Methods of regularization for computing orbits in celestial mechanics
Numerical and analytical methods for orbit computation in celestial mechanics during and beyond collision by introduction of regularized coordinates
ORBIT CALCULATION↗
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Spectral structure of the diffuse X-ray sky
A description of diffuse celestial X-ray flux is drawn from data taken by rocket borne detectors. It was concluded that the diffuse flux is intra- and extra-galactic in origin and is caused by Compton scattering of .052 rad black body photons of relativistic electrons leaking out of the galaxies.
Boldt, E. A.↗
Dynamical Reference Frame: Current Relevance and Future Prospects
Planetary and lunar ephemerides are no longer used for the determination of inertial space. Instead, the new fundamental reference frame, the International Celestial Reference Frame (ICRF), is inherently less susceptible to extraneous, non-inertial rotations than a dynamical reference frame determined by the ephemerides would be. Consequently, the ephemerides are now adjusted onto the ICRF, and they are fit to two modern, accurate observational data types: ranging (radar, lunar laser, spacecraft) and Very Long Baseline Interferometry (VLBI) (of spacecraft near planets). The uncertainties remaining in the inner planet ephemerides are on the order of 1 kilometer, both in relative positions between the bodies and in the orientation of the inner system as a whole. The predictive capabilities of the inner planet ephemerides are limited by the uncertainties in the masses of many asteroids. For this reason, future improvements to the ephemerides must await determinations of many asteroid masses. Until then, it will be necessary to constantly update the ephemerides with a continuous supply of observational data.
VLBI (VERY LONG BASELINE INTERFEROMETRY)↗
Mariner 9 celestial mechanics experiment - Gravity field and pole direction of Mars.
Analysis of the Mariner 9 radio-tracking data shows that the Martian gravity field is rougher than that of earth or the moon, and that the accepted direction of the Mars rotation axis is in error by about 0.5 deg. Contours of equivalent surface heights deduced from a sixth-degree solution for the Martian gravity field are presented. These contours represent the deviations from sphericity of a uniformly dense body with an external potential which is given by the first sixth-degree solution. In addition to Doppler observations, ranging or group-delay measurements have been made regularly since orbit insertion.
Lorell, J.↗
Research in the Restricted Problems of Three and Four Bodies Final Scientific Report
Seven studies have been conducted on research in the existence and nature of solutions of the restricted problems of three and four bodies. The details and results of five of these research investigations have already been published, and the latest two studies will be published shortly. A complete bibliography of publications is included in this report. This research has been primarily qualitative and has yielded new information on the behavior of trajectories near the libration points in the Earth-Moon-Sun and Sun-Jupiter-Saturn systems, and on the existence of periodic trajectories about the libration points of the circular and elliptical restricted four-body models. We have also implemented Birkhoff's normalization process for conservative and nonconservative Hamiltonian systems with equilibrium points. This makes available a technique for analyzing stability properties of certain nonlinear dynamical systems, and we have applied this technique to the circular and elliptical restricted three-body models. A related study was also conducted to determine the feasibility of using cislunar periodic trajectories for various space missions. Preliminary results suggest that this concept is attractive for space flight safety operations in cislunar space. Results of this research will be of interest to mathematicians, particularly those working in ordinary differential equations, dynamical systems and celestial mechanics; to astronomers; and to space guidance and mission analysts.
Richards, Paul B.↗
Applications of laser ranging and VLBI observations for selenodetic control
The observation equations necessary to utilize lunar laser ranging and very long baseline interferometry measurements were developed for the establishment of a primary control network on the moon. The network consists of coordinates of moon points in the selenodetic Cartesian coordinate system, which is fixed to the lunar body, oriented along the three principal axes of inertia of the moon, and centered at the lunar center of mass. The observation equations derived are based on a general model in which the unknown parameters included: the selenodetic Cartesian coordinates, the geocentric coordinates of earth stations, parameters of the orientation of the selenodetic coordinate system with respect to a fixed celestial system, the parameters of the orientation of the average terrestrial coordinate system with respect to a fixed celestial coordinate system, and the geocentric coordinates of the center of mass of the moon, given by a lunar ephemeris.
Fajemirokun, F. A.↗
Comet/Asteroid Protection System (CAPS): Preliminary Space-Based Concept and Study Results
There exists an infrequent, but significant hazard to life and property due to impacting asteroids and comets. There is currently no specific search for long-period comets, smaller near-Earth asteroids, or smaller short-period comets. These objects represent a threat with potentially little or no warning time using conventional ground-based telescopes. These planetary bodies also represent a significant resource for commercial exploitation, long-term sustained space exploration, and scientific research. The Comet/Asteroid Protection System (CAPS) is a future space-based system concept that provides permanent, continuous asteroid and comet monitoring, and rapid, controlled modification of the orbital trajectories of selected bodies. CAPS would expand the current detection effort to include long-period comets, as well as small asteroids and short-period comets capable of regional destruction. A space-based detection system, despite being more costly and complex than Earth-based initiatives, is the most promising way of expanding the range of detectable objects, and surveying the entire celestial sky on a regular basis. CAPS would provide an orbit modification system capable of diverting kilometer class objects, and modifying the orbits of smaller asteroids for impact defense and resource utilization. This Technical Memorandum provides a compilation of key related topics and analyses performed during the CAPS study, which was performed under the Revolutionary Aerospace Systems Concepts (RASC) program, and discusses technologies that could enable the implementation of this future system.
Mazanek, Daniel D.↗
Measurement error analysis in determination of small-body gravity fields
We consider analytically the use of existing instrumentation in determining asteroid gravity fields from orbiting spacecraft. Asteroids (Eros as an example) are modeled as homogeneous triaxial ellipsoids, with gravitational potential given by a sperical-harmonic expansion. Mass concentrations are modeled as point masses. The character of spacecraft orbits about asteroids is discussed, along with detectibility of gravitational coefficients and of mass concentrations. A Kalman-filtering treatment of the observation process, for Eros as example, shows that using DSN tracking and onboard gravity gradiometry, radar altimetry, and celestial angle measurements, a single orbit yields asteroid mass to 0.03% and coefficients C20 to C44 to 1% accuracies.
Friedlander, A. L.↗
Spacecraft attitude sensor
A system for sensing the attitude of a spacecraft includes a pair of optical scanners having a relatively narrow field of view rotating about the spacecraft x-y plane. The spacecraft rotates about its z axis at a relatively high angular velocity while one scanner rotates at low velocity, whereby a panoramic sweep of the entire celestial sphere is derived from the scanner. In the alternative, the scanner rotates at a relatively high angular velocity about the x-y plane while the spacecraft rotates at an extremely low rate or at zero angular velocity relative to its z axis to provide a rotating horizon scan. The positions of the scanners about the x-y plane are read out to assist in a determination of attitude. While the satellite is spinning at a relatively high angular velocity, the angular positions of the bodies detected by the scanners are determined relative to the sun by providing a sun detector having a field of view different from the scanners.
Davidson, A. C.↗
Meteoritic material at four Canadian impact craters
Eleven impact melt and six basement rock samples from four craters were analyzed by neutron activation for Au, Co, Cr, Fe, Ge, Ir, Ni, Os, Pd, Re and Se. Wanapitei Lake, Ontario: the impact melts show uniform enrichments corresponding to 1-2% C1-chondrite material. Interelement ratios (Co/Cr, Ni/Cr, Ni/Ir) suggest that the impacting body was a C1-, C2-, or LL-chondrite. Nicholson Lake, North West Territory: Ni, Cr and Co are distinctly more enriched than Ir and Au which tentatively suggests an olivine-rich achondrite (nakhlite or ureilite). Gow Lake, Saskatchewan and Mistastin, Labrador: small enrichments in Ir and Ni; both the low Ir/Ni ratios and low Cr content suggest iron meteorites, but the signals are too weak for conclusive identification. A tentative comparison of meteoritic signatures at 10 large, greater than or equal to 4 km craters and their presumed celestial counterparts (13 Apollo and Amor asteroids) shows more irons and achondrites among known projectile types, and a preponderance of S-type objects, having no known meteoritic equivalent, among asteroids. It is not yet clear that these differences are significant, in view of the tentative nature of the crater identifications and the limited statistics.
Wolf, R.↗
Astrodynamics 1989; Proceedings of the AAS/AIAA Astrodynamics Conference, Stowe, VT, Aug. 7-10, 1989. Parts 1 & 2
The conference focuses of analytical and numerical aspects of astrodynamics and celestial mechanics with emphasis on planetary mission design, trajectory analysis and design, orbit determination, attitude determination and control, guidance systems, and dynamics and control of large flexible space structures. Trajectory computation techniques, satellite dynamics, and geocentric satellite orbit analysis are presented, along with earth orbiter mission analysis, trajectory optimization applications, planetary spacecraft orbit determination, and orbiting debris considerations. Neutral upper-atmosphere density is addressed, and guidance analysis, planetary mission design and analysis, trajectory analysis, estimation/identification techniques are discussed in addition to the dynamics and control of space structures or multi-body systems.
Thornton, Catherine L.↗
On the status of the rotation of Venus
Owing to its extremely slow rotation, Venus must be regarded as a triaxial body with differences of all three principal moments of inertia comparable in magnitude, thus rendering it a body essentially different from a rapidly rotating planet. The dynamical problem then arises of how such a body, with a rotation-period comparable with its orbital period, would be affected by couples exerted upon it by the gravitational action of the sun. Equations for the rotatory motion are set up in a form suitable for numerical solution by machine-calculations, but the problem so presented can be adequately investigated only for a hypothetical planet. Results obtained on this limited basis nevertheless suggest that for the actual planet the direction of the rotation axis may move almost randomly between the two hemispheres defined by the orbital plane and thus that the present direction near the south celestial pole of the orbit may be only a temporary situation.
Lyttleton, R. A.↗
Linear polarization sensitivity specifications for space-borne instruments
The radiometric accuracy of space-borne instruments such as radiometers and spectroradiometers which make measurements of the earth and other celestial objects can be compromised by the linear polarization sensitivity (LPS) induced by the optical system. Most of these optical systems contain optical elements whose reflectance or transmission is polarization dependent, such as diffraction gratings, folding and scanning mirrors, dichroic filters, and optical fibers. Optical system incorporating such elements generally display linear polarization sensitivity; different linear polarization states incident with equal radiometric power will be measured as different power levels. If the incident polarization state is unknown, the linear polarization sensitivity cannot be compensated during the data reduction. The light reflected from the earth and other planets and moons is usually partially linearly polarized, but in a random distribution. Thus, to make accurate radiometric measurements of these bodies, a radiometer or spectrometer should have a low level of linear polarization sensitivity. This paper contains a mathematical description of LPS, contains references to systems which have imposed a LPS specification, describes some of the sources of LPS, describes how to model LPS by polarization ray tracing, and discusses methods to reduce the LPS of an optical system.
Maymon, Peter W.↗
Earth/Moon System Star Tracking Sensor for Improved Deep Space Laser Communications
The goal of this research is to improve deep space communication links by exploring a new concept in stellar navigation that uses images of the Earth/Moon system to obtain precise pointing information so that the laser signal from the satellite can be directed at the ground station with unprecedented accuracy. Currently, the concept for satellite pointing relies on a dual axis star tracker that compares images of the celestial sphere to a star catalog to obtain a 3-axis orientation solution. Most star trackers are designed with a wide field of view (required to obtain enough bright starts to achieve a navigational fix) and only provide reliable pitch and yaw estimates thus necessitating the use of a second star tracker looking at an axis perpendicular to the first one to obtain an accurate estimate of the roll of the spacecraft. In the new concept the optical design will be modified to ensure that both the Earth and the Moon will be within a narrow field of view centered on Earth relative to the field of view of most star tracking systems. Because of the proximity of the bodies, it is possible to obtain highly accurate estimates of the pitch, yaw and roll of the spacecraft relative to the Earth/Moon system. The new tracker will allow for accurate 3-axis control of the spacecraft from a single tracker thus allowing the second star tracker, which would normally be pointed in a direction perpendicular to the one pointed at earth, to obtain the spacecraft roll estimate. This wide field star tracker facilitates functions like the initial satellite pointing during the acquisition phase of establishing the laser communication link or solving the lost in space problem should the system need to be reset. This new design will be tested in simulation and compared for 3-axis pointing accuracy against a standard commercial star tracker.
Star tracker↗
Microsat and Lunar-Based Imaging of Radio Bursts
No present or approved spacecraft mission has the capability to provide high angular resolution imaging of solar or magnetospheric radio bursts or of the celestial sphere at frequencies below the ionospheric cutoff. Here, we describe a MIDEX-class mission to perform such imaging in the frequency range approx. 30 kHz to 15 MHz. This mission, the Solar Imaging Radio Array (SIRA), is solar and exploration-oriented, with emphasis on improved understanding and application of radio bursts associated with solar energetic particle (SEP) events and on tracking shocks and other components of coronal mass ejections (CMEs). SIRA will require 12 to 16 micro-satellites to establish a sufficient number of baselines with separations on the order of kilometers. The constellation consists of microsats located quasi-randomly on a spherical shell, initially of approx. 10 km diameter. The baseline microsat is 3-axis stabilized with body-mounted solar arrays and an articulated, earth pointing high gain antenna. The constellation will likely be placed at L1, which is the preferred location for full-time solar observations. We also discuss briefly follow-on missions that would be lunar-based with of order 10,000 dipole antennas.
interferometry↗
Can Eccentric Debris Disks Be Long-lived? A First Numerical Investigation and Application to Zeta(exp 2) Reticuli
Context. Imaging of debris disks has found evidence for both eccentric and offset disks. One hypothesis is that they provide evidence for massive perturbers, for example, planets or binary companions, which sculpt the observed structures. One such disk was recently observed in the far-IR by the Herschel Space Observatory around Zeta2 Reticuli. In contrast with previously reported systems, the disk is significantly eccentric, and the system is several Gyr old. Aims. We aim to investigate the long-term evolution of eccentric structures in debris disks caused by a perturber on an eccentric orbit around the star. We hypothesise that the observed eccentric disk around Zeta2 Reticuli might be evidence of such a scenario. If so, we are able to constrain the mass and orbit of a potential perturber, either a giant planet or a binary companion. Methods. Analytical techniques were used to predict the effects of a perturber on a debris disk. Numerical N-body simulations were used to verify these results and further investigate the observable structures that may be produced by eccentric perturbers. The long-term evolution of the disk geometry was examined, with particular application to the Zeta2 Reticuli system. In addition, synthetic images of the disk were produced for direct comparison with Herschel observations. Results. We show that an eccentric companion can produce both the observed offsets and eccentric disks. These effects are not immediate, and we characterise the timescale required for the disk to develop to an eccentric state (and any spirals to vanish). For Zeta2 Reticuli, we derive limits on the mass and orbit of the companion required to produce the observations. Synthetic images show that the pattern observed around Zeta2 Reticuli can be produced by an eccentric disk seen close to edge-on, and allow us to bring additional constraints on the disk parameters of our model (disk flux and extent). Conclusions. We conclude that eccentric planets or stellar companions can induce long-lived eccentric structures in debris disks. Observations of such eccentric structures thus provide potential evidence of the presence of such a companion in a planetary system. We considered the specific example of Zeta2 Reticuli, whose observed eccentric disk can be explained by a distant companion (at tens of AU) on an eccentric orbit (ep greater than approx. 0.3).
planetary systems↗