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Some higher order analyses of earth and lunar orbiters
The accurate modelling of the translational behavior of a drag-free satellite in an almost circular near-earth orbit is investigated. All short and long period position fluctuations in the satellite's coordinates down to 1 m are determined. The general zonal and tesseral harmonic effects are considered as well as lunar and solar effects. A noncanonical approach is followed. A mean orbital plane is chosen so that no short period out-of-plane fluctuations greater than second order occur. Short period radial and cross-track fluctuations and in-track fluctuations are computed. Long period and secular rates of the mean elements which define the slowly varying plane of reference are determined to third order in the small quantities. The equations of motion are integrated analytically away from critical inclination and tesseral resonance. The resonant situation of a sun-synchronous orbit is discussed as a special case. The long-period behavior of a lunar orbiter is also considered, including the effects due to the inclination of the earth's apparent orbit about the moon and those described by Cassini laws on the equations of motion. Both resonant and nonresonant low orbits, and high orbits are discussed.
Update on the Wide-field Infrared Survey Explorer (WISE)
The Wide-field Infrared Survey Explorer (WISE), a NASA MIDEX mission, will survey the entire sky in four bands from 3.3 to 23 microns with a sensitivity 1000 times greater than the IRAS survey. The WISE survey will extend the Two Micron All Sky Survey into the thermal infrared and will provide an important catalog for the James Webb Space Telescope. Using 1024(sup 2) HgCdTe and Si:As arrays at 3.3, 4.7, 12 and 23 microns, WISE will find the most luminous galaxies in the universe, the closest stars to the Sun, and it will detect most of the main belt asteroids larger than 3 km. The single WISE instrument consists of a 40 cm diamond-turned aluminum afocal telescope, a two-stage solid hydrogen cryostat, a scan mirror mechanism, and reimaging optics giving 5 resolution (full-width-half-maximum). The use of dichroics and beamsplitters allows four color images of a 47' x47' field of view to be taken every 8.8 seconds, synchronized with the orbital motion to provide total sky coverage with overlap between revolutions. WISE will be placed into a Sun-synchronous polar orbit on a Delta 7320-10 launch vehicle. The WISE survey approach is simple and efficient. The three-axis-stabilized spacecraft rotates at a constant rate while the scan mirror freezes the telescope line of sight during each exposure. WISE has completed its mission Preliminary Design Review and its NASA Confirmation Review, and the project is awaiting confirmation from NASA to proceed to the Critical Design phase. Much of the payload hardware is now complete, and assembly of the payload will occur over the next year. WISE is scheduled to launch in late 2009; the project web site can be found at www.wise.ssl.berkeley.edu.
NASA’s Atmosphere Observing System (AOS), From A Precipitation Perspective
NASA is developing the Atmosphere Observing System (AOS) mission as part of its Earth System Observatory (ESO) in response to priorities identified in the 2017 Earth Science Decadal Survey. AOS addresses the Decadal Survey’s call for missions measuring the targeted observables “clouds, convection, and precipitation”; “aerosol and cloud radiative properties”, and “aerosol vertical profiles”. AOS is currently in Phase A, the concept and technology development phase, with plans for satellite launches in the late 2020’s and early 2030’s, and suborbital measurements to include field campaigns after those satellite launches. Key precipitation-related instrumentation includes Doppler radars capable of measuring clouds and precipitation, and passive microwave radiometers with channels between 89-700 GHz. Other instrumentation includes dual-wavelength backscatter lidars, a multi-wavelength and multi-angle polarimeter, a far infrared imaging radiometer, and aerosol and moisture limb sounders that will contribute to studies of coupled aerosol-cloud-precipitation processes. From the perspective of precipitation science, a Ku-band Doppler radar in a 55° inclined orbit provided by JAXA will continue the heritage of precipitation radar measurements made by the Tropical Rainfall Measuring Mission (TRMM) and Global Precipitation Mission (GPM), while adding information about Doppler-derived particle vertical motions. With assumptions about particle terminal velocities, the Doppler measurements will enable estimates of the vertical air motion in storms. A higher frequency (W and/or Ka band) radar on a satellite in a polar sun-synchronous orbit will add similar information with greater sensitivity to clouds and to light precipitation. Passive microwave radiometers for AOS will be less capable than those from TRMM and GPM from a precipitation-measurement perspective, but more capable of adding information about cloud processes. Synergies among these and other instruments are expected to advance process-level understanding of aerosols, clouds, and precipitation.
Effect of environmental torques on short-term attitude prediction for a rolling-wheel spacecraft in a sun-synchronous orbit
A numerical evaluation and an analysis of the effects of environmental disturbance torques on the attitude of a hexagonal cylinder rolling wheel spacecraft were performed. The resulting perturbations caused by five such torques were found to be very small and exhibited linearity such that linearized equations of motion yielded accurate results over short periods and the separate perturbations contributed by each torque were additive in the sense of superposition. Linearity of the torque perturbations was not affected by moderate system design changes and persisted for torque-to-angular momentum ratios up to 100 times the nominal expected value. As these conditions include many possible applications, similar linear behavior might be anticipated for other rolling-wheel spacecraft.
Landsat at 45: How it Changed the Way We See the Earth
On October 24, 1946, more than 10 years before the launch of the first artificial satellite Sputnik, scientists at the White Sands Missile Range in New Mexico placed a camera on top of a captured German V-2 ballistic missile. As the rocket flew to an altitude of about 65 miles - just above the generally recognized border of outer space - the 35-millimeter motion picture camera snapped a frame every one and a half seconds. Minutes later, the missile came crashing back down and slammed into the ground at more than 340 mph, but the film survived and gave us our first glimpse of Earth from space. Earth Resources Technology Satellite aka Landsat It was images like those first grainy black and white pictures and later those taken by America's first astronauts in the 1960's that inspired the development of the Earth Resources Technology Satellite (ERTS). From the unique vantage point of space, we could now observe Earth using a variety of different instruments to monitor changes over time. The ERTS-1 satellite, wisely renamed Landsat-1, was launched aboard a Delta rocket on July 23, 1972, into a Sun-synchronous polar orbit at an altitude of about 560 miles. In this unique orbit, Landsat could observe the same point on the Earth every 18 days, always with the same solar illumination, allowing for precise monitoring of changes on the ground over time. Landsat-1, derived from the highly successful Nimbus weather satellites, carried two instruments that allowed it to take images not only in visible light but also in infrared, well-suited to track changes in vegetation over time. Designed to last only one year, Landsat-1 actually operated for nearly three years, by which time it had been joined in space by Landsat-2, a near identical copy of the original. Since then, ever more sophisticated instruments were flown aboard Landsat-3 through -8, with Landsat-9 planned for launch in 2020, acquiring millions of images of Earth over more than four decades. At first, images from Landsat were processed by NASA and hardcopies sold to users for a fee, a somewhat tedious process. Since 2008, images have been made available to all interested users by the US Geological Survey (USGS) at no cost via the Internet in near real time. So, how can Landsat help? In short, Landsat looks. And looks. And proves Yogi right. Space-based images from Landsat and other similar satellites offer a unique and critical capability to observe land use over time by providing repetitive observations of the Earth otherwise unavailable. The data provided by the images can be used by scientists and politicians to inform wise decisions in areas such as agriculture, climate, ecosystems and biodiversity, energy, forest management, human health, fire, natural disasters, urban growth and water management. This overview article doesn't allow for examples from each of these disciplines, but details can be found at the following website: https://landsat.gsfc.nasa.gov/how_landsat_helps/. One third of the US economy is influenced by climate, weather and natural hazards, providing strong economic incentives to sustain a healthy space-based Earth observation program. One example, however, may be illustrative of how Landsat and other space-based observations can be helpful in monitoring and documenting some effects of global climate change. It had been noted since the 1970's that permafrost in subarctic areas like Siberia was melting at an accelerating rate. It also became apparent that this led to the formation of hundreds of melt lakes and the liberation of large quantities of methane, a gas that in the short-term has more potent greenhouse effects than carbon dioxide. The methane turned the water in these lakes blue, making them easy to track over time by satellite. Additionally, the newly released methane has been carbon dated to tens of thousands of years ago, meaning that it had remained frozen since the last Ice Age and therefore hadn't been accounted for in models of the Earth's overall carbon balance. Release of sufficient methane by an increasingly warming climate could actually cause a positive feedback loop in global warming, melting more permafrost and releasing yet more methane. Further monitoring by Landsat and other platforms will reveal whether this process is reversible or whether we've passed the tipping point. In addition to the highly successful Landsat series of satellites, NASA and other agencies such as the National Oceanic and Atmospheric Administration (NOAA) operate a fleet of other Earth observing platforms, many with more specific research goals such as monitoring sea ice levels or atmospheric carbon content. Several instruments aboard the International Space Station also contribute to this overall effort to better understand short- and long-term changes to the Earth. Many of these missions are guided by the 2009 Decadal Survey published by the National Research Council of the National Academy of Sciences. Europe, Russia and China all see the value of space-based Earth observation by deploying their own fleet of satellites.
Development of a Nonlinear Probability of Collision Tool for the Earth Observing System
The Earth Observing System (EOS) spacecraft Terra, Aqua, and Aura fly in constellation with several other spacecraft in 705-kilometer mean altitude sun-synchronous orbits. All three spacecraft are operated by the Earth Science Mission Operations (ESMO) Project at Goddard Space Flight Center (GSFC). In 2004, the ESMO project began assessing the probability of collision of the EOS spacecraft with other space objects. In addition to conjunctions with high relative velocities, the collision assessment method for the EOS spacecraft must address conjunctions with low relative velocities during potential collisions between constellation members. Probability of Collision algorithms that are based on assumptions of high relative velocities and linear relative trajectories are not suitable for these situations; therefore an algorithm for handling the nonlinear relative trajectories was developed. This paper describes this algorithm and presents results from its validation for operational use. The probability of collision is typically calculated by integrating a Gaussian probability distribution over the volume swept out by a sphere representing the size of the space objects involved in the conjunction. This sphere is defined as the Hard Body Radius. With the assumption of linear relative trajectories, this volume is a cylinder, which translates into simple limits of integration for the probability calculation. For the case of nonlinear relative trajectories, the volume becomes a complex geometry. However, with an appropriate choice of coordinate systems, the new algorithm breaks down the complex geometry into a series of simple cylinders that have simple limits of integration. This nonlinear algorithm will be discussed in detail in the paper. The nonlinear Probability of Collision algorithm was first verified by showing that, when used in high relative velocity cases, it yields similar answers to existing high relative velocity linear relative trajectory algorithms. The comparison with the existing high velocity/linear theory will also be used to determine at what relative velocity the analysis should use the new nonlinear theory in place of the existing linear theory. The nonlinear algorithm was also compared to a known exact solution for the probability of collision between two objects when the relative motion is strictly circular and the error covariance is spherically symmetric. Figure I shows preliminary results from this comparison by plotting the probabilities calculated from the new algorithm and those from the exact solution versus the Hard Body Radius to Covariance ratio. These results show about 5% error when the Hard Body Radius is equal to one half the spherical covariance magnitude. The algorithm was then combined with a high fidelity orbit state and error covariance propagator into a useful tool for analyzing low relative velocity nonlinear relative trajectories. The high fidelity propagator is capable of using atmospheric drag, central body gravitational, solar radiation, and third body forces to provide accurate prediction of the relative trajectories and covariance evolution. The covariance propagator also includes a process noise model to ensure realistic evolutions of the error covariance. This paper will describe the integration of the nonlinear probability algorithm and the propagators into a useful collision assessment tool. Finally, a hypothetical case study involving a low relative velocity conjunction between members of the Earth Observation System constellation will be presented.
Doubly-periodic orbits in the Sun-Earth-Moon system
A series of periodic orbits in the Earth-Moon circular restricted problem of three bodies was found which is ideally suited for exploring the Earth's geomagnetic tail. The mean apsidal motion of the basic highly elliptical Earth orbit was maintained at about one degree per day by a sequence of lunar swingbys, keeping the apogees in the anti-Sun direction. The orbits were periodic in reference frames rotating at both lunar and solar rates. Apogee distances were alternately raised and lowered by the lunar swingby maneuvers. Several categories of these Sun-synchronous double lunar swingby orbits were identified. The strength and flexibility of this trajectory concept was demonstrated with real world simulations.
Comments on SEE: Comparative Advantages and and Experimental Consequences
The Satellite Energy Exchange experiment measures the periodic, near-miss encounters between a sheppard satellite and a small test body (satellite) in approximately the same orbit about a primary. Several important experimental requirements have been chosen to enhance capabilities: (a) The satellite be flown in a sun-synchronous orbit at an altitude of about 1350 Km, (b) Passive temperature system stabilized by spacecraft axial rotation with sunshade baffles at the end of the spacecraft, (c) Test bodies with different material composition be available for experiments, (d) The containment spacecraft fly about the sheppard mass in a zero-g environment whereas the test bodies, experience average zero-g environment over an orbital period, (e) Primary attitude and station-keeping uses magnetic field alignment plus micro-Newton thrusters such as Field Emission Electric Propulsion, and (f) Very low power (nW) laser tracking systems minimize impulse delivered to test bodies. With the above conditions, SEE has the capabilities: (1) Long duration (several years life-time) flight experiment (2) Long-term, active (with historical time record), self-calibration of satellite mass distribution (capsule geodesy) over lifetime of the spacecraft. (3) Novel passive thermal stabilization systems designed to attain cryogenic temperatures around 78K. (4) Novel spacecraft stabilization systems. (5) Ability to measure G to 1 part in 10(exp 6-7) depending on ultimate duration of experiment. (6) Ability to place limits on both temporal and spacial variations on G. (7) Ability to set experimental limits on the Post Newtonian parameters (PPN) alpha(2) and zeta(2). (8) Ability to measure (or place limits on) the non Einsteinian eccentricity of the Earth-Sun system (and the parameter alpha(1)) for long duration flight. (9) Ability to measure Delta((dot)-G)/G to 1 part in 10(exp 12-13). The MiniSTEP, competes in a limited way with Project SEE. It is designed to improve the measurement of the equivalence principle by seven orders of magnitude using active, low temperature (1.8 K) cooling for SQUID based, differential superconducting circuits. The experiment consists of a small cylinder concentrically located within a larger cylinder at its null gravitational point. The satellite is operated in zero-g mode using four differential accelerometers consisting to two test bodies of different material composition. The SQUIDS are needed to measure test body motion to precisions of 10(exp -18) over a four orbit period. The entire satellite moves in a very precise zero-g mode since the accelerometers are rigidly attached to the satellite. This limits the experiment to an approximately six month due to limitations on helium storage used in cryogenic cooling and thrust control to maintain the zero-g operation.