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The following topics are discussed: (1) the Unified Model of Lunar Translation/Rotation (UMLTR); (2) the effect of figure-figure interactions on lunar physical librations; (3) the effect of translational-rotational coupling on the lunar orbit; and(4) an error analysis for estimating lunar inertias from LURE (Lunar Laser Ranging Experiment) data.
Recent interest in using electrodynamic tethers (EDTs) for orbital maneuvering in Low Earth Orbit (LEO) has prompted the development of the Marshall ElectroDynamic Tether Orbit Propagator (MEDTOP) model. The model is comprised of several modules which address various aspects of EDT propulsion, including calculation of state vectors using a standard orbit propagator (e.g., J2), an atmospheric drag model, realistic ionospheric and magnetic field models, space weather effects, and tether librations. The natural electromotive force (EMF) attained during a radially-aligned conductive tether results in electrons flowing down the tether and accumulating on the lower-altitude spacecraft. The energy that drives this EMF is sourced from the orbital energy of the system; thus, EDTs are often proposed as de-orbiting systems. However, when the current is reversed using satellite charged particle sources, then propulsion is possible. One of the most difficult challenges of the modeling effort is to ascertain the equivalent circuit between the spacecraft and the ionospheric plasma. The present study investigates the use of the NASA Charging Analyzer Program (NASCAP) to calculate currents to and from the tethered satellites and the ionospheric plasma. NASCAP is a sophisticated set of computational tools to model the surface charging of three-dimensional (3D) spacecraft surfaces in a time-varying space environment. The model's surface is tessellated into a collection of facets, and NASCAP calculates currents and potentials for each one. Additionally, NASCAP provides for the construction of one or more nested grids to calculate space potential and time-varying electric fields. This provides for the capability to track individual particles orbits, to model charged particle wakes, and to incorporate external charged particle sources. With this study, we have developed a model of calculating currents incident onto an electrodynamic tethered satellite system, and first results are shown here.
The ESE observational architecture of the future vision is dramatically different from that of today. The vision suggests observations from multiple orbits, collaborating space assets, and even seamless integration of space and other assets. Observations from GEO or from Libration points rather than from LEO suggest spacecraft carrying instruments with large deployable apertures. Minimization of launch costs suggests that these large apertures have long life, be extremely mass and volume efficient, and have low life cycle cost. Another significant challenge associated with high latitude orbits is high precision pointing and control. Finally, networks of spacecraft flying in predetermined constellation will be required either to apply complementary assets to an observation or to extend the virtual aperture beyond that attainable with a single spacecraft. These changes dictate development of new technology on several fronts, which are outlined in this paper. A section on high speed communications will outline requirements and approaches now envisioned. Sensorwebs will be developed from the viewpoint of work already begun for both space and for terrestrial networks. Precision guidance, navigation and control will be addressed from the perspective of precision flying for repeat pass interferometry and extreme pointing stability for advanced altimetry. A separate section will address requirements for distributed systems. Large lightweight deployables will be discussed with an emphasis on inflatable technology and its predicted benefits for large aperture instruments. For each technology area listed, current state-of-the-art, technological approaches for future development, and projected levels of performance are outlined.
The Mercury Laser Altimeter onboard MESSENGER involves unique design elements that deal with the challenges of being in orbit around Mercury. The Mercury Laser Altimeter (MLA) is one of seven instruments on NASA's MErcury Surface, Space ENvironment, GEochemistry, and Ranging (MESSENGER) spacecraft. MESSENGER was launched on 3 August 2004, and entered into orbit about Mercury on 18 March 2011 after a journey through the inner solar system. This involved six planetary flybys, including three of Mercury. MLA is designed to map the topography and landforms of Mercury's surface. It also measures the planet's forced libration (motion about the spin axis), which helps constrain the state of the core. The first science measurements from orbit taken with MLA were made on 29 March 2011 and continue to date. MLA had accumulated about 8.3 million laser ranging measurements to Mercury's surface, as of 31 July 2012, i.e., over six Mercury years (528 Earth days). Although MLA is the third planetary lidar built at the NASA Goddard Space Flight Center (GSFC), MLA must endure a much harsher thermal environment near Mercury than the previous instruments on Mars and Earth satellites. The design of MLA was derived in part from that of the Mars Orbiter Laser Altimeter on Mars Global Surveyor. However, MLA must range over greater distances and often in off-nadir directions from a highly eccentric orbit. In MLA we use a single-mode diode-pumped Nd:YAG (neodymium-doped yttrium aluminum garnet) laser that is highly collimated to maintain a small footprint on the planet. The receiver has both a narrow field of view and a narrow spectral bandwidth to minimize the amount of background light detected from the sunlit hemisphere of Mercury. We achieve the highest possible receiver sensitivity by employing the minimum receiver detection threshold.
The equations of the physical libration of the moon are developed using a representation of the earth-moon orbit as a Kepler ellipse referred to the lunar equator and expanding the lunar potential in terms of these Kepler elements. The Improved Lunar Ephemeris is used to calculate solar perturbations, and a linear integration of all effects arising from lunar gravitational harmonics through the fourth degree is performed. Aside from unobservable constant offsets of the principal axes, the main effects of the higher harmonics on longitude are: 10-sec six-yearly (argument omega), 1.2-sec three-yearly, 0.5-sec annual, and 0.1-sec monthly; on pole direction they are on the order of 0.5-sec six-yearly and 1.0-sec monthly. The higher harmonics must hence be taken into account in analyzing ranging data of 10 cm accuracy.
This guidebook is intended as a tool to facilitate initial analyses of proposed tether applications in space. Topics disscussed include: orbit and orbit transfer equations; orbital perturbations; aerodynamic drag; thermal balance; micrometeoroids; gravity gradient effects; tether control strategies; momentum transfer; orbit transfer by tethered release/rendezvous; impact hazards for tethers; electrodynamic tether principles; and electrodynamic libration control issues.
The James Webb Space Telescope (JWST) is planned to be launched in 2011 to the Sun- Earth L2 libration point. The resultant delta-Vs (dV) from momentum unloads will perturb the orbit and necessitate frequent station-keeping maneuvers. The station-keeping dV budget is highly sensitive to the direction of the resultant dV vector. A simple spacecraft reorientation prior to each momentum unload will allow some control over the direction of the resultant dV vector. For each inertial momentum vector direction, an optimum spacecraft attitude is determined which gives a resultant dV vector that requires the least amount of station-keeping dV. Using this procedure, the station-keeping dV budget for JWST can be reduced by 60%.
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.
Simplified expressions for the poles of Jupiter's Galilean satellites are derived, assuming that the satellites' poles are normal to their orbits. The resulting short trigonometric series depend upon the nodal motions of the satellites and librate about the pole of Jupiter. The precision of the final expressions is better than 0.01 degrees.
Laser technology has been used in planetary exploration for many years but it has only been in the last decade that laser altimeters and ranging systems have been selected as flight instruments alongside cameras, spectrometers, magnetometers, etc. Today we have an active laser system operating at Mars and another destined for the asteroid Eros. A few years ago a laser ranging system on the Clementine mission changed much of our thinking about the moon and in a few years laser altimeters will be on their way to Mercury, and also to Europa. Along with the increased capabilities and reliability of laser systems has came the realization that precision ranging to the surface of planetary bodies from orbiting spacecraft enables more scientific problems to be addressed, including many associated with planetary rotation, librations, and tides. In addition, new Earth-based laser ranging systems working with similar systems on other planetary bodies in an asynchronous transponder mode will be able to make interplanetary ranging measurements at the few cm level and will advance our understanding of solar system dynamics and relativistic physics.
Observations of Enceladus have revealed active jets of material erupting from cracks on its surface. It has been proposed that diurnal tidal stress may open these cracks daily when they experience tensile stresses across them, allowing eruptions to occur. An analysis of the tidal stress on jet source regions, as identified by the triangulation of jet observations, finds that there is a correlation between observations and tensile stress on the cracks. However, not all regions are predicted to be in tension when jets were observed to be active. Enceladus' rotation state, such as a physical libration or obliquity, will affect the diurnal stresses on these cracks, changing when in its orbit they experience tension and compression. We will use observations of jet activity from 2005-2007 to place constraints on rotation states of Enceladus.
Properties of satellite rotation that are observable in principle, include the rotation period, the orientation of the spin axis relative to the orbit plane, precession of the spin axis due to gravitational torques, nonprincipal axis rotation or wobble, and deviations from uniform principle axis rotation or libration. Considerable order is observed in current satellite rotation states, and it is of interest to ascertain how this order came about and why some satellites do not conform to the dominant norm. There is a strong coupling between the spin and orbital motions that is primarily responsible for maintaining the ordered rotation states in most cases, but this coupling is equally responsible for destroying any chance of orderly rotation for Saturn's satellite Hyperion. Understanding the processes which constrain current rotation states as well as those of an evolutionary nature which could have brought the individual satellites to their observed rotation and orbit states allows us to sometimes infer interior properties of some satellite or even of its primary planet, although, attempts to deduce primordial rotation states are usually frustrated. The observed rotational properties of the planetary satellites are summarized, and the understanding of the processes maintaining and those leading to the observed states are outlined. Some of the inferences that can be drawn about intrinsic properties of the bodies themselves are indicated.
ElectroDynamic (ED) Tethers can generate continuous low thrust in a low Earth orbit. An induced current running through the length of the tether reacts with the geomagnetic field to produce thrust. The amount of thrust scales with tether lens!th and current. The International Space Station (ISS) requires periodic reboost to maintain an approximately circular orbit t above the Earth. The baseline reboost method is a traditional bi-propellant rocket thruster and tankage system which must to be refueled via Soyuz / Progress or other launch vehicle. The estimated propellant costs associated with keeping ISS in the designated orbit over a 10-year life have been extremely high. The ED Tether would draw energy from the renewable ISS Solar Array electrical power system. Propulsion requirements for ISS vary depending on solar wind and other conditions. It is projected that a ED Tether could provide the majority of the required reboost thrust for ISS for a nominal solar year. For above nominal solar wind years the ISS would have to use the rocket reboost system, but at a greatly reduced level. Thus resulting in substantial cost savings, via the reduction in the number of Earth-to-orbit launch vehicle flights to the ISS that must bring reboost propellant. However, the purposes of this paper is to further Previous research on an ISS ED Tether and examine the operational and technical issues working against using a ED Tether on ISS. Issues such as Shuttle rendezvous and flight path concerns raise serious safety concerns and restrictions on tether use. Tether issues such as tether librations and off angle thrust raise concerns about impacts to microgravity payloads and the long-term effect on ISS orbital path and inclination. Operational issues such as peak power available to an ED Tether and allowable duty cycle may impose severe restrictions on tether design and ultimately limit the practicality of an ED Tether on ISS. Thus while at first glance the cost numbers appear to be strongly in favor of an ED Tether the limitations imposed by safety, operations and technical concerns may severely undermine the economic model. Possible Solutions to these problems have been investigated and proposed, however some items like off angle thrust are still being actively investigated for an adequate solution.
Flight-mechanics problems associated with large-scale transport of lunar mass to a space colony or manufacturing facility are discussed. The proposed transport method involves launch of payloads from a mass-driver on the lunar surface, onto ballistic trajectories to a passive mass-catcher located near the L2 libration point, with the caught mass subsequently being transported to the colony. Arrival velocities at L2, sensitivities in arrival dispersion due to launch errors, and effects of launch site location are treated, via numerically integrated orbits in the restricted three-body problem. From any launch site it is possible to define a target point reached with zero dispersion due to errors in a selected component of launch velocity. Effects of lunar geometrical librations and of obliquity, as well as the conditions for biasing a trajectory away from L2 so as to reduce stationkeeping costs, are dealt with along with transfer orbits from L2 to the colony. The theory of capture and the theory of resonance lead to a colony orbit, with period approximately two weeks, reached from L2 with velocity increment as low as 9.02 m/sec.
We now believe that while there are about 2000 earth orbit crossing rocks greater than 1 kilometer in diameter, there may be as many as 100,000 or more objects in the 100m size range. Can anything be done about this fundamental existence question facing us? The answer is a resounding yes! We have the technology to prevent collisions. By using an intelligent combination of Earth and space based sensors coupled with an infrastructure of high-energy laser stations and other secondary mitigation options, we can deflect inbound asteroids, meteoroids, and comets and prevent them from striking the Earth. This can be accomplished by irradiating the surface of an inbound rock with sufficiently intense pulses so that ablation occurs. This ablation acts as a small rocket incrementally changing the shape of the rock's orbit around the Sun. One-kilometer size rocks can be moved sufficiently in a month while smaller rocks may be moved in a shorter time span.We recommend that the World's space objectives be immediately reprioritized to start us moving quickly towards a multiple option defense capability. While lasers should be the primary approach, all mitigation options depend on robust early warning, detection, and tracking resources to find objects sufficiently prior to Earth orbit passage in time to allow mitigation. Infrastructure options should include ground, LEO, GEO, Lunar, and libration point laser and sensor stations for providing early warning, tracking, and deflection. Other options should include space interceptors that will carry both laser and nuclear ablators for close range work. Response options must be developed to deal with the consequences of an impact should we move too slowly.
This slide presentation reviews the near term future of human space exploration in terms of possible mission scenarios, propulsion technologies, orbital dynamics that lead to Low-Energy Transfer from Earth-Moon LI to Solar Libration Points and Return Potential Staging Point for Human Mars Missions. It also examines the required evolution of mission architecture, solar electric propulsion concept, vehicle concepts for future Mars missions, and an overview of a Mars Mission, Also in this presentation are pictures of several historic personages and occasions, and a view of a Mars Meteorite (i.e., ALH84001.0)
In the planar circular restricted three-body problem, the evolution of near-commensurable orbits is studied under change in the mass ratio, mu. The evolution involves preservation of two adiabatic invariants. Transition from circulation to libration may occur; such transitions are of two types. Type I transition occurs when the evolutionary track in phase space passes through near-zero eccentricity; as in the ordinary case (no transition), pre- and post-evolutionary states are linked by solution of a two-point boundary-value problem. Type II transition occurs when the evolutionary track encounters an unstable phase equilibrium or periodic orbit. There is then a discontinuous change in one adiabatic invariant, and pre- and post-evolutionary states are linked by solution of a three-point boundary-value problem. No evolutionary track can encounter a stable phase equilibrium, but the class of all stable phase equilibria is mapped into itself under mu change.
One of the most intriguing scientific questions about Mercury is whether the planet possesses a liquid core. One way that this can be ascertained is through the measurement of the longitudinal libration of Mercury about its rotation axis. The MESSENGER (Mercury Surface, Space, Environment, Geochemistry, and Ranging) mission to Mercury will attempt this measurement by deriving the rotation of the planet from remotely sensed observations of the Mercury gravity field and the planet's shape. For a fully fluid core the libration is expected to be an approximately 350-m-amplitude oscillation (at the equator) about the mean rotation of the planet. Thus, the shape of the planet undergoes a librational oscillation in the same way that features on the surface participate in the motion. In this sense altimetric topography can be considered analogous to imaging, with the important exception that for altimetry, the long wavelengths corresponding to low degrees and orders in a spherical harmonic expansion, can be precisely determined from orbital measurements. The rotation of the planet thus introduces a time dependence of the topographic image in an inertial (i.e. fixed) reference frame and the libration is a variation in the planetary rotation rate, manifest as an oscillation of the topographic image. Similarly, gravity measures the distribution of mass within a planet and as such can be viewed as providing a vertically integrated 'image' of the internal density structure. For a librating planet the gravitational field will also reveal a variation in the rotation rate, manifest as an oscillation of the field with respect to an inertial reference frame. While the long-wavelength gravity field contains contributions from the radial distribution of mass with depth, the long wavelength terms are most sensitive to the mass distribution of the deep interior. Thus, both the topography and the gravity independently can be used to determine the (irregular) rotation of a planet, although the topographical method measures the rotation of the crust while the gravity measures the rotation of the distributed mass, and these are not necessarily identical. For example, for a planet that contains a fluid outer core that is effectively decoupled from the mantle the gravity field will not librate in the manner of a solid body. The libration obtained from the variable rotation of the gravity field will represent a combination of contributions due to a librating mantle and a differentially rotating fluid core. Differential rotation of the Earth's inner core had been theoretically predicted from three dimensional geodynamical models and subsequently reported from seismic observations. A difference between the libration of the lithosphere as determined from altimetry and the deep interior as determined from gravity, if it could be detected, might provide further insight into the nature of core-mantle coupling. Additional information is contained in the original extended abstract.