(sub n) and drive the growth rate up toward the Harris neutral sheet (B(sub n) = 0) value when the pitch angle diffusion rate is comparable to Omega(sub n).

Brittnacher, M.↗

Orbit, reentry, and landing attachment for globes

Navigational device, invented to aid recovery of spacecraft from any orbit, also illustrates motions of satellites relative to earth and their entry-ranging requirements. Device rapidly and accurately defines lateral range requirements for spacecraft returning to any desired site without manual or computerized calculation of orbital equations of motion.

Pritchard, E. B.↗

Summary Report of Mission Acceleration Measurements for STS-73, Launched October 20, 1995

The microgravity environment of the Space Shuttle Columbia was measured during the STS-73 mission using accelerometers from five different instruments: the Orbital Acceleration Research Experiment, the Space Acceleration Measurement System, the Three-dimensional Microgravity Accelerometer, the Microgravity Measuring Device, and Suppression of Transient Accelerations by Levitation Evaluation System. The Microgravity Analysis Workstation quasi-steady environment calculation and comparison of this calculation with Orbital Acceleration Research Experiment data was used to assess how appropriate a planned attitude was expected to be for one Crystal Growth Facility experiment sample. The microgravity environment related to several different Orbiter, crew, and experiment operations is presented and interpreted in this report. Data are examined to show the effects of vernier reaction control system jet firings for Orbiter attitude control. This is compared to examples of data when no thrusters were firing, when the primary reaction control system jets were used for attitude control, and when single vernier jets were fired for test purposes. In general, vernier jets, when used for attitude control, cause accelerations in the 3 x 10(exp -4) g to 7 x 10(exp -4) g range. Primary jets used in this manner cause accelerations in the 0.01 to 0.025 g range. Other significant disturbance sources characterized are water dump operations, with Y(sub b) axis acceleration deviations of about 1 x 10(exp -6) g; payload bay door opening motion, with Y(sub o) and Z(sub o) axis accelerations of frequency 0.4 Hz; and probable Glovebox fan operations with notable frequency components at 20, 38, 43, 48, and 53 Hz. The STS-73 microgravity environment is comparable to the environments measured on earlier microgravity science missions.

Rogers, Melissa J. B.↗

Comparison of heating rate calculations with experimental data on a modified Shuttle orbiter at Mach 6

Heating-rate calculations from an 'engineering' code and a 'benchmark' Navier-Stokes code are compared with experimental wind tunnel data obtained on a 'modified' 0.0075-scale Shuttle orbiter at a Mach number of 6 and a freestream Reynolds number of 1.9 x 10 to the 6th/m. Comparisons are presented along the windward symmetry plane, in a circumferential direction around the body, and along the wing leading edge at angles of attack of 30 and 40 deg. Both codes provide accurate predictions of the heating rate over most of the body, but because the run time for the engineering code is relatively short, it is an ideal tool for both parametric and design studies.

Hamilton, H. H., II↗