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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 55 records · Page 3

Long Period Variations in Tidal and Librational Forcing of Europa

The gravitational field of Jupiter exerts a profound influence on the energy balance, thermal evolution, and stress regime of Europa. It widely appreciated that dissipation associated with the spheroidal tidal deformation is a major source of heat. Another possibly important source of dissipation is the toroidal deformation field associated with forced librations. Both tidal and librational deformations depend on the distance and direction Jupiter, as seen from Europa. These quantities vary with time as a result of the finite values of orbital eccentricity and spin pole obliquity, though the obliquity effects have been ignored in most previous studies. Variations in eccentricity and obliquity of the Galilean satellites occur on a very wide range of time scales, as angular momentum is exchanged among the orbital and rotational components of the coupled system. The orbital periods are only a few days in length, and the secular changes in orbital period associated with tidal and librational dissipation have characteristic time scales of 10-9 years or longer. On intermediate time scales, the satellites perturb each other, and the Sun and Saturn make additional contributions. The present values of satellite orbital inclinations and obliquities are not particularly representative their respective longer term variations. As a result, the tidal stress and dissipation regimes at present may not provide adequate explanation of the sources of surface features seen on the satellites.

Bills, Bruce G.↗

Lunar Navigation with Libration Point Orbiters and GPS

NASA is currently studying a Vision for Space Exploration based on spiral development of robotic and piloted missions to the moon and Mars, but research into how to perform such missions has continued ever since the first era of lunar exploration. One area of study that a number of researchers have pursued is libration point navigation and communication relay concepts. These concepts would appear to support many of NASA's current requirements for navigation and communications coverage for human and robotic spacecraft operating in lunar space and beyond. In trading libration point concepts against other options, designers must consider issues such as the number of spacecraft, required to provide coverage, insertion and stationkeeping costs, power and data rate requirements, frequency allocations, and many others. The libration points, along with a typical cis-lunar trajectory, are equilibrium locations for an infinitesimal mass in the rotating coordinate system that follows the motion of two massive bodies in circular orbits with respect to their common barycenter. There are three co-linear points along the line connecting the massive bodies: between the bodies, beyond the secondary body, and beyond the primary body. The relative distances of these points along the line connecting the bodies depend on the mass ratios. There are also two points that form equilateral triangles with the massive bodies. Ideally, motion in the neighborhood of the co-linear points is unstable, while motion near the equilibrium points is stable. However, in the real world, the motions are highly perturbed so that a satellite will require stationkeeping maneuvers.

Carpenter, J. Russell↗

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.↗

Applying Dynamical Systems Theory to Optimize Libration Point Orbit Stationkeeping Maneuvers for WIND

NASA's WIND mission has been operating in a large amplitude Lissajous orbit in the vicinity of the interior libration point of the Sun-Earth/Moon system since 2004. Regular stationkeeping maneuvers are required to maintain the orbit due to the instability around the collinear libration points. Historically these stationkeeping maneuvers have been performed by applying an incremental change in velocity, or (delta)v along the spacecraft-Sun vector as projected into the ecliptic plane. Previous studies have shown that the magnitude of libration point stationkeeping maneuvers can be minimized by applying the (delta)v in the direction of the local stable manifold found using dynamical systems theory. This paper presents the analysis of this new maneuver strategy which shows that the magnitude of stationkeeping maneuvers can be decreased by 5 to 25 percent, depending on the location in the orbit where the maneuver is performed. The implementation of the optimized maneuver method into operations is discussed and results are presented for the first two optimized stationkeeping maneuvers executed by WIND.

WIND↗

Transfer Trajectory Options for Servicing Sun-Earth-Moon Libration Point Missions

Future missions to the Sun-Earth Libration L1 and L2 regions will require scheduled servicing to maintain hardware and replenish consumables. While there have been statements made by various NASA programs regarding servicing of vehicles at these locations or in Cis-lunar space, a practical transfer study has not been extensively investigated in an operational fashion to determine the impacts of navigation and maneuver errors. This investigation uses dynamical systems and operational models to design transfer trajectories between the Sun-Earth Libration region (QuasiHalo orbit) and the Earth-Moon vicinity (Distant Retrograde Orbit, QuasiHalo Orbit, Halo Orbit, and Near Rectilinear Halo Orbit). We address the total delta V cost of transfers between each pair of locations using a Monte Carlo analysis.

Earth↗

Mission Design Strategies for Rendezvous and Servicing of Sun-Earth Libration Point Missions

With the launch of the James Webb Space Telescope (JWST) and future launches of the Roman Space Telescope (RST) and larger telescopes such as the proposed Habitable Worlds Observatory (HWO), the questions of where and how to rendezvous to enable servicing of these telescope missions arise. To aid in determining the allowable locations to rendezvous for servicing from a trajectory design approach, our previous research and analysis has shown feasible transfer trajectories between the Sun-Earth Libration L2 region (Quasi-Halo orbit) and the Earth Moon vicinity (Distant Retrograde Orbit (DRO), Quasi-Halo Orbit, Halo Orbit, and Near Rectilinear Halo Orbit (NRHO)), along with the related transfer constraints and the corresponding total fuel mass costs. We now focus on operational-like optimal scenarios for these transfers to complete a rendezvous to permit servicing at various Libration orbit locations. In this paper, we address how operational navigation and maneuver execution uncertainties impact the rendezvous timing and fuel mass (via ΔV). While optimization techniques are applied to ensure minimal ΔVs, we also analyze various transfer trajectory durations and rendezvous arrival geometries. The analysis presented includes dynamical system approaches and applies optimization through several tools including the Adaptive Trajectory Design (ATD) module as an initial guess, numerical computation using the General Mission Analysis Tool (GMAT) and Systems Tool Kit (STK) with higher fidelity perturbation modeling, and recently developed optimization tools that incorporate dynamical systems directly into the optimization process. Transfer trajectory options examined include a direct transfer from Earth versus departures from the previously examined Earth-Moon regime orbits, e.g. NRHOs and DROs. A return from Sun-Earth to lunar vicinity for a complete servicing after a rendezvous in Sun-Earth orbit is also considered. The resultant ΔV’s for each scenario is provided with discussions on various transfer trades, rendezvous considerations, and orbital limitations from the dynamical systems. A Poincare-like mapping of trajectory and rendezvous conditions categorize feasible and optimum transfer approaches, dependent on Sun-Earth orbit mission parameters. The focus of this research addresses questions for upcoming trades regarding servicing options for current and future Sun-Earth L1 and L2 missions. By doing a comprehensive analysis approach (dynamical systems + high fidelity optimization with true operational constraints), this paper will serve as a guide for mission architecture and operational trade considerations.

Maneuver Design↗

A uniformly valid solution for motion about the interior libration point of the perturbed elliptic-restricted problem

Bounded motion about Lagrange collinear libration points is considered for a perturbed elliptic-restricted problem. A practical application is the motion of a satellite near a libration point collinear with the sun and the earth-moon barycenter. Such a system is treated here as an earth-sun-satellite elliptic restricted problem with lunar perturbations. The method of dual time scales is utilized to develop a uniformly valid three-dimensional analytical solution to the satellite's equations of motion. The analytical development applies somewhat generally to that class of four-body problems where the second primary mass is much greater than the first, and the third primary mass is much greater than the second.

Richardson, D. L.↗

Excitation and relaxation of the wobble, precession, and libration of the moon

The rate of meteorite-impact excitation of the free wobble, free precession, and free libration of the moon above a given amplitude is estimated for two crater-size scaling laws and is compared with the rate of damping by tidal and rotational distortion as well as by a possible core-mantle interaction. Criteria for the probable existence and the probable nonexistence of observable amplitudes of the free motions are developed in terms of upper bounds on the damping factor for the various motions and in terms of ranges for the kinematic viscosity of a possible core. It is shown that although observable amplitudes are compatible with reasonable values of the damping factor and kinematic viscosity, other reasonable values could keep the amplitudes below the observable level most of the time. It is found that the free libration is the least likely motion to be observed and that a lunar core with earthlike properties might keep some of the free motions damped, but not all of them. Uncertainties in some of the assumptions used in the analysis are discussed.

Peale, S. J.↗

A lunar density model consistent with topographic, gravitational, librational, and seismic data

A series of models of the lunar interior are derived from topographic, gravitational, librational, and seismic data. The librational parameters and low-degree gravity harmonics result primarily from surface height variations and only secondarily from lateral density variations. The moon departs from isostasy, even for the low-degree harmonics, with a maximum superisostatic stress of 200 bars under the major mascon basins. The mean crustal thicknesses under different physiographic regions are: mascons, 30-35 km; irregular maria, 50-60 km; and highlands, 90-110 km. A possible composition consistent with our model is an anorthositic crust, underlain by a predominantly forsterite upper mantle which grades into a refractory rich lower mantle surrounding a pyrrhotite core.

Bills, B. G.↗

The first libration-point satellite - Mission overview and flight history

On August 12, 1978, a scientific spacecraft called International Sun-Earth Explorer-3 (ISEE-3) was launched towards the interior sun-earth libration point, L1. The spacecraft was placed into a 'halo orbit' around the L1 point on November 20, 1978, thus becoming the first libration-point satellite. During its 100-day transfer trajectory, ISEE-3 lingered in a region where the gravitational effects of the sun and the earth are comparable, leading to some interesting tradeoffs concerning the maneuver strategy for halo-orbit insertion. Following orbit insertion, stationkeeping maneuvers were required to maintain the delicate equilibrium in the halo orbit. Details are presented for all of the velocity change maneuvers that were executed prior to the completion of the first halo orbit on May 14, 1979. Orbit selection, trajectory design, and the scientific objectives of the ISEE-3 mission are also discussed.

Farquhar, R. W.↗

Analysis of solar radiation pressure induced coupled librations of a gravity stabilized axisymmetric satellite

This paper presents an analysis of solar radiation pressure induced coupled librations of gravity stabilized cylindrical spacecraft with a special reference to geostationary communication satellites. The Lagrangian approach is used to obtain the corresponding equations of motion. The solar induced torques are assumed to be free of librational angles and are represented by their Fourier expansion. The response and periodic solutions are obtained through linear and nonlinear analyses, using the method of harmonic balance in the latter case. The stability conditions are obtained using Routh-Hurwitz criteria. To establish the ranges of validity the analytic response is compared with the numerical solution. Finally, values of the system parameters are suggested to make the satellite behave as desired. Among these is a possible approach to subdue the solar induced roll resonance. It is felt that the approximate analysis presented here should significantly reduce the computational efforts involved in the design and stability analysis of the systems.

Shrivastava, S. K.↗

Non-linear stability around the triangular libration points

The configuration space around the triangular libration points in the Earth-Moon system is partitioned according to the stability of the motion. The regions around L4 and L5 are established where particles placed with zero initial velocity will librate. The complexity of the partitioning is revealed.

Mckenzie, R.↗

The free librations of a dissipative moon

It is noted that dissipation in the moon produces a small offset (approximately 0.23 arcsec) of the moon's rotation axis from the plane defined by the ecliptic and lunar orbit normals. Both solid body tidal friction and viscous fluid friction at a core-mantle interface are thought to be plausible mechanisms. The merits of both are discussed, and it is found that solid friction requires a low lunar tidal Q (approximately 28), whereas turbulent fluid friction requires a core with a radius of approximately 330 km to cause the signature observed by lunar laser ranging. Large (approximately 0.4-8.0 arcsec) free librations of the lunar figure have also been detected through laser ranging. Both a very recent impact on the moon and fluid turbulence in the lunar core are considered plausible mechanisms for generating these librations.

Yoder, C. F.↗

On the use of a sunward-libration-point orbiting spacecraft as an IMF monitor for magnetospheric studies

Magnetospheric studies often require knowledge of the orientation of the IMF. In order to test the accuracy of using magnetometer data from a spacecraft orbiting the sunward libration point for this purpose, the angle between the IMF at ISEE 3, when it was positioned around the libration point, and at ISEE 1, orbiting Earth, has been calculated for a data set of two-hour periods covering four months. For each period, a ten-minute average of ISEE 1 data is compared with ten-minute averages of ISEE 3 data at successively lagged intervals. At the lag time equal to the time required for the solar wind to convect from ISEE 3 to ISEE 1, the median angle between the IMF orientation at the two spacecraft is 20 deg, and 80% of the cases have angles less than 38 deg. The results for the angles projected on the y-z plane are essentially the same.

Kelly, T. J.↗

Phobos' gravity field and its influence on its orbit and physical librations

A model describing the physical libration in longitude and latitude for Phobos is derived. The major effect is the well-known longitude variation with the anomalistic orbital period and amplitude. Several additional meter-sized periodic librations in longitude exist. The latitude variation is dominated by the forced precession of Phobos' figure axis with the precession of Phobos' orbital plane. The contribution of Phobos' topography to its gravity field is estimated using the control network model of Duxbury and Callahan (1989).

Borderies, N.↗

Sun-earth libration point trajectories that avoid the solar exclusion zone

Three-dimensional orbits in the restricted three-body problem have been the subject of a number of recent studies. One type of three-dimensional, quasi-periodic orbit that emanates from the general vicinity of the collinear libration points is known as a 'Lissajous' trajectory. Future mission plans include trajectories near the interior libration point. (L1) in the sun-earth system and may consider Lissajous orbits as part of the trajectory design. Such orbits may be constrained, however, to remain beyond the region of the solar disk as viewed from earth. This effort involves the numerical determination of Lissajous trajectories of arbitrary, but predetermined, length that never violate such a constraint as a result of maneuvers directed, in general, perpendicular to the ecliptic plane.

Howell, K. C.↗

Optimal cycling between cislunar and cismartian libration points with reusable nuclear electric transfer vehicles

A cyclical Mars exploration scenario is described which combines the use of libration points in the earth-moon and sun-Mars systems with a pair of reusable nuclear electric propulsion (NEP) transfer vehicles. In this approach, the NEP transfer vehicles are stationed at the cislunar and cismartian libration points, and involves short cislunar point escape and capture spirals. It eliminates any spiral requirements at Mars by utilizing the cismartian point as a transportation node. Chemical/aerobrake vehicles are used to transport humans between earth and the cislunar point as well as between Mars and the cismartian point.

Sponaugle, Steven J.↗