Analytical investigation of the dynamics of tethered constellations in Earth orbit (phase 2)

Simulation of two short distance crawling maneuvers of the elevator both with and without environmental perturbations acting upon the system is discussed. These simulation runs were performed in order to provide results useful for the interpretation of the data from the tests, on the ground, of a scaled down engineering model of the elevator. In these simulation runs the elevator crawls along the tether in accordance to the developed mirror image motion control law (MIMCL). Results from the simulation of the 4 km long maneuver run were compared to those obtained by adopting the modified hyperbolic tangent control law (MHTCL). A preprocessor was developed for setting up the initial conditions of a tethered system with L platforms, M longitudinal dampers, and N lumped masses (platforms plus tether beads). A short test run of the 4-platform system with 3 longitudinal dampers and 10 lumper mass without any perturbation acting upon the system is illustrated. In support of the Tether Applications Working Group, SAO is preparing a catalog of tether simulations, has prepared a set of simulator test cases, obtained results from SKYHOOK, and solicited results from simulators at other institutions, and prepared a paper on a specific analytic solution

Analytical investigation of the dynamics of tethered constellations in earth orbit

This Quarterly Report on Tethering in Earth Orbit deals with three topics: (1) Investigation of the propagation of longitudinal and transverse waves along the upper tether. Specifically, the upper tether is modeled as three massive platforms connected by two perfectly elastic continua (tether segments). The tether attachment point to the station is assumed to vibrate both longitudinally and transversely at a given frequency. Longitudinal and transverse waves propagate along the tethers affecting the acceleration levels at the elevator and at the upper platform. The displacement and acceleration frequency-response functions at the elevator and at the upper platform are computed for both longitudinal and transverse waves. An analysis to optimize the damping time of the longitudinal dampers is also carried out in order to select optimal parameters. The analytical evaluation of the performance of tuned vs. detuned longitudinal dampers is also part of this analysis. (2) The use of the Shuttle primary Reaction Control System (RCS) thrusters for blowing away a recoiling broken tether is discussed. A microcomputer system was set up to support this operation. (3) Most of the effort in the tether plasma physics study was devoted to software development. A particle simulation code has been integrated into the Macintosh II computer system and will be utilized for studying the physics of hollow cathodes

Ab initio determination of an extended Heisenberg Hamiltonian in CuO2 layers

Accurate ab initio calculations on embedded Cu_4O_{12} square clusters, fragments of the La_2CuO_4 lattice, confirm a value of the nearest neighbor antiferromagnetic coupling (J=124 meV) previously obtained from ab initio calculations on bicentric clusters and in good agreement with experiment. These calculations predict non negligible antiferromagnetic second-neighbor interaction (J'=6.5 meV) and four-spin cyclic exchange (K=14 meV), which may affect the thermodynamic and spectroscopic properties of these materials. The dependence of the magnetic coupling on local lattice distortions has also been investigated. Among them the best candidate to induce a spin-phonon effect seems to be the movement of the Cu atoms, changing the Cu-Cu distance, for which the variation of the nearest neighbor magnetic coupling with the Cu-O distance is {\Delta J}/{\Delta d_{Cu-O}}\sim 1700 cm^{-1} A^{-1}.Comment: 11 pages, 5 figures, submitted to Phys. Rev.

Participation in the Analysis of the Far-Infrared/Submillimeter Interferometer

We have contributed to the development of the Submillimeter Probe of the Evolution of Cosmic Structure (SPECS) by analyzing various aspects related to the tethers that connect the spacecraft of this space interferometer. We have focused our analysis on key topics as follows: (a) helping in the configuration selection; (b) computing the system eigenfrequencies as a function of baseline length; (c) developing techniques and conceptual design of devices for damping the tether oscillations; (d) carrying out numerical simulations of tethered formation to assess the effects of environmental perturbations upon the baseline length variation; (e) devising control laws for fast retargeting of the interferometer at moderate baseline lengths; (f) estimating the survivability to micrometeoroid impacts of a tether at L2; and (g) developing a conceptual design of a high-strength and survivable tether

A "Free-Lunch" tour of the Jovian System

An ED-tether mission to Jupiter is presented. A bare tether carrying cathodic devices at both ends but no power supply, and using no propellant, could move 'freely' among Jupiter's 4 great moons. The tour scheme would have current naturally driven throughout by the motional electric field, the Lorentz force switching direction with current around a 'drag' radius of 160,00 kms, where the speed of the jovian ionosphere equals the speed of a spacecraft in circular orbit. With plasma density and magnetic field decreasing rapidly with distance from Jupiter, drag/thrust would only be operated in the inner plasmasphere, current being near shut off conveniently in orbit by disconnecting cathodes or plugging in a very large resistance; the tether could serve as its own power supply by plugging in an electric load where convenient, with just some reduction in thrust or drag. The periapsis of the spacecraft in a heliocentric transfer orbit from Earth would lie inside the drag sphere; with tether deployed and current on around periapsis, magnetic drag allows Jupiter to capture the spacecraft into an elliptic orbit of high eccentricity. Current would be on at succesive perijove passes and off elsewhere, reducing the eccentricity by lowering the apoapsis progressively to allow visits of the giant moons. In a second phase, current is on around apoapsis outside the drag sphere, rising the periapsis until the full orbit lies outside that sphere. In a third phase, current is on at periapsis, increasing the eccentricity until a last push makes the orbit hyperbolic to escape Jupiter. Dynamical issues such as low gravity-gradient at Jupiter and tether orientation in elliptic orbits of high eccentricity are discussed

Non-singular orbital elements for special perturbations in the two-body problem

Seven spatial elements and a time element are proposed as the state variables of a new special perturbation method for the two-body problem. The new elements hold for zero eccentricity and inclination and for negative values of the total energy. They are developed by combining a spatial transformation into projective coordinates (as in the Burdet–Ferrándiz regularization) with a time transformation in which the exponent of the orbital radius is equal to one instead of two (as commonly done in the literature). By following this approach, we discover a new linearization of the two-body problem, from which the orbital elements can be generated by the variation of parameters method. The geometrical significance of the spatial quantities is revealed by a new intermediate frame which differs from a local vertical local horizontal frame by one rotation in the instantaneous orbital plane. Four elements parametrize the attitude in space of this frame, which in turn defines the orientation of the orbital plane and fixes the departure direction for the longitude of the propagated body. The remaining three elements determine the motion along the radial unit vector and the orbital longitude. The performance of the method, tested using a series of benchmark orbit propagation scenarios, is extremely good when compared to several regularized formulations, some of which have been modified and improved here for the first time

Space tethers: parameters reconstructions and tests

In the last several years, the need for an alternative to chemical propulsive systems for low-orbit satellite deorbiting has become increasingly evident; a Tethered System can provide adequate thrust or drag without the complications of combustions and with a minimal impact on the environment. In this context, the authors are part of a team that is studying various tether applications and building a prototype of an electrodynamic tether system. The goal of this paper is to characterize tether materials in order to find valid solutions for future space tether missions. Mission requirements (e.g., the survivability to hypervelocity impacts and the capability to damp oscillations in electrodynamic tethers) influence the choice of tether parameters such as cross section geometry (round wires or tapes), materials, length, and cross section sizes. The determination of the elastic characteristics and damping coefficients is carried out through a campaign of experiments conducted with both direct stress/strain measurements and the laboratory facility SPAcecRraft Testbed for Autonomous proximity operatioNs experimentS (SPARTANS) on a low friction table at the University of Padova. In the latter case, the stiffness and damping of a flexible line were verified by applying different tensile load profiles and then measuring the tether-line dynamic response in terms of tension spike amplitude, oscillation decay, and estimation of the damping coefficient

Saturn power generation with electrodynamic tethers in polar orbit

A power generation scheme based on bare electrodynamic tethers (EDT), working in passive mode is investigated for the purpose of supplying power to scientific missions at Saturn. The system employs a spinning EDT on a lowaltitude polar orbit which permits to efficiently convert plasmasphere energy into useful power. After optimizing the tether design for power generation we compute the supplied power along the orbit and the impact of the Lorentz force on the orbital elements as function of the tether and orbit characteristics. Although uncertainties in the current ionosphere density modeling strongly affect the performance of the system the peak power density of the EDT appears be greater than conventional power systems

Metrological characterization of a vision-based system for relative pose measurements with fiducial marker mapping for spacecrafts

An improved approach for the measurement of the relative pose between a target and a chaser spacecraft is presented. The selected method is based on a single camera, which can be mounted on the chaser, and a plurality of fiducial markers, which can be mounted on the external surface of the target. The measurement procedure comprises of a closed-form solution of the Perspective from n Points (PnP) problem, a RANdom SAmple Consensus (RANSAC) procedure, a non-linear local optimization and a global Bundle Adjustment refinement of the marker map and relative poses. A metrological characterization of the measurement system is performed using an experimental set-up that can impose rotations combined with a linear translation and can measure them. The rotation and position measurement errors are calculated with reference instrumentations and their uncertainties are evaluated by the Monte Carlo method. The experimental laboratory tests highlight the significant improvements provided by the Bundle Adjustment refinement. Moreover, a set of possible influencing physical parameters are defined and their correlations with the rotation and position errors and uncertainties are analyzed. Using both numerical quantitative correlation coefficients and qualitative graphical representations, the most significant parameters for the final measurement errors and uncertainties are determined. The obtained results give clear indications and advice for the design of future measurement systems and for the selection of the marker positioning on a satellite surface

Spherical collectors versus bare tethers for drag, thrust, and power generation

Performances of ED-tethers using either spherical collectors or bare tethers for drag, thrust, or power generation, are compared. The standard Parker-Murphy model of current to a full sphere, with neither space-charge nor plasmamotion effects considered, but modified to best fit TSS1R results, is used (the Lam, Al'pert/Gurevich space-charge limited model will be used elsewhere) In the analysis, the spherical collector is assumed to collect current well beyond its random-current value (thick-heath). Both average current in the bare-tether and current to the sphere are normalized with the short-circuit current in the absence of applied power, allowing a comparison of performances for all three applications in terms of characteristic dimensionless numbers. The sphere is always substantially outperformed by the bare-tether if ohmic effects are weak, though its performance improves as such effects increase