A simplified explicit guidance scheme for orbital injection.
Onboard computer equations for rocket vehicle guidance to elliptical orbit, discussing iteration absence from computations and digital simulation results
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Onboard computer equations for rocket vehicle guidance to elliptical orbit, discussing iteration absence from computations and digital simulation results
Onboard computer equations for rocket vehicle guidance to elliptical orbit, discussing iteration absence from computations and digital simulation results
Moderately elliptic reference orbit perturbed motion, applying linearized perturbation equations for circular orbit
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The satellites of Uranus all have significant non-zero eccentricities and in the case of Miranda a significant inclination as well. The Voyager 2 encounter with Uranus in January 1986, provided more accurate estimates of the masses and sizes of the satellites. Orbital history and possible tidal heating were reexamined by using the Voyager data. The relevant orbital dynamics equations are described.
The spacecraft and payloads of the Space Station Polar Platform program are described in a brief overview. Present plans call for one platform in a descending morning-equator-crossing orbit at 824 km and two or three platforms in ascending afternoon-crossing orbits at 542-824 km. The components of the NASA Earth Observing System (EOS) and NOAA payloads are listed in tables and briefly characterized, and data-distribution requirements and the mission development schedule are discussed. A drawing of the platform, a graph showing the spectral coverage of the EOS instruments, and a glossary of acronyms are provided.
A generic planar 3 degree of freedom simulation was developed that supports hardware in the loop simulations, guidance and control analysis, and can directly generate flight software. This simulation was developed in a small amount of time utilizing rapid prototyping techniques. The approach taken to develop this simulation tool, the benefits seen using this approach to development, and on-going efforts to improve and extend this capability are described. The simulation is composed of 3 major elements: (1) Docker dynamics model, (2) Dockee dynamics model, and (3) Docker Control System. The docker and dockee models are based on simple planar orbital dynamics equations using a spherical earth gravity model. The docker control system is based on a phase plane approach to error correction.
An analysis of land surface microwave emission time series shows that the characteristic diurnal signature associated with subsurface emission in sandy deserts carry over to arid and semi-arid region worldwide. Prior work found that diurnal variation of Special Sensor Microwave/Imager (SSM/I) brightness temperatures in deserts was small relative to International Satellite Cloud Climatology Project land surface temperature (LST) variation and that the difference varied with surface type and was largest in sand sea regions. Here we find more widespread subsurface emission effects in Advanced Microwave Scanning Radiometer-EOS (AMSR-E) measurements. The AMSR-E orbit has equator crossing times near 01:30 and 13 :30 local time, resulting in sampling when near-surface temperature gradients are likely to be large and amplifying the influence of emission depth on effective emitting temperature relative to other factors. AMSR-E measurements are also temporally coincident with Moderate Resolution Imaging Spectroradiometer (MODIS) LST measurements, eliminating time lag as a source of LST uncertainty and reducing LST errors due to undetected clouds. This paper presents monthly global emissivity and emission depth index retrievals for 2003 at 11, 19, 37, and 89 GHz from AMSR-E, MODIS, and SSM/I time series data. Retrieval model fit error, stability, self-consistency, and land surface modeling results provide evidence for the validity of the subsurface emission hypothesis and the retrieval approach. An analysis of emission depth index, emissivity, precipitation, and vegetation index seasonal trends in northern and southern Africa suggests that changes in the emission depth index may be tied to changes in land surface moisture and vegetation conditions
NASA’s Orbital Debris Program Office (ODPO) and Hypervelocity Impact Technology (HVIT) team have coordinated to better understand the risks to upper stages and spacecraft from non-spherical orbital debris. It is well understood that fragmentation (collision or explosion) events in orbit produce fragments of various materials, sizes, and shapes. To further characterize these parameters, the ODPO is developing the next-generation Orbital Debris Engineering Model (ORDEM) version 4.0 to include orbital debris shape distributions. Ground-based assets, such as radar and optical sensors, can provide size estimates and some insight into material based on radar return or optical filter photometry/spectroscopy, respectively. Characterizing an object’s shape requires more laboratory analyses to infer how shape affects these measurements. More importantly, in addition to size and material/density, the shape of fragments in orbit will alter the ballistic limit equations used in orbital debris risk assessments with NASA’s Bumper Code. The ODPO plans to release ORDEM 4.0 in the coming years. Performing ground-based laboratory impact tests on high-fidelity spacecraft mockups provides the means to directly measure size, mass, material/density, and shape of fragments, all key parameters needed to characterize real-world break up events. The DebriSat test, the results of which are provided, showcases the details of this type of experiment. The goal of this collaborative research between the ODPO and the HVIT team is to include a shape parameter in the environmental and breakup models used to assess risk for various space structures. This paper examines ground-based laboratory impact tests and the associated fragment shape categories. Provided these defined shapes, the approach is simplified by assuming a right circular cylinder (RCC) approximation with varying length-to-diameter ratios. Highlights of impact tests conducted by the HVIT team using non-spherical projectiles based on the RCC approximation are presented. Hydrocode simulations have also been performed to expand on the complexity of variations with non-spherical projectiles. Lastly, ray-tracing simulations of various RCCs of known material are provided to support the ongoing research on optical reflectance distributions with known shapes and to highlight how this may modify the current optical size estimation model. The status and plan forward are outlined for NASA's orbital debris shape effect investigation using a multidisciplinary approach by the ODPO and the HVIT team.
NASA’s Orbital Debris Program Office (ODPO) and Hypervelocity Impact Technology (HVIT) team have coordinated to better understand the risks to upper stages and spacecraft from non-spherical orbital debris. It is well understood that fragmentation (collision or explosion) events in orbit produce fragments of various materials, sizes, and shapes. To further characterize these parameters, the ODPO is developing the next-generation Orbital Debris Engineering Model (ORDEM) version 4.0 to include orbital debris shape distributions. Ground-based assets, such as radar and optical sensors, can provide size estimates and some insight into material based on radar return or optical filter photometry/spectroscopy, respectively. Characterizing an object’s shape requires more laboratory analyses to infer how shape affects these measurements. More importantly, in addition to size and material/density, the shape of fragments in orbit will alter the ballistic limit equations used in orbital debris risk assessments with NASA’s Bumper Code. The ODPO plans to release ORDEM 4.0 in the coming years. Performing ground-based laboratory impact tests on high-fidelity spacecraft mockups provides the means to directly measure size, mass, material/density, and shape of fragments, all key parameters needed to characterize real-world break up events. The DebriSat test, the results of which are provided, showcases the details of this type of experiment. The goal of this collaborative research between the ODPO and the HVIT team is to include a shape parameter in the environmental and breakup models used to assess risk for various space structures. This paper examines ground-based laboratory impact tests and the associated fragment shape categories. Provided these defined shapes, the approach is simplified by assuming a right circular cylinder (RCC) approximation with varying length-to-diameter ratios. Highlights of impact tests conducted by the HVIT team using non-spherical projectiles based on the RCC approximation are presented. Hydrocode simulations have also been performed to expand on the complexity of variations with non-spherical projectiles. Lastly, ray-tracing simulations of various RCCs of known material are provided to support the ongoing research on optical reflectance distributions with known shapes and to highlight how this may modify the current optical size estimation model. The status and plan forward are outlined for NASA's orbital debris shape effect investigation using a multidisciplinary approach by the ODPO and the HVIT team.
An analytical derivation of frozen orbit eccentricities and their location over the range of possible orbital inclinations in the J2 + J3 problem is presented. A gravitational field with only J2 and J3 terms is considered, because the equation defining frozen orbits in this field is an algebraic equation of the third order and an analytical formula for roots of this equation exists. An equation for the frozen orbit eccentricity is derived in a convenient form using only two independent parameters: the inclination and a parameter which is the product of the ratio of the radius of the central body to the orbital semimajor axis and the ratio of the J2 and J3 coefficients. The equation is solved, and, on the basis of its roots, frozen orbits in the J2 + J3 problem are classified.
Gauss' method for solving Kepler's equation is extended to arbitrary epochs and orbital eccentricities. Although originally developed for near parabolic orbits in the vicinity of pericenter, a generalization of the method leads to a highly efficient algorithm which compares favorably to other methods in current use. A key virtue of the technique is that convergence is obtained by a method of successive substitutions with an initial approximation that is independent of the orbital parameters. The equations of the algorithm are universal, i.e., independent of the nature of the orbit whether elliptic, hyperbolic, parabolic or rectilinear.
The equations of celestial mechanics that govern the temporal rates of change of orbital elements are completely derived using elementary dynamics and proceeding only from Newton's equation and its solution. Two orbital equations and the four most meaningful orbital elements - semimajor axis, eccentricity, inclination, and longitude of pericenter - are written in terms of the orbital energy (E) and angular momentum (H) per unit mass. The six resulting equations are differentiated with respect to time to see the effect on the orbital elements of small changes in E and H. The usual perturbation equations in terms of disturbing-force components are then derived by computing the manner in which perturbing forces change E and H. The results are applied in a qualitative discussion of the orbital evolution of particles in nonspherical gravitational fields, through atmospheres, and under the action of tides.
A well-known hazard associated with exposure to the space environment is the risk of failure due to an impact from a micrometeoroid and orbital debris (MMOD) particle. As NASA prepares to return astronauts to the moon with the Artemis program, the next generation of spacesuit is in development to support future extravehicular activities (EVAs.) An MMOD impact to the spacesuit is of great concern as a large leak could prevent an astronaut from safely reaching an airlock in time resulting in a loss of life. The exploration extravehicular mobility unit (xEMU) must meet MMOD requirements for multiple environments including those in low earth orbit (LEO) as well as the meteoroid and secondary lunar regolith ejecta environments found on the lunar surface. The subject of this paper is an internal xEMU configuration design developed by NASA Johnson Space Center (JSC) personnel. This paper will expand on the hypervelocity impact (HVI) testing and ballistic limit equation (BLE) definition work that was partially presented at the 2nd International Orbital De-bris (IOC-II) Conference held in Sugar Land, TX in December 2023. The xEMU shares similarities with the legacy Extravehicular Mobility Unit (EMU) spacesuit that is currently used for ISS EVAs, however differences in the layup (e.g., materials, thicknesses, and layers) of the fabric environmental protection garment (EPG), portable life support system (xPLSS) and helmet required an extensive test program to determine ballistic performance. Over 100 hypervelocity impact (HVI) tests were performed by the NASA/JSC HVIT and White Sands Test Facility (WSTF) teams on the xEMU EPG, xPLSS and helmet to generate ballistic limit equations (BLEs) for MMOD impacts. Additionally, over 50 low speed tests (< 1km/s) were performed by the NASA/JSC HVIT and Southwest Research Institute (SwRI) teams on the xEMU EPG, xPLSS and helmet to generate BLEs for lunar ejecta impacts. Post testing, ballistic limit equations used to define the performance of the various regions on the xEMU spacesuit were developed from a generic set of BLEs. The HVI and low speed testing was performed to establish a physical basis for the equations with the co-efficients and exponents of the generic BLEs adjusted to fit the test data. The xEMU BLEs were added to the NASA/JSC software application used for space-craft MMOD risk assessments (BUMPER-3). A finite element model (FEM) of the xEMU spacesuit, which defines the size and shape of the spacesuit as well as the locations of the various shielding configurations, was created based on a solid model provided by the xEMU program office. Using the FEM file and added xEMU BLEs, BUMPER-3 assessments of the xEMU spacesuit for probability of no penetration (PNP) were performed. For the LEO assessment of a typical ISS EVA, the orbital debris and meteoroids environments were defined using the latest engineering models, ORDEM 3.2 and MEM-3 respectively. The lunar sur-face assessment again used the MEM-3 engineering model to define the meteoroid environ-ment along with the current released lunar surface ejecta model, NASA SP-8013 (developed during the Apollo Program). The Space Team in the Natural Environments Branch at Mar-shall Space Flight Center (MSFC) will soon release the new Lunar Meteoroid Ejecta Engineering Model (LMEEM), at which time the xEMU lunar surface EVA will be reassessed. Assessment of the MMOD risk for an 8-hour, 2-person EVA in both LEO and on the lunar surface showed that the xEMU spacesuit meets the program technical requirement of 1 in 2500 failure odds. Similar to the legacy EMU spacesuit, the majority of the MMOD risk (96% of the LEO EVA risk and 99% of the lunar surface EVA risk) is concentrated in regions of xEMU that are comprised primarily of softgoods (arms, legs, and gloves) rather than the hardgoods (xPLSS, hard upper torso and helmet).
The problem of a weak gravitational wave impinging upon a nonrelativistic bound system of two point masses is considered. The geodesic equation for each mass is expanded in terms of two small parameters, v/c and dimensionless wave amplitude, in a manner similar to the post-Newtonian expansion; the geodesic equations are resolved into orbital and center-of-mass equations of motion. The effect of the wave on the orbit is determined by using Lagrange's planetary equations to calculate the time evolution of the orbital elements. The gauge properties of the solutions and, in particular, the gauge invariance of the secular effects are discussed.
Numerical integration of equations for time rate change of lunar satellite orbits for Apollo project
The Moderate Resolution Imaging Spectroradiometer (MODIS) on the Earth Observing System (EOS) Terra Mission began to produce data in February 2000. The EOS Aqua mission was launched successfully May 4,2002 with another MODIS on it and "first light" observations occurred on June 24,2002. The Terra MODIS is in a sun-synchronous orbit going north to south in the daylight portion of the orbit crossing the equator at about 1030 hours local time. The Aqua spacecraft operates in a sun-synchronous orbit going south to north in the daylight portion of the orbit crossing the equator at approximately 1330 hours local time. The spacecraft, instrument, and data systems for both MODIS instruments are performing well and are producing a wide variety of data products useful for scientific and applications studies in relatively consistent fashion extending from November 2000 to the present. Within the approximately 40 MODIS data products, several are new and represent powerful and exciting capabilities such the ability to provide observations over the globe of fire occurrences, microphysical properties of clouds and sun-stimulated fluorescence from phytoplankton in the surface waters of the ocean. The remainder of the MODIS products exceeds or, at a minimum, matches the capabilities of products from heritage sensors such as, for example, the Advanced Very High Resolution Radiometer (AVHRR). Efforts are underway to provide data sets for the greater Earth science community and to improve access to these products at the various Distributed Active Archive Centers (DAAC's) or through Direct Broadcast (DB) stations.
All the equations involved in extending the PS phi solution to include the long periodic and second order secular effects of the zonal harmonics are presented. Topics covered include DSphi elements and relations for their conconical transformation into the PS phi elements; the solution algorithm based on the Von Zeipel method; and the elimination of long periodic terms and analytical integration of primed variables. The equations were entered into the ASOP program, checked out, and verified. Comparisons with numerical integrations show the long period theory to be accurate within several meters after 800 revolutions.