Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “ORBIT EQUATION”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 109 records · Page 6
All sourcesNASA NTRSDOE OSTI
NASA NTRSDate not supplied

Micrometeoroid and Orbital Debris (MMOD) Testing, Ballistic Limit Equation Definition and Risk Assessment of the Exploration Extravehicular Mobility Unit (XEMU)

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 MMOD risk assessment of the internal xEMU configuration design developed by NASA Johnson Space Center (JSC) personnel. 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.

Micrometeoroid↗
NASA NTRS1986

Linear stability analysis of the Vlasov-Poisson equations in high density plasmas in the presence of crossed fields and density gradients

The equations for the single-particle orbits in a nonneutral high density plasma in the presence of inhomogeneous crossed fields are obtained. Using these orbits, the linearized Vlasov equation is solved as an expansion in the orbital radii in the presence of inhomogeneities and density gradients. A model distribution function is introduced whose cold-fluid limit is exactly the same as that used in many previous studies of the cold-fluid equations. This model function is used to reduce the linearized Vlasov-Poisson equations to a second-order ordinary differential equation for the linearized electrostatic potential whose eigenvalue is the perturbation frequency.

Kaup, D. J.↗
NASA NTRS1987

Development of OPTIMOD - The new Space Shuttle Orbiter/Payload Thermal Integration Model

The development of the Orbiter/Payload Thermal Integration Model (OPTIMOD), a simplified Space Shuttle Orbiter thermal math model to be used for payload thermal integration analysis, is described. The Orbiter lower fuselage math model has been reduced to the minimum level of detail consistent with accuracy requirements. Instead, an 'environment radiation sensor', a simple closed-end cylinder oriented in a fixed position with respect to the Orbiter, is introduced. Equations are presented which relate the cylinder surface heating rates to external fuselage steady-state temperatures. These equations were derived from a regression correlation analysis of steady-state Orbiter thermal solutions for 2372 points on orbit, representing a complete range of vehicle-earth-sun orientations. An exponential equation is developed to relate the steady-state data to time-variant temperatures for the particular transient attitude timeline being simulated. The accuracy of OPTIMOD is shown to be excellent in the payload bay and to compare favorably with previous models in Orbiter elements outside the bay.

Russell, David J.↗
NASA NTRS1980

Influence of the interplanetary magnetic field on cometary and primordial dust orbits - Applications of Lorentz Scattering

The equations describing the change in orbital elements of interplanetary dust due to Lorentz-force accelerations are presented in a simplified form. Such accelerations depend on the charge state of the dust; results of theoretical calculations for five possible dust materials are presented. Under present-day conditions, it is possible that semiconducting material such as graphite might carry a net voltage near zero, compared with a roughly 10-V charge expected for other grains. The scattering of dust by a randomly changing magnetic field can be viewed analogously to the dust diffusing in space; the equations presented thus can be used to interpret observations of the present distribution of dust in terms of its possible sources and sinks. The stronger magnetic fields of the early solar system would have led to more vigorous scattering of the dust; particles as large as 1 mm could have been significantly transported by Lorentz scattering during this time.

Consolmagno, G. J.↗
NASA NTRS2002

An Overview of the Earth Observing System Moderate Resolution Imaging Spectroradiometer (MODIS) Data Products Status and Availability for Environmental Applications and Global Change Studies

The Moderate Resolution Imaging Spectroradiometer (MODIS) on the Earth Observing System (EOS) Terra Mission began to produce data in February 2000. 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 spacecraft, instrument, and data systems 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 exceed or, at a minimum, match 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. The MODIS instrument on the EOS Aqua mission should also be expected to be in orbit and functioning in the Spring of 2002. The Aqua spacecraft will operate 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. Subsequently the Aqua MODIS observations will substantially add to the capabilities of the Terra MODIS for environmental applications and global change studies.

Salomonson, Vincent V.↗
NASA NTRS2003

An Overview of the Earth Observing System Moderate Resolution Imaging Spectroradiometer (MODIS) Data Products and Availability for Environmental Applications and Global Change Studies

The Moderate Resolution Imaging Spectroradiometer (MODIS) on the Earth Observing System (EOS) Terra Mission began to produce data in February 2000. 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 spacecraft, instrument, and data systems 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 (DAACs) or through Direct Broadcast (DB) stations. The EOS Aqua mission was launched successfully May 4,2002 with another MODIS on it. 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. Subsequently the Aqua MODIS observations will substantially add to the capabilities of the Terra MODIS for environmental applications and global change studies.

Salomonson, V. V.↗
NASA NTRS2004

Dynamics of Earth orbiting formations

In this paper the equations of motion of a formation consisting of n spacecraft in Earth orbit are derived via Lagrange's equations. The equations of motion of the formation are developed with respect to both (1) a bound Keplerian reference orbit, and (2) a specific spacecraft in the formation. The major orbital perturbations acting on a formation in low Earth orbit are also included in the analysis. In contrast to the traditional approach based on the balance of linear momentum, the use of Lagrange's equations leads to a high-level matrix derivation of the formation equations of motion. The matrix form of the nonlinear motion equations is then linearized about a bound Keplerian reference orbit. Next, it is demonstrated that under the assumption of a circular reference orbit, the linearized equations of motion reduce to the well-known Hill-Clohessy-Wiltshire equations. The resulting linear and nonlinear dynamic equations lead to maximal physical insight into the structure of formation dynamics, and are ideally suited for use in the design and validation of formation guidance and control laws.

formation flying↗
NASA NTRS2018

Terra and Aqua MODIS Intercomparison Using LEO-GEO Double Difference Method

The Moderate Resolution Imaging Spectroradiometer (MODIS) onboard the Terra and Aqua satellites havesuccessfully operated since their launch in 1999 and in 2002, providing more than 18 and 16 years ofcontinuous global observations, respectively. The inter-comparison between the two MODIS instruments can bevery supportive for the instrument calibration and uncertainty assessment. Aqua and Terra MODIS have almostidentical relative spectral response, spatial resolution, and dynamic range for each band. Therefore, a sitedependent correction for a sensor spectral band pair is not necessary for their comparison. However, Terra is inthe morning orbit with an equator crossing time of 10:30 am, and Aqua is in the afternoon orbit with equatorcrossing time of 1:30 pm. Consequently, there is a dearth of simultaneous nadir overpasses (SNOs)between the two satellites. Major challenges in cross-sensor comparison of instruments on different satellitesinclude differences in observation time, solar angle, and view angle over selected pseudo-invariant sites.In this work, the inter-comparisons of thermal emissive bands are performed over a pseudo-invariant target,using the observations from a sensor onboard a geostationary satellite as a bridge. Himawari8 was launched onOctober 7, 2014. The Advanced Himawari Imager (AHI) onboard Himawari8 can be used as a reference tobridge the comparison between Terra and Aqua MODIS. AHI has 16 channels; with spatial resolutions from 0.5km to 2 km at nadir and produces a full disk observations every 10 minutes. The band spectral coveragematchup, comparable spatial resolution and near-simultaneous observation between MODIS and AHI providefeasibility to implement a double difference method. This comparison method minimizes the impact of thedifference in observation time and solar angle. The comparison results will be used as an assessment for MODISinstrument calibration and will be helpful for future enhancement of the L1B product.

Himawari8↗
NASA NTRS1986

Efficient inverse solution of Kepler's equation

A bicubic polynomial approximation to Kepler's equation for elliptic orbits is shown to provide accurate starting values for efficient numerical solution of this equation for eccentric anomaly. In the approximate equation, a cubic in mean anomaly is set equal to a cubic in eccentric anomaly. The coefficients in the two cubics are obtained as functions of eccentricity by specifying values of function and slope at the midpoint and the endpoint of the complete interval (0 to pi). The initial estimate of eccentric anomaly to use in an iteration formula is obtained by evaluating the cubic in mean anomaly and finding the single real root of the cubic in eccentric anomaly. Numerical results are presented which indicate that the estimate accuracy of this method is roughly an order of magnitude better than that of other recently-reported formulas.

Boltz, Frederick W.↗
NASA NTRSDate not supplied

Handling Singularities in Meteoroid Environment Modeling

A meteoroid environment model must describe, at a bare minimum, the local density or flux of meteoroids. To accomplish this, many models make use of analytic equations to convert orbital distributions to number density, or to compute the effects of a planet's gravity on flux and speed. However, these equations often contain singularities that are unrealistic. For instance, the orbit-to-density conversion used by Jones (2006) is unbound at peri- and aphelion, and the gravitational focusing algorithms presented by Staubach et al. (1997) are unbound along the anti-radiant line. We present methods for removing these singularities that result in more realistic descriptions of the meteoroid environment.

Althea Valkyrie Moorhead↗
NASA NTRS2019

The Mutual Orbit, Mass, and Density of Transneptunian Binary Gǃkúnǁ’hòmdímà (229762 2007 UK126)

We present high spatial resolution images of the binary transneptunian object Gǃkúnǁ'hòmdímà (229762 2007 UK126) obtained with the Hubble Space Telescope and with the Keck observatory on Mauna Kea to determine the orbit of Gǃò'é ǃhúGǃò'é ǃhú, the much smaller and redder satellite. Gǃò'é ǃhú orbits in a prograde sense, on a circular or near-circular orbit with a period of 11.3 days and a semimajor axis of 6000 km. Tidal evolution is expected to be slow, so it is likely that the system formed already in a low-eccentricity configuration, and possibly also with the orbit plane of the satellite in or close to the plane of Gǃkúnǁ'hòmdímà's equator. From the orbital parameters we can compute the system mass to be 1.4 × 10(exp 20) kg. Combined with estimates of the size of Gǃkúnǁ'hòmdímà from thermal observations and stellar occultations, we can estimate the bulk density as about 1 g cm(exp −3). This low density is indicative of an ice-rich composition, unless there is substantial internal porosity. We consider the hypothesis that the composition is not unusually ice-rich compared with larger TNOs and comet nuclei, and instead the porosity is high, suggesting that mid-sized objects in the 400 to 1000 km diameter range mark the transition between small, porous objects and larger objects that have collapsed their internal void space as a result of their much higher internal pressures and temperatures.

W. M. Grundy↗
NASA NTRS2019

The Mutual Orbit, Mass, and Density of Transneptunian Binary Gǃkúnǁ'hòmdímà (229762 2007 UK126)

We present high spatial resolution images of the binary transneptunian object Gǃkúnǁ'hòmdímà (229762 2007 UK126) obtained with the Hubble Space Telescope and with the Keck observatory on Mauna Kea to determine the orbit of Gǃò'é ǃhúGǃò'é ǃhú, the much smaller and redder satellite. Gǃò'é ǃhú orbits in a prograde sense, on a circular or near-circular orbit with a period of 11.3 days and a semimajor axis of 6000 km. Tidal evolution is expected to be slow, so it is likely that the system formed already in a low-eccentricity configuration, and possibly also with the orbit plane of the satellite in or close to the plane of Gǃkúnǁ'hòmdímà's equator. From the orbital parameters we can compute the system mass to be 1.4 × 1020 kg. Combined with estimates of the size of Gǃkúnǁ'hòmdímà from thermal observations and stellar occultations, we can estimate the bulk density as about 1 g cm−3. This low density is indicative of an ice-rich composition, unless there is substantial internal porosity. We consider the hypothesis that the composition is not unusually ice-rich compared with larger TNOs and comet nuclei, and instead the porosity is high, suggesting that mid-sized objects in the 400 to 1000 km diameter range mark the transition between small, porous objects and larger objects that have collapsed their internal void space as a result of their much higher internal pressures and temperatures.

W M Grundy↗
NASA NTRS1973

Parameter estimation supplement to the Mission Analysis Evaluation and Space Trajectory Operations program (MAESTRO)

This Parameter Estimation Supplement describes the PEST computer program and gives instructions for its use in determination of lunar gravitation field coefficients. PEST was developed for use in the RAE-B lunar orbiting mission as a means of lunar field recovery. The observations processed by PEST are short-arc osculating orbital elements. These observations are the end product of an orbit determination process obtained with another program. PEST's end product it a set of harmonic coefficients to be used in long-term prediction of the lunar orbit. PEST employs some novel techniques in its estimation process, notably a square batch estimator and linear variational equations in the orbital elements (both osculating and mean) for measurement sensitivities. The program's capabilities are described, and operating instructions and input/output examples are given. PEST utilizes MAESTRO routines for its trajectory propagation. PEST's program structure and subroutines which are not common to MAESTRO are described. Some of the theoretical background information for the estimation process, and a derivation of linear variational equations for the Method 7 elements are included.

Bjorkman, W. S.↗