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Encke's method as modified by Potter to increase the accuracy of orbit computations of gravitationally interacting bodies is applied to the problem of relative motion of non-interacting space vehicles. This technique is then combined with a simple transformation of the independent variable to arrive at a system of equations from which the relative motion may be determined with increased precision.
This paper is concerned with the derivation of the equations of motion for maneuvering flexible spacecraft both in orbit and in an earth-based laboratory. The structure is assumed to undergo large rigid-body maneuvers and small elastic deformations. A perturbation approach is presented in which the quantities defining the rigid-body maneuver are regarded as the unperturbed motion and the elastic motions and deviations from the rigid-body motions are regarded as the perturbed motion. The perturbation equations are linear, non-self-adjoint, and with time-dependent coefficients. A maneuver force distribution exciting the least amount of elastic deformation of the spacecraft is developed. Numerical results highlight the vibration caused by rotational maneuvers.
The atmospheric portion of the trajectories for the aeroassisted coplanar orbit transfer was investigated. The equations of motion for the problem are expressed using reduced order model and total vehicle energy, kinetic plus potential, as the independent variable rather than time. The order reduction is achieved analytically without an approximation of the vehicle dynamics. In this model, the problem of coplanar orbit transfer is seen as one in which a given amount of energy must be transferred from the vehicle to the atmosphere during the trajectory without overheating the vehicle. An optimal control problem is posed where a linear combination of the integrated square of the heating rate and the vehicle drag is the cost function to be minimized. The necessary conditions for optimality are obtained. These result in a 4th order two-point-boundary-value problem. A parametric study of the optimal guidance trajectory in which the proportion of the heating rate term versus the drag varies is made. Simulations of the guidance trajectories are presented.
We propose a new type of energy-efficient multi-bit magnetic memory based on current-driven, field-free, controlled domain wall motion. A meandering domain wall channel with precisely interspersed pinning regions provides the multi-bit capability of a magnetic tunnel junction memory. The magnetic free layer of the memory device has perpendicular magnetic anisotropy (PMA) and interfacial Dzyaloshinskii-Moriya interaction (DMI) so that spin-orbit torques (SOTs) induce efficient domain wall motion. Using micromagnetic simulations, we find two different cell designs: two-way switching and four-way switching. The memory cell design choices and the physics of pinning mechanisms are discussed in detail. Furthermore, we show that switching reliability and speed may be significantly improved by replacing the ferromagnetic free layer with a synthetic antiferromagnetic (SAF) layer. Switching behavior and material choices will be discussed for the two memory implementations.
Images of earth can be produced with an assumed synthetic aperture radar (SAR) on a satellite platform undergoing a nutating relative motion from geosynchronous altitude. From a 50 deg inclined circular orbit, the contiguous United States can be imaged in about 3 h of segmented operation at 100-m resolution with 4-azimuth-look averaging. The 2450-MHz transmitter radiates 1312 W of average power from a steerable 15-m-diam antenna. The SAR can image daily an area bounded longitudinally and latitudinally.
Variational equations were applied to the case of a rapidly spinning triaxial body moving in an elliptic orbit, in which the orbital plane is regressing at a constant rate. The explicit differential equations obtained in this application were integrated by the method of averaging to develop secular analytical expressions, which, to first-order in a small parameter, describe the complete space motions of the rigid body under the influence of nonresonant gravity-gradient perturbations. The effects of aerodynamic torque on the rotational motion of an orbiting satellite are studied, as another example of the application of the variational equations derived and the method of averaging.
Motivated by the heavy reliance upon the analytic orbit theory in orbit determination operations at the Goddard Space Flight Center (GSFC), a comparison study is performed for three classical analytical theories of artificial satellite motion about an oblate earth. The three analytical theories are: (1) Brouwer, (2) a modified Brouwer, i.e., Brouwer-Lyddane and Cohen, and (3) Vinti. Comparison results for each theory are produced for a number of representative satellites of current or past interest which proved amenable to analytic theory application. The uniformity of these results has significant implications for current and future mission operations and planning activities. Subsidiary topics arising from the results of this study which relate to the optimum usage of the individual theories are also discussed
The development and utilization of an optimized computer program to analyze orbital stabilization by repeated calculations is presented. The stability of comets in the Opik-Oort Cloud about the Sun against perturbations by the Galactic center involve the same basic type of calculation. The supposed persistence of these bodies in orbits over the life of the solar system, depends upon the stability of bodies of negligible mass in orbits around a body whose mass is small compared to the central mass about which they revolve. The question remains of preferential orientation of extremely eccentric comet orbits, possibly to explain the asymmetry observed among new comet motions. A third application of the computing programs is suited to meteoroids that may exist in orbits about asteroids and that may endanger science spacecraft making flybys too near to asteroids. As in the double-comet case, solar activity and solar gravitational perturbations limit the attendance to an asteroid by small meteroids in their orbits. It is found that the mass distances planned for asteroid fly-bys are adequate.
The central detector in the present EIC design includes a 4 m long solenoid with an integrated strength of up to 12 Tm. The electron beam passes on-axis through the solenoid, but the hadron beam has an angle of 25 mrad. Thus the solenoid couples horizontal and vertical betatron motion in both electron and hadron storage rings, and causes a vertical closed orbit excursion in the hadron ring. The solenoid also couples the transverse and longitudinal motions of both beams, when crab cavities are also considered. In this paper, we present schemes for closed orbit correction and coupling compensation at the IP, including crabbing.
We describe a fast, approximate method to characterize the orbits of satellites around a central binary in numerical simulations. A goal is to distinguish the free eccentricity—the random motion of a satellite relative to a dynamically cool orbit—from oscillatory modes driven by the central binary’s time-varying gravitational potential. We assess the performance of the method using the Kepler-16, Kepler-47, and Pluto–Charon systems. We then apply the method to a simulation of orbital damping in a circumbinary environment, resolving relative speeds between small bodies that are slow enough to promote mergers and growth. These results illustrate how dynamical cooling can set the stage for the formation of Tatooine-like planets around stellar binaries and the small moons around the Pluto–Charon binary planet.
During the Spacelab 2 mission, while the Plasma Diagnostics Package was attached to the Remote Manipulator System, differential ion vector measurements were obtained in the near wake at a distance of 4-5 Shuttle radii. The Orbiter's wake was found to fill in at a much faster rate than can be explained by simple thermal motion. The measurements strongly suggest that filling of the Orbiter's wake is produced by the process of 'collisionless plasma expansion into a vacuum' and that, for oblique angles of the magnetic field and velocity vectors, the near wake plasma depletion a few radii downstream is not sensitive to the body scale size.
Averaging techniques applied to the variation of parameters (VOP) formulation of the equations of motion are being investigated as methods for long-term prediction of artificial satellite orbits. Analytically averaged equations were compared with numerically averaged equations with respect to accuracy and efficiency for computation of zonal and nonresonant third-body perturbations. Numerically averaged equations were also evaluated for computation of long-period effects from resonant third-body, tesseral harmonic, and atmospheric drag perturbations. Guidelines will be presented for application of averaged VOP equations to a broad class of orbits.
Two accelerometers provided acceleration data during the STS-75 mission in support of the third United States Microgravity Payload (USMP-3) experiments. The Orbital Acceleration Research Experiment (OARE) and the Space Acceleration Measurement System (SAMS) provided a measure of the microgravity environment of the Space Shuttle Columbia. The OARE provided investigators with quasi-steady acceleration measurements after about a six hour time lag dictated by downlink constraints. SAMS data were downlinked in near-real-time and recorded on-board for post-mission analysis. An overview of the mission is provided as are brief discussions of these two accelerometer systems. Data analysis techniques used to process SAMS and OARE data are discussed Using a combination of these techniques, the microgravity environment related to several different Orbiter, crew, and experiment operations is presented and interpreted. The microgravity environment represented by SAMS and OARE data is comparable to the environments measured by the instruments on earlier microgravity science missions. The OARE data compared well with predictions of the quasi-steady environment. The SAMS data show the influence of thruster firings and crew motion (transient events) and of crew exercise, Orbiter systems, and experiment operations (oscillatory events). Thruster activity on this mission appears to be somewhat more frequent than on other microgravity missions with the combined firings of the F5L and F5R jets producing significant acceleration transients. The specific crew activities performed in the middeck and flight deck, the SPREE table rotations, the waste collection system compaction, and the fuel cell purge had negligible effects on the microgravity environment of the USMP-3 carriers. The Ku band antenna repositioning activity resulted in a brief interruption of the ubiquitous 17 Hz signal in the SAMS data. In addition, the auxiliary power unit operations during the Flight Control System checkout appeared to have a significant impact on the microgravity environment.
Space-based astrometry promises to provide a powerful new tool for astrophysics. At a precision level of a few microarcsonds, a wide range of phenomena are opened up for study. In this paper we discuss the capabilities of the SIM Lite mission, the first space-based long-baseline optical interferometer, which will deliver parallaxes to 4 microarcsec. A companion paper in this volume will cover the development and operation of this instrument. At the level that SIM Lite will reach, better than 1 microarcsec in a single measurement, planets as small as one Earth can be detected around many dozen of the nearest stars. Not only can planet masses be definitely measured, but also the full orbital parameters determined, allowing study of system stability in multiple planet systems. This capability to survey our nearby stellar neighbors for terrestrial planets will be a unique contribution to our understanding of the local universe. SIM Lite will be able to tackle a wide range of interesting problems in stellar and Galactic astrophysics. By tracing the motions of stars in dwarf spheroidal galaxies orbiting our Milky Way, SIM Lite will probe the shape of the galactic potential history of the formation of the galaxy, and the nature of dark matter. Because it is flexibly scheduled, the instrument can dwell on faint targets, maintaining its full accuracy on objects as faint as V=19. This paper is a brief survey of the diverse problems in modern astrophysics that SIM Lite will be able to address.
The Transiting Exoplanet Survey Satellite (TESS) mission was designed to perform an all-sky search of planets around bright and nearby stars. Here we report the discovery of two sub-Neptunes orbiting around TOI 1062 (TIC 299799658), a V = 10.25 G9V star observed in the TESS Sectors 1, 13, 27, and 28. We use precise radial velocity observations from HARPS to confirm and characterize these two planets. TOI 1062b has a radius of 2.265(-0.091,+0.096) Rꚛ, a mass of 10.15 ± 0.8 Mꚛ, and an orbital period of 4.1130 ± 0.0015 days. The second planet is not transiting, has a minimum mass of 9.78(−1.18,+1.26) Mꚛ and is near the 2:1 mean motion resonance with the innermost planet with an orbital period of 7.972(−0.024,+0.018) days. We performed a dynamical analysis to explore the proximity of the system to this resonance, and to attempt further constraining the orbital parameters. The transiting planet has a mean density of 4.85(−0.74,+0.84) g/cu. cm and an analysis of its internal structure reveals that it is expected to have a small volatile envelope accounting for 0.35% of the mass at most. The star’s brightness and the proximity of the inner planet to what is know as the radius gap make it an interesting candidate for transmission spectroscopy, which could further constrain the composition and internal structure of TOI 1062b.
A new solar weather mission has been proposed, involving a dozen or more small spacecraft spaced at regular, constant intervals in a mutual heliocentric circular orbit between the orbits of Earth and Venus. These solar weather buoys (SWBs) would carry instrumentation to detect and measure the material in solar flares, solar energetic particle events, and coronal mass ejections as they flowed past the buoys, serving both as science probes and as a radiation early warning system for the Earth and interplanetary travelers to Mars. The baseline concept involves placing a mothercraft carrying the SWBs into a staging orbit at the Sun-Earth L1 libration point. The mothercraft departs the L1 orbit at the proper time to execute a trailing-edge lunar flyby near New Moon, injecting it into a heliocentric orbit with its perihelion interior to Earth s orbit. An alternative approach would involve the use of a Double Lunar Swingby (DLS) orbit, rather than the L1 orbit, for staging prior to this flyby. After injection into heliocentric orbit, the mothercraft releases the SWBs-all equipped with low-thrust pulsed plasma thrusters (PPTs)-whereupon each SWB executes a multi-day low-thrust finite bum around perihelion, lowering aphelion such that each achieves an elliptical phasing orbit of different orbital period from its companions. The resulting differences in angular rates of motion cause the spacecraft to separate. While the lead SWB achieves the mission orbit following an insertion burn at its second perihelion passage, the remaining SWBs must complete several revolutions in their respective phasing orbits to establish them in the mission orbit with the desired longitudinal spacing. The complete configuration for a 14 SWB scenario using a single mothercraft is achieved in about 8 years, and the spacing remains stable for at least a further 6 years. Flight operations can be simplified, and mission risk reduced, by employing two mothercraft instead of one. In this scenario: the second mothercraft stays in a libration-point or DLS staging orbit until the first mothercraft has achieved nearly 180 separation from the Earth. The timing of the second mothercraft's subsequent lunar flyby is planned such that this spacecraft will be located 180 from the first mothercraft upon completion of its heliocentric circularization maneuvers. Both groups of satellites then only have to spread out over 180 to obtain full 360 coverage around the Sun.
We present previously unpublished July 2005 H-band coronagraphic data of the young, planet-hosting star HR 8799 from the newly-released Keck/NIRC2 archive. Despite poor observing conditions, we detect three of the planets (HR 8799 bcd), two of them (HR 8799 bc) without advanced image processing. Comparing these data with previously published 1998-2011 astrometry and that from re-reduced October 2010 Keck data constrains the orbits of the planets. Analyzing the planets' astrometry separately, HR 8799 d's orbit is likely inclined at least 25 deg from face-on and the others may be on in inclined orbits. For semimajor axis ratios consistent with a 4:2:1 mean-motion resonance our analysis yields precise values for HR 8799 bcd's orbital parameters and strictly constrains the planets' eccentricities to be less than 0.18-0.3. However, we find no acceptable orbital solutions with this resonance that place the planets in face-on orbits; HR 8799 d shows the largest deviation from such orbits. Moreover, few orbits make HR 8799 d coplanar with b and c, whereas dynamical stability analyses used to constrain the planets' masses typically assume coplanar and/or fare.on orbits. This paper illustrates the significant science gain enabled with the release of the NIRC2 archive.
The solution to the motion of a satellite in an eccentric orbit and in resonance with the second-degree sectorial harmonic of the potential field is developed. The method of solution used parallels the well known von Zeipel method of general perturbations. The solution consists of expressions for the variations of the Delaunay variables. These expressions are composed of the perturbations developed by Brouwer in 1959 for the motion of an artificial satellite plus first-order perturbations due to the second-degree sectorial harmonic (in terms of the Legendre normal elliptic integrals of the first and second kind).