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At least 145 records · Page 8

Universal time - Results from lunar laser ranging

A least squares analysis of lunar laser ranging observations from the McDonald Observatory is used to estimate universal time. In addition to the ranging observations, the analysis simultaneously takes into account the parameters representing the locations of McDonald and the lunar retroreflectors, the orbits of the earth and the moon, and the moon's physical libration. The root-mean-square of the postfit range residuals for the 5-year period from October 1970 to November 1975 is 28 cm. The results are compared with those obtained by the Bureau International de l'Heure and by Stolz et al. (1976), and the reasons for discrepancies are discussed. It is suggested that problems in modeling the moon's motion make difficult the determination of UT with the accuracy inherent in the ranging observations.

King, R. W.↗

A method of revitalizing Sampson's theory of the Galilean satellites

A method is developed by which Sampson's theory of motion of Jupiter's Galilean satellites can be revitalized by use of algebraic manipulation software on a digital computer. The technique seeks (1) to remove algebraic errors existing in the current Sampson theory, (2) to introduce some neglected effects due to solar interactions and the 3-7 commensurability between the outer two satellites, (3) to allow for nonzero amplitude and phase of the libration, (4) to allow future revision of the arbitrary constants of integration, (5) to express the final results as analytic functions of variations in the numerous arbitrary constants of integration and arbitrary parameters, and (6) to provide analytic partial derivatives by means of which the numerical values of coefficients in the expressions for the coordinates can be adjusted. The level of precision desired is one arc second (Jovicentric) for the coordinates (2, 3.3, 5.2, and 9.1 km, respectively, for satellites I through IV).

Lieske, J. H.↗

Solar Radiation Pressure Effects on the Orbital Motion at SEL2 for the James Webb Space Telescope

Due to James Webb Space Telescope’s large sunshield, which will always be facing the Sun to protect the observatory’s instruments, Solar Radiation Pressure (SRP) has an important effect on its orbital motion around SEL2. Moreover, SRP is highly dependent on the observatory’s attitude with respect to the Sun observatory line. This paper explores the impact of SRP for different attitude profiles on the size of a reference orbit.

Libration Point Orbit↗

Theory of motion of Jupiter's Galilean satellites

Final results are presented for a theory enabling one to calculate the positions of the Galilean satellites and their partial derivatives. Extensive use of algebraic manipulation software on a digital computer is made to generate the final expressions. The theory is, in effect, a revitalization of Sampson's (1921) theory. Algebraic and mathematical errors existing in Sampson's work are removed, some neglected effects due to solar interactions and the 3-7 commensurability are introduced, allowance is made for nonzero amplitude and phase of the free libration, and the final results are expressed as analytic functions of variations in 49 arbitrary constants of integration and physical parameters. The theory is constructed in a manner which readily allows for future revision, and analytic expressions are provided for the partial derivatives with respect to the 49 parameters.

Lieske, J. H.↗

Long Term Missions at the Sun-Earth Libration Point L1: ACE, SOHO, and WIND

Three heliophysics missions -- the Advanced Composition Explorer (ACE), Solar Heliospheric Observatory (SOHO), and the Global Geoscience WIND -- have been orbiting the Sun-Earth interior libration point L1 continuously since 1997, 1996, and 2004, respectively. ACE and WIND (both NASA missions) and SOHO (an ESA-NASA joint mission) are all operated from the NASA Goddard Space Flight Center (GSFC). While ACE and SOHO have been dedicated libration point orbiters since their launches, WIND has had also a remarkable 10-year career flying a deep-space, multiple lunar-flyby trajectory prior to 2004. That era featured 36 targeted lunar flybys with excursions to both L1 and L2 before its final insertion in L1 orbit. A figure depicts the orbits of the three spacecraft, showing projections of the orbits onto the orthographic planes of a solar rotating ecliptic frame of reference. The SOHO orbit is a quasi-periodic halo orbit, where the frequencies of the in-plane and out-of-plane motions are practically equal. Such an orbit is seen to repeat itself with a period of approximately 178 days. For ACE and WIND, the frequencies of the in-plane and out-of-plane motions are unequal, giving rise to the characteristic Lissajous motion. ACE's orbit is of moderately small amplitude, whereas WIND's orbit is a large-amplitude Lissajous of dimensions close to those of the SOHO halo orbit. As motion about the collinear points is inherently unstable, stationkeeping maneuvers are necessary to prevent orbital decay and eventual escape from the L1 region. Though the three spacecraft are dissimilar (SOHO is a 3-axis stabilized Sun pointer, WIND is a spin-stabilized ecliptic pole pointer, and ACE is also spin-stabilized with its spin axis maintained between 4 and 20 degrees of the Sun), the stationkeeping technique for the three is fundamentally the same. The technique consists of correcting the energy of the orbit via a delta-V directed parallel or anti-parallel to the Spacecraft-to-Sun line. SOHO achieves this using thrusters oriented in line with the solar direction. WIND achieves the delta-V via pulsing radial thrusters when aligned with the Sun. ACE uses axial thrusters to apply delta-V with a component that is 94% or more aligned with the ACE-Sun line. Sunward thrust adds energy to the orbit preventing decay back toward Earth. Thrust directed anti-Sunward takes energy out of the L1 orbit, thereby preventing escape from the Earth-Moon system into independent heliocentric orbit. Libration point orbit stationkeeping delta-V costs grow exponentially with time elapsed from the last maneuver performed. The doubling time constant is approximately 16 days. For the sake of fuel conservation, and for limiting the absolute magnitude of propulsion performance errors, stationkeeping maneuvers should be performed before the delta-V grows too large; for our purposes 'too large' is considered to be greater than 0.5 m/sec. In practice, the typical interval between burns for this trio is about three months, and the typical delta-V is much smaller than 0.5 m/sec. Typical annual stationkeeping costs have been around 1.0 m/sec for ACE and WIND, and much less than that for SOHO. All three spacecraft have ample fuel remaining; barring contingencies all three could, in principle, be maintained at L1 for decades to come. This paper will review the L1 orbits and the mission history of ACE, WIND, and SOHO, and describe the stationkeeping techniques and orbit maneuver experience. The Lissajous phase control that was practiced for ACE during the period from 1999 to 2001 will also be briefly discussed. The final section will consider the future of these ongoing missions.

Roberts, Craig E.↗

Orbital Maintenance for the Wide Field Infrared Survey Telescope: Effects of Solar Radiation Pressure and Navigation Accuracies on Station Keeping.

The Wide-Field Infrared Survey Telescope (WFIRST) is a NASA observatorydesigned to answer questions about dark energy and astrophysics, planned for alaunch in 2025 to orbit around the Sun-Earth L2 (SEL2) Libration Point. Due tothe instability of the SEL2 vicinity, WFIRST must perform station keeping maneuversto remain in orbit. This paper reviews different navigation solutions and SRP modelingtechniques that are being considered when planning these maneuvers. In this paper,we will describe station keeping strategy, we will explore the possibility of using an on-boardnavigation system and finally study how Solar Radiation Pressure (SRP) affectsits orbital motion and controllability.

Solar↗

Commensurabilities of satellites' apsidal precession periods

The orientation of the major axis of Saturn's satellite Rhea librates about alignment with Titan's major axis. This behavior is a result of Titan's gravitational influence on Rhea. Similar effects may be important in the Uranian satellite system if they are enhanced by commensurabilities of apsidal precession periods. Extensive observations will be required if this possibility is to be confirmed. The effects of possible stable alignments have not been included in past analyses of the motions of Uranus' satellites, so the results of those studies should be accepted only tentatively.

Greenberg, R.↗

Orientation of the moon by numerical integration

The differential equations of rotational motion of the moon are solved by numerical integration methods. Euler's dynamical equations transformed to a convenient form are treated by techniques analogous to ordinary orbit determination procedures. The proposed method is fully consistent with the ephemeris of the moon and can utilize a variety of observational material for the solution of the selected parameters. Examples are given of comparison between the proposed method and Eckhardt's 1970 model of the physical librations of the moon. The merits of the new method are discussed in the light of conventional data sources like earth-based or satellite-based photography as well as newly available data types like laser ranging to retroreflectors on the moon.

Papo, H. B.↗

Mapping the stability region of the 3:2 Neptune-Pluto resonance

Pluto and Charon are most likely the remnants of a large number of objects that existed in the Uranus-Neptune region at early epochs of the solar system. Numerical integrations have shown that, in general, such objects were ejected from the planetary region on timescales of approximately 10(exp 7) years after Neptune and Uranus reached their current masses. It is thought that the Pluto-Charon system survived to current times without being dynamically removed in this way because it is trapped in a set of secular and mean motion resonances with Neptune. The best-known Pluto-Neptune orbit coupling is the 3:2 mean motion resonance discovered almost 30 years ago by C. Cohen and E. Hubbard. These workers showed that the resonance angle, delta is equivalent to 3(lambda(sub P)) - 2(lambda(sub N)) - omega-bar(sub P) where omega-bar(sub P) is the longitude of perihelion of the Pluto-Charon system, and lambda(sub N) and lambda(sub P) are the mean longitude of Neptune and Pluto-Charon respectively, librates about 180 deg with an amplitude, A(sub delta), of 76 deg. A numerical simulation project to map out the stability region of the 3:2 resonance is reported. The results of these simulations are important to understanding whether Pluto's long-term heliocentric stability requires only the 3:2 resonance, or whether it instead requires one or more of the other Pluto-Neptune resonances. Our study also has another important application. By investigating stability timescales as a function of orbital elements, we gain insight into the fraction of orbital phase space which the stable 3:2 resonance occupies. This fraction is directly related to the probability that the Pluto-Charon system (and possibly other small bodies) could have been captured into this resonance.

Levison, H. F.↗

Spacecraft Formation Control: Managing Line-of-Sight Drift Based on the Dynamics of Relative Motion

In a quest to improve space-based observational capability, an increasing number of investigators are proposing missions with precision formation flying architectures. Typical missions include the Micro- Arcsecond X-ray Imaging Mission (MAXIM), Stellar Imager (SI), and the New Worlds Observer (NWO). Missions designed to explore targets in deep-space generally require holding a formation configuration fixed in inertial space during science observation. Analysis in this paper is specifically aimed at the NWO architecture, characterizing the natural drift of the line-of-sight and the separation range for two spacecraft operating in the vicinity of the Earth/Moon-Sun L(sub 2) libration point. Analysis employs a linear form of the relative dynamics associated with an n-body gravity field. The study is designed to identify favorable observation directions, characterized by minimal line-of-sight drift, along the mission timeline.

Luquette, Richard J.↗

Improved ephemerides of the Galilean satellites

Over 4800 earth-based observations of Jupiter's Galilean satellites have been analyzed in order to develop improved ephemerides of the satellites for the Voyager mission, using the new theory of motion of the Galilean satellites. Included are over 1700 eclipses of the satellites by Jupiter spanning the interval 1878-1974, 85 mutual events (eclipses and occultations) observed in 1973, and over 2900 exposures on photographic plates from 1967-1978. The resulting ephemerides (labeled E-2) were employed for the Voyager I encounter and are in error by less than 200 km at the time of Jupiter close approach. A very small (0.066 deg) amplitude of the Laplacian free libration is indicated by the data.

Lieske, J. H.↗

Automating Initial Guess Generation for High Fidelity Trajectory Optimization Tools

Many academic studies in spaceflight dynamics rely on simplified dynamical models, such as restricted three-body models or averaged forms of the equations of motion of an orbiter. In practice, the end result of these preliminary orbit studies needs to be transformed into more realistic models, in particular to generate good initial guesses for high-fidelity trajectory optimization tools like Mystic. This paper reviews and extends some of the approaches used in the literature to perform such a task, and explores the inherent trade-offs of such a transformation with a view toward automating it for the case of ballistic arcs. Sample test cases in the libration point regimes and small body orbiter transfers are presented.

design process↗

Dynamic analysis of satellites with deployable hinged appendages

The nonlinear equations of motion determining the planar dynamical behavior of an orbiting satellite deploying both one and two rigid appendages have been formulated using Lagrange's equations. The analysis accounts for large angle rotations, Coriolis effects, and the gravitational gradient, and the resulting coupled governing equations are integrated numerically. The analysis is applied to the Space Shuttle based deployment of rigid truss-like members, and results show that spacecraft inertia parameters, appendage mass and length, deployment velocity, and initial conditions all influence the system response. It is found that the resulting librational movement is related to the size of the deployment payload, and that gravitational forces lead to vehicle stabilization.

Oakes, Kevin F.↗

First evaluation of the main parameters in the dynamics of the Small Expendable Deployer System (SEDS) for a tethered satellite

The dynamics of the motion of the Small Expendable Deployer System (SEDS) is studied by using a simplified model in which no external forces (except the gravity gradient field) are applied on the tethered body and the tether is assumed massless. The dynamics of SEDS operation is modeled as a sequence of two phases: the deployment phase and the swing phase. For the first one the velocity dependent forces are found to force the tether forward from the local vertical. When the deployment ends, Coriolis effects vanish and the swing phase begins, which is characterized by a wide free libration. The time duration as well as velocity, acceleration and tension of the tethered body are estimated for both deployment and swing phases.

Deluca, Luigi↗

Orbital resonances in the solar system

Orbital resonances are defined as any system of two or more satellites (including planets) orbiting the same primary and whose orbital mean motions are in a ratio of small whole numbers. Known orbital resonances in the solar system are identified, including those involving Jupiter's satellites Io, Europa, and Ganymede; Saturn's satellites Mimas and Tethys, Enceladus and Dione, and Titan and Hyperion; Saturn's ring gaps and Mimas; various asteroids and Jupiter; and the planets Neptune and Pluto. The stability of orbital resonances is examined, the origin of orbital commensurabilities is investigated, and a simple model of the simplest kind of eccentricity-type resonance is outlined. A method is described by which tides carry a noncommensurate pair of satellites into a stable libration, and current ideas concerning the formation of the gaps in Saturn's rings and the asteroid belt are discussed. Various approaches to the analysis of orbital resonances are laid out and illustrated. Three two-body commensurabilities in Saturn's satellite system are analyzed numerically.

Peale, S. J.↗

Wide-Field Infrared Survey Telescope and Starshade Formation Flying Dynamics at Sun-Earth L2

The formation flying of an occulter with a telescope at the Sun-Earth L2 (SEL2) Libration Point can be a challenging problem. A good knowledge of the Restricted Three Body Problem dynamics is required to understand how these two spacecraft interact with each other in the SEL2 unstable environment, and how other perturbations such as Solar Radiation Pressure (SRP) affect their mutual trajectories. This paper focuses on the transfer trajectories to achieve specific relative positions between two spacecraft as they fly in formation at SEL2, andanalyzes the relevance of SRP in this formation, using the Wide-Field Infrared Survey Telescope (WFIRST) and the Starshade occulter as an example. Given that WFIRST and Starshade have very different area-to-mass ratios, SRP will affect their motion in different ways, and their relative position can be key to reduce the V cost. In this paper we intend on providing an explanation on how the relative position between both spacecrafts affects the transfer V from one observation to the other using dynamical system theory and Floquet modes.

Pressure↗

Rotation histories of the natural satellites

Recent advances in the theory of rotation are combined with traditional approaches to study the rotational evolution of the 33 known natural satellites. A calculation similar to that reported by Burns and Safronov (1973) is applied to each satellite to obtain the characteristic time of decay of any wobble motion to smooth rotation about the principal axis of maximum moment of inertia. Stability criteria and capture probabilities are calculated for the 3/2 spin resonance. Results show that only the regular satellites and Iapetus, Hyperion, Triton, and the moon are tidally evolved. Of these, 13 have confirmed synchronous rotation periods; capture probabilities into the 3/2 resonance indicate that none of the remaining 10 should be captured in nonsynchronous, commensurate spin states. For the most part, the irregular satellites retain their original spins except for a relaxation to principal axis rotation. Tidal evolution of the obliquities of the satellites is evaluated in the framework of the generalization of Cassini's laws for the moon. Nearly resonant, forced librations in longitude of 4.8 and 0.5 deg are calculated on the basis of the observed shapes of Phobos and Deimos, respectively.

Peale, S. J.↗

Formation Control of the MAXIM L2 Libration Orbit Mission

The Micro-Arcsecond Imaging Mission (MAXIM), a proposed concept for the Structure and Evolution of the Universe (SEU) Black Hole Imaging mission, is designed to make a ten million-fold improvement in X-ray image clarity of celestial objects by providing better than 0.1 microarcsecond imaging. To achieve mission requirements, MAXIM will have to improve on pointing by orders of magnitude. This pointing requirement impacts the control and design of the formation. Currently the architecture is comprised of 25 spacecraft, which will form the sparse apertures of a grazing incidence X-ray interferometer covering the 0.3-10 keV bandpass. This configuration will deploy 24 spacecraft as optics modules and one as the detector. The formation must allow for long duration continuous science observations and also for reconfiguration that permits re-pointing of the formation. In this paper, we provide analysis and trades of several control efforts that are dependent upon the pointing requirements and the configuration and dimensions of the MAXIM formation. We emphasize the utilization of natural motions in the Lagrangian regions that minimize the control efforts and we address both continuous and discrete control via LQR and feedback linearization. Results provide control cost, configuration options, and capabilities as guidelines for the development of this complex mission.

Folta, David↗