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At least 199 records · Page 11

Optimal impulsive time-fixed orbital rendezvous and interception with path constraints

Minimum-fuel, impulsive, time-fixed solutions are obtained for the problem of orbital rendezvous and interception with interior path constraints. Transfers between coplanar circular orbits in an inverse-square gravitational field are considered, subject to a circular path constraint representing a minimum or maximum permissible orbital radius. Primer vector theory is extended to incorporate path constraints. The optimal number of impulses, their times and positions, and the presence of initial or final coasting arcs are determined. The existence of constraint boundary arcs and boundary points is investigated as well as the optimality of a class of singular arc solutions. To illustrate the complexities introduced by path constraints, an analysis is made of optimal rendezvous in field-free space subject to a minimum radius constraint.

Taur, D.-R.↗

A two parameter survey of periodic orbits in the restricted problem of three bodies

Within the context of the restricted problem of three bodies the effects caused by varying the mass ratio of the primaries and the eccentricity of their orbits, upon periodic orbits of the infinitesimal mass which are numerical continuations of circular orbits in the ordinary problem of two bodies are shown. A recursive power series technique is used to numerically integrate the equations of motion as well as the first variational equations in order to generate a two parameter family of perodic orbits and identify the linear stability characteristics. Seven such families are investigated with equally spaced mass ratios from 0.0 to 1.0 and eccentricities of the orbits of the primaries in a range 0.0 to 0.6. Stable orbits are associated with large distances of the infinitesimal mass from the perturbing primary, nearly circular motion of the primaries, and small mass ratios of the primaries. Unstable orbits for the infinitesimal mass are associated with small distances from the perturbing primary, highly elliptic orbits of the primaries and large mass ratios.

Shelus, P. J.↗

An Analysis of Gravity-Field Estimation Based on Intersatellite Dual-1-Way Biased Ranging

The GRACE (Gravity Recovery And Climate Experiment) mission is designed to make global, highly accurate measurements of the Earth's gravity field with high spatial resolution. Ancillary GPS occultation measurements are also to be carried out for atmospheric monitoring. In the dual-1-way biased ranging of this mission, the range between two satellites separated by 100 to 200 km in nearly polar, coplanar, circular orbits, is measured to very high precision, to within an additive constant, through the exchange of K- and Ka-band sinusoidal signals. Such biased ranging data, along with GPS L-band range and phase data, can be processed and fit over successive multiday intervals to obtain accurate estimates of the Earth's gravity field. This report approximately models and analyzes this process, from the generation of the RF signals at the two satellites through the extraction of the geopotential. The steps include generation of the transmitted signals, processing the received signals to extract high-rate baseband phase, carrying out a dual-1-way combination of baseband phase to extract high-rate biased range for each band, combining K- and Ka-band ranges to correct for the ionosphere effect, and processing the resulting high-rate biased range values to extract three types of reduced-rate observables: biased range, range rate and range acceleration. The version of dual-1-way biased ranging developed by this report improves upon previous versions in a number of ways: highly accurate satellite-timetag corrections derived from concurrent GPS data, better baseband phase extraction using highly digital processing, highly accurate USO-rate calibration derived from concurrent GPS data, an improved method for extracting high-rate biased range from baseband phase, improved filtering for extracting reduced- rate observables from high-rate biased range, and parallel extraction of three observable types.

SINUSOIDAL SIGNALS↗

Optimal low-thrust, three-burn orbit transfers with large plane changes

Optimal low-thrust, three-burn solutions have been obtained for orbit transfers between a 28.5-degree inclined low earth orbit and a series of 63.4-degree inclined circular orbits as well as a series of 63.4-degree inclined elliptical orbits with twelve hour periods. Solutions have also been obtained for orbit transfers between 97-degree inclined orbits and a 57-degree inclined low earth orbit. Thrust to weight ratios as low as 0.02 were considered. A hybrid nonlinear programming method was used to obtain the solutions. Analysis of the optimal steering during various burns reveals a natural division of the steering strategies into two categories based on whether a burn results in a change predominantly in semi-major axis or orbit plane. The similarity of these optimal steering strategies to previously obtained simple near-optimal steering strategies is discussed.

Zondervan, K. P.↗

The Dynamical Evolution of the Earth-Moon Progenitors: Results and Interpretation - 2

Substantial evidence indicates that the Earth-Moon system formed about 100 m.y. after the oldest meteorites and that the inner solar system had five terrestrial planets for several tens of millions of years before the hypothesized Moon-forming impact. We present and discuss some results from a series of N-body integrations in which the mass ratio of the Earth-Moon progenitors is 8:1 or 1:1. We want to know if it is plausible to have the Earth-Moon progenitors collide between 8 m.y. and 200 m.y. after the other planets had formed and to have the resulting system look "similar" to the solar system. If a collision occurs, the integrations tell us which two bodies collide and the time of the collision. We also determine the angular momentum deficit (AMD) of the resulting terrestrial planets. Additionally, we calculate several parameters of the collision. We use the AMD of the terrestrial planets to compare the resulting system to our own. The AMD or a planet is the difference between its orbital angular momentum and its orbital angular momentum if it were in a circular orbit with zero inclination.

Rivera, E.↗

Calculating Statistical Orbit Distributions Using GEO Optical Observations with the Michigan Orbital Debris Survey Telescope (MODEST)

NASA's Orbital Debris measurements program has a goal to characterize the small debris environment in the geosynchronous Earth-orbit (GEO) region using optical telescopes ("small" refers to objects too small to catalog and track with current systems). Traditionally, observations of GEO and near-GEO objects involve following the object with the telescope long enough to obtain an orbit suitable for tracking purposes. Telescopes operating in survey mode, however, randomly observe objects that pass through their field of view. Typically, these short-arc observation are inadequate to obtain detailed orbits, but can be used to estimate approximate circular orbit elements (semimajor axis, inclination, and ascending node). From this information, it should be possible to make statistical inferences about the orbital distributions of the GEO population bright enough to be observed by the system. The Michigan Orbital Debris Survey Telescope (MODEST) has been making such statistical surveys of the GEO region for four years. During that time, the telescope has made enough observations in enough areas of the GEO belt to have had nearly complete coverage. That means that almost all objects in all possible orbits in the GEO and near- GEO region had a non-zero chance of being observed. Some regions (such as those near zero inclination) have had good coverage, while others are poorly covered. Nevertheless, it is possible to remove these statistical biases and reconstruct the orbit populations within the limits of sampling error. In this paper, these statistical techniques and assumptions are described, and the techniques are applied to the current MODEST data set to arrive at our best estimate of the GEO orbit population distribution.

Matney, M.↗

Light Echos in Kerr Geometry: A Source of High Frequency QPOs from Random X-ray Bursts

We propose that high frequency quasi-periodic oscillations (HFQPOs) can be produced from randomly-formed X-ray bursts (flashes) by plasma interior to the ergosphere of a rapidly-rotating black hole. We show by direct computation of their orbits that the photons comprising the observed X-ray light curves, if due to a multitude of such flashes, are affected significantly by the black hole's dragging of inertial frames; the photons of each such burst arrive to an observer at infinity in multiple (double or triple), distinct 'bunches' separated by a roughly constant time lag of t/M approximately equal to 14, regardless of the bursts' azimuthal position. We argue that every other such 'bunch' represents photons that follow trajectories with an additional orbit around the black hole at the photon circular orbit radius (a photon 'echo'). The presence of this constant lag in the response function of the system leads to a QPO feature in its power density spectra, even though the corresponding light curve consists of a totally stochastic signal. This effect is by and large due to the black hole spin and is shown to gradually diminish as the spin parameter a decreases or the radial position of the burst moves outside the static limit surface (ergosphere). Our calculations indicate that for a black hole with Kerr parameter of a/M=0.99 and mass of M=10*Msun the QPO is expected at a frequency of approximately 1.3-1.4 kHz. We discuss the plausibility and observational implications of our model/results as well as its limitations.

Fukumura, K.↗

Light Echoes in Kerr Geometry: A Source of High Frequency QPOs from Random X-ray Bursts

We propose that high frequency quasi-periodic oscillations (HFQPOs) can be produced from randomly-formed X-ray bursts (flashes) by plasma interior to the ergosphere of a rapidly-rotating black hole. We show by direct computation of their orbits that the photons comprising the observed X-ray light curves, if due to a multitude of such flashes, are affected significantly by the black hole's dragging of inertial frames; the photons of each such burst arrive to an observer at infinity in multiple (double or triple), distinct "bunches" separated by a roughly constant time lag of Deltat(t(sub lag))/M approx. 14, regardless of the bursts' azimuthal position. We argue that every other such "bunch" represents photons that follow trajectories with an additional orbit around the black hole at the photon circular orbit radius (a photon "echo"). The presence of this constant lag in the response function of the system leads to a QPO feature in its power density spectra, even though the corresponding light curve consists of a totally stochastic signal. This effect is by and large due to the black hole spin and is shown to gradually diminish as the spin parameter a decreases or the radial position of the burst moves outside the static limit surface (ergosphere). Our calculations indicate that for a black hole with Kerr parameter of a/M = 0.99 and mass of M = 10Stellar Mass the QPO is expected at a frequency of v(sub QPO) approx. 1.3 - 1.4 kHz. We discuss the plausibility and observational implications of our model/results as well as its limitations. Subject headings: accretion, accretion disks - black hole physics - X-rays: galaxies - stars: oscillations

Fukumura, Keigo↗

High Frequency QPOs due to Black Hole Spin

We present detailed computations of photon orbits emitted by flares at the innermost stable circular orbit (ISCO) of accretion disks around rotating black holes. We show that for sufficiently large spin parameter, i.e. a > 0.94 M, flare a sufficient number of photons arrive at an observer after multiple orbits around the black hole, to produce an "photon echo" of constant lag, i.e. independent of the relative phase between the black hole and the observer, of T approximates 14 M. This constant time delay, then, leads to a power spectrum with a QPO at a frequency nu approximates 1/14M, even for a totally random ensemble of such flares. Observation of such a QPO will provide incontrovertible evidence for the high spin of the black hole and a very accurate, independent, measurement of its mass.

Kazanas, Demos↗

Altair Descent and Ascent Reference Trajectory Design and Initial Dispersion Analyses

The Altair Lunar Lander is the linchpin in the Constellation Program (CxP) for human return to the Moon. Altair is delivered to low Earth orbit (LEO) by the Ares V heavy lift launch vehicle, and after subsequent docking with Orion in LEO, the Altair/Orion stack is delivered through translunar injection (TLI). The Altair/Orion stack separating from the Earth departure stage (EDS) shortly after TLI and continues the flight to the Moon as a single stack. Altair performs the lunar orbit insertion (LOI) maneuver, targeting a 100-km circular orbit. This orbit will be a polar orbit for missions landing near the lunar South Pole. After spending nearly 24 hours in low lunar orbit (LLO), the lander undocks from Orion and performs a series of small maneuvers to set up for descending to the lunar surface. This descent begins with a small deorbit insertion (DOI) maneuver, putting the lander on an orbit that has a perilune of 15.24 km (50,000 ft), the altitude where the actual powered descent initiation (PDI) commences. At liftoff from Earth, Altair has a mass of 45 metric tons (mt). However after LOI (without Orion attached), the lander mass is slightly less than 33 mt at PDI. The lander currently has a single descent module main engine, with TBD lb(sub f) thrust (TBD N), providing a thrust-to-weight ratio of approximately TBD Earth g's at PDI. LDAC-3 (Lander design and analysis cycle #3) is the most recently closed design sizing and mass properties iteration. Upgrades for loss of crew (LDAC-2) and loss of mission (LDAC-3) have been incorporated into the lander baseline design (and its Master Equipment List). Also, recently, Altair has been working requirements analyses (LRAC-1). All nominal data here are from the LDAC-3 analysis cycle. All dispersions results here are from LRAC-1 analyses.

Kos, Larry D.↗

Design Considerations for a Dedicated Gravity Recovery Satellite Mission Consisting of Two Pairs of Satellites

Future satellite missions dedicated to measuring time-variable gravity will need to address the concern of temporal aliasing errors; i.e., errors due to high-frequency mass variations. These errors have been shown to be a limiting error source for future missions with improved sensors. One method of reducing them is to fly multiple satellite pairs, thus increasing the sampling frequency of the mission. While one could imagine a system architecture consisting of dozens of satellite pairs, this paper explores the more economically feasible option of optimizing the orbits of two pairs of satellites. While the search space for this problem is infinite by nature, steps have been made to reduce it via proper assumptions regarding some parameters and a large number of numerical simulations exploring appropriate ranges for other parameters. A search space originally consisting of 15 variables is reduced to two variables with the utmost impact on mission performance: the repeat period of both pairs of satellites (shown to be near-optimal when they are equal to each other), as well as the inclination of one of the satellite pairs (the other pair is assumed to be in a polar orbit). To arrive at this conclusion, we assume circular orbits, repeat groundtracks for both pairs of satellites, a 100-km inter-satellite separation distance, and a minimum allowable operational satellite altitude of 290 km based on a projected 10-year mission lifetime. Given the scientific objectives of determining time-variable hydrology, ice mass variations, and ocean bottom pressure signals with higher spatial resolution, we find that an optimal architecture consists of a polar pair of satellites coupled with a pair inclined at 72deg, both in 13-day repeating orbits. This architecture provides a 67% reduction in error over one pair of satellites, in addition to reducing the longitudinal striping to such a level that minimal post-processing is required, permitting a substantial increase in the spatial resolution of the gravity field products. It should be emphasized that given different sets of scientific objectives for the mission, or a different minimum allowable satellite altitude, different architectures might be selected.

Wiese, D. N.↗

Q4 – A CubeSat Mission to Demonstrate Omnidirectional Optical Communications

We are proposing a technology demonstration mission for JPL’s Inter-Satellite Optical Communicator (ISOC). The ISOC has the potential to enable up to 1 Gbps data rates over a distance up to 200 km in free space. Key features of the ISOC include full sky coverage and the ability to maintain multiple links simultaneously. The Q4 mission consists of (4) 6U CubeSats furnished with ISOCs to demonstrate high data rate communications among the spacecraft. More specifically, we seek to demonstrate the omnidirectionality of the ISOC by providing simultaneous optical links between one spacecraft and the other three. Q4 will be a demonstrator for small spacecraft swarm capabilities. Following a proposed deployment from the ISS, the CubeSats will utilize their onboard thrusters to enter their desired orbit. The orbit consists of one “leader” spacecraft in a circular orbit with a 400 km LEO altitude and three “follower” spacecraft in slightly elliptical orbits rotating azimuthally about the leader. The main mission will consist of three consecutive phases: First, the spacecraft will demonstrate pointing, acquisition, and tracking using newly developed protocols. Next, link establishment and different channel access methods (CDMA and TDMA) will be tested. Finally, Delay Tolerant Network protocols will be implemented to allow fast data sharing among the spacecraft. The distance between the communicating spacecraft will be increased as the mission progresses to characterize the link quality as a function of distance. All communications over the course of the mission will be recorded and analyzed on the ground using bit error rate as a metric for success. The current design for each the four Q4 CubeSats contains an XACT advanced ADCS system for precision beam pointing. Other components currently under consideration include MiPS cold gas thrusters for orbital maneuvering and gimbaled eHaWK 84W solar arrays. In this paper we present design considerations for the Q4 CubeSats, link budget calculations, results from preliminary mission analysis, and expected results.

Velazco, Jose E↗

Assessing Utility of Different Orbits for a Lunar PNT Constellation

"As the Artemis program establishes a long-term presence on the lunar surface, lunar surface users will need an accurate source of Position, Navigation, and Timing (PNT). Under the LunaNet framework, NASA has proposed the Lunar Navigation System (LNS), a constellation of satellites in lunar orbit which will broadcast LunaNet’s Augmented Forward Signal (AFS) [1] to the lunar surface. LNS will have the objective of providing user position accuracies of 10 m and timing accuracies of 10 microseconds on the lunar surface and up to 200 km above the surface. Several classes of orbits are possibilities for the LNS constellation, including circular orbits, eccentric orbits, and various families of 3-body orbits. Each of these orbit classes have both advantages and disadvantages in their utility as PNT constellations. In this study we examine a wide variety of potential LNS constellations and evaluate their performance against several metrics, including: a. Dilution of Precision (DOP) performance over the lunar service volume and the South Pole region, during both the constellation buildup and after the constellation is completed. b. Number of satellites required to achieve required DOP performance. c. Relative dynamics of LNS satellites with respect to surface users. d. Signal in space error (SISE) performance, assuming orbit determination that includes the Global Positioning System (GPS), crosslinks, and monitor sites on the surface of the moon. e. Constellation insertion, station keeping, and disposal costs. f. Specific Concept of Operations (CONOPS) and engineering challenges associated with establishing and operating the constellations. (E.g., frequent station keeping, variable signal strength, divergent CONOPS for different planes of the constellation.) The system’s performance is considered both independently and in combination with other proposed systems, such as NASA’s Lunar Communication Relay and Navigation System (LCRNS) and ESA’s Moonlight constellation. The study concludes that a 3-plane Walker constellation at 6 lunar radii (slightly higher than GPS’s 4.2 earth radii from a geometry perspective, but significantly closer in an absolute sense) is a good candidate for the LNS constellation, providing the user with good SISE and DOP performance, while not requiring excessive station keeping or complex CONOPS. However, other viable concepts exist and could be chosen if early South Pole coverage is a driving factor in the system design."

navigation↗

Orbital evolution

The orbital evolution of a large satellite is governed primarily by tidal interactions between the satellite and the planet it orbits. Tides raised on a planet by a satellite transfer energy and angular momentum to the satellite orbit; this changes the semimajor axes of satellite orbits, increasing the size of those orbits where the satellite mean motion is smaller than the planetary angular velocity, and decreasing those where the opposite is true. Substantial changes caused by such tides for satellites of the terrestrial planets may explain the absence of satellites about Mercury and Venus. For Jovian and Saturnian satellites, such tides probably are only important in bringing about some of the observed orbital resonances. Tides raised on satellites generally cause decreasing orbital eccentricities, indicating why close satellites always have nearly circular orbits. Different processes of orbital evolution dominate for small bodies; their effects probably are critical in positioning material in the primordial dust cloud so that satellite coagulation may occur. A qualitative description is given of the orbital results of gas drag, radiation pressure, Poynting-Robertson drag and electromagnetic forces.

Burns, J. A.↗