Anticipated orbital perturbations of satellite 1959 delta two
Numerical integration of equations of motion for Explorer VI satellite - lunar, solar, oblateness, and atmospheric drag perturbations
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Numerical integration of equations of motion for Explorer VI satellite - lunar, solar, oblateness, and atmospheric drag perturbations
Semianalytic theory for lunar satellite motion including perturbative effects
Artificial planetary satellites long term orbital evolution under strong perturbations, considering solar and lunar gravitational effects
The behavior of low altitude near-circular lunar orbits is a key design issue for some missions in the proposed Space Exploration Initiative. The lunar gravity field strongly perturbs low altitude orbits, so an effective orbit maintenance strategy is needed. This strategy must contend with the long term orbit evolution due to the zonal gravity field. Two possible orbit control scenarios are passive control using a frozen orbit and active orbit control using maneuvers. A maneuver strategy can be designed which optimizes the propellant required for long term orbit sustenance. The long term requirements dominate the total propellant required for orbit control. Additional propellant may be required to offset the impact of medium period gravity field effects. Careful selection of maneuver times and directions, however, can eliminate any medium period penalty.
OSMEAN is sophisticated program that converts between osculating and mean classical orbital elements. Enables engineer to exploit advantages of each approach for design and planning or orbital trajectories and maneuvers. Converts mean elements to osculating elements or vice-versa. Conversion based on mathematical modeling of all first-order aspherical terrestrial, lunar, and solar gravitational perturbations plus second-order aspherical term based on second-degree central-body zonal perturbation. Written in FORTRAN 77.
Steady magnetic field measurements of magnitude 30 to 100 gamma on the lunar surface impose problems of interpretation when coupled with the nondetectability of a lunar field at 0.4 lunar radius altitude and the limb induced perturbations of the solar wind at the Explorer orbit. The lunar time-varying magnetic field clearly indicates the presence of eddy currents in the lunar interior and permits calculation of an electrical conductivity profile. The problem is complicated by the day-night asymmetry of the moon's electromagnetic environment, the possible presence of the transverse magnetic mode, and the variable wave directions of the driving function. The electrical conductivity is calculated to be low near the surface, rising to a peak of .006/ohm meter at 250 km, dropping steeply inwards to a value of about .00005/ohm meter, and then rising toward the interior. A transition at 250 km depth from a high conductivity to a low conductivity material is inferred, suggesting an olivine-like core at approximately 800 C, although other models are possible.
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.
Analytic formulations for satellite perturbations due to solar radiation pressure and lunar and solar gravitational forces
The Lunar Atmosphere and Dust Environment Explorer (LADEE) is a Lunar science orbiter mission currently under development to address the goals of the National Research Council decadal surveys and the recent "Scientific Context for Exploration of the Moon" (SCEM) [1] report to study the pristine state of the lunar atmosphere and dust environment prior to significant human activities. LADEE will determine the composition of the lunar atmosphere and investigate the processes that control its distribution and variability, including sources, sinks, and surface interactions. LADEE will also determine whether dust is present in the lunar exosphere, and reveal the processes that contribute to its sources and variability. These investigations are relevant to our understanding of surface boundary exospheres and dust processes throughout the solar system, address questions regarding the origin and evolution of lunar volatiles, and have potential implications for future exploration activities. LADEE employs a high heritage science instrument payload including a neutral mass spectrometer, ultraviolet spectrometer, and dust sensor. In addition to the science payloads, LADEE will fly a laser communications system technology demonstration that could provide a building block for future space communications architectures. LADEE is an important component in NASA's portfolio of near-term lunar missions, addressing objectives that are currently not covered by other U.S. or international efforts, and whose observations must be conducted before large-scale human or robotic activities irrevocably perturb the tenuous and fragile lunar atmosphere. LADEE will also demonstrate the effectiveness of a low-cost, rapid-development program utilizing a modular bus design launched on the new Minotaur V launch vehicle. Once proven, this capability could enable future lunar missions in a highly cost constrained environment. This paper describes the LADEE objectives, mission design, and technical approach.
Second order theory for trajectories near lunar libration point based on four body model including sun, earth, moon, and satellite
The orbital evolution of objects at or near geosynchronous orbit (GEO) has been simulated to investigate possible hazards to working geosynchronous satellites. Orbits of both large satellites and small particles have been simulated, subject to perturbations by nonspherical geopotential terms, lunar and solar gravity, and solar radiation pressure. Large satellites in initially circular orbits show an expected cycle of inclination change driven by lunar and solar gravity, but very little altitude change. They thus have little chance of colliding with objects at other altitudes. However, if such a satellite is disrupted, debris can reach thousands of kilometers above or below the initial satellite altitude. Small particles in GEO experience two cycles driven by solar radiation: an expected eccentricity cycle and an inclination cycle not expected. Particles generated by GEO insertion stage solid rocket motors typically hit the earth or escape promptly; a small fraction appear to remain in persistent orbits.
Continued tidal evolution of the earth-moon system will lengthen the day and expand the lunar orbit. Both of these changes increase the present 26,000-year equinoctial precession period. In less than two billion years, this period will become comparable to the approximately 49,000- and 69,000-year periods of important terms describing the precession of the earth's orbit plane due to planetary perturbations. These events occur when the lunar orbital semimajor axis drifts past approximately 66.5 and 68.0 earth radii, respectively, and will be accompanied by large oscillations of the obliquity and severe climatic alterations. The current rate of lunar recession implies that these resonances should have been encountered already, had present conditions been the norm throughout geologic time.
Space agencies are planning missions to the vicinity of the Sun-Earth L sub 2 point, some involving a distributed system of telescope spacecraft, configured in a plane about a hub. An improved understanding is developed of their relative motion. First, the telescope equations of motion are written relative to L sub 2 in the context of the classical circular restricted three-body problem, and expanded in terms of the distance from L sub 2. A basic examination is presented of the spacecraft configuration requirements and effects of small orbit insertion errors. Next, the telescope equations of motion relative to the hub are written and further expanded in terms of the hub-L sub 2 and hub-telescope distances. An analytical solution is developed and a halo telescope orbit investigated, with appropriate initial conditions. Then, the force model is extended to include perturbations to an accuracy of 10 to 20 m, east as additive contributions to the circular restricted problem. Perturbations include Earth's orbital eccentricity, lunar motion, solar radiation pressure, and small thrusting forces. Simulations are presented, along with solution sensitivity to errors in hub position knowledge.
The interplanetary magnetic field is only slightly perturbed by the presence of the moon in the solar wind flow. A statistical study of umbral increases and of penumbral variations was conducted with respect to variation in the solar wind plasma value beta, the distance from the moon, and the selenographic longitude of the limb regions of the lunar surface in the solar wind flow. All lunar wake anomalies show a strong positive correlation with the plasma value beta, while only penumbral increases show a marked variation with distance from the moon. There is no clear correlation of penumbral anomaly occurrence with selenographic longitude of the exposed lunar limb in the solar wind flow.
The interplanetary magnetic field is only slightly perturbed by the presence of the moon in the solar-wind flow. A statistical study of the umbral increases and penumbral decreases and increases was conducted with variation of the solar-wind plasma beta value, the distance from the moon and the selenographic longitude of the limb regions of the lunar surface in the solar-wind flow. All lunar-wake anomalies show a strong positive correlation with the plasma beta value, whereas only penumbral increases show a marked variation with distance from the moon. There is no clear correlation of occurrence of penumbral anomaly with selenographic longitude of the exposed lunar limb in the solar-wind flow.
The spacecraft P1 of the new ARTEMIS (Acceleration, Reconnection, Turbulence, and Electrodynamics of the Moon's Interaction with the Sun) mission passed the lunar wake for the first time on February 13, 2010. We present magnetic field and plasma data of this event and results of 3D hybrid simulations. As the solar wind magnetic field was highly dynamic during the passage, a simulation with stationary solar wind input cannot distinguish whether distortions were caused by these solar wind variations or by the lunar wake; therefore, a dynamic real-time simulation of the flyby has been performed. The input values of this simulation are taken from NASA OMNI data and adapted to the P1 data, resulting in a good agreement between simulation and measurements. Combined with the stationary simulation showing non-transient lunar wake structures, a separation of solar wind and wake effects is achieved. An anisotropy in the magnitude of the plasma bulk flow velocity caused by a non-vanishing magnetic field component parallel to the solar wind flow and perturbations created by counterstreaming ions in the lunar wake are observed in data and simulations. The simulations help to interpret the data granting us the opportunity to examine the entire lunar plasma environment and, thus, extending the possibilities of measurements alone: A comparison of a simulation cross section to theoretical predictions of MHD wave propagation shows that all three basic MHD modes are present in the lunar wake and that their expansion governs the lunar wake refilling process.
Orbital analysis precision improvement requiring second order oblateness and lunar, air drag and tesseral harmonics perturbations
Lunar satellite motion semianalytic solution, considering perturbative effects due to gravitational fields, solar radiation pressure and libration