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NASA NTRS1947

Formulas for additional mass corrections to the moments of inertia of airplanes

Formulas are presented for the calculation of the additional mass corrections to the moments of inertia of airplanes. These formulas are of particular value in converting the virtual moments of inertia of airplanes or models experimentally determined in air to the true moments of inertia. A correlation of additional moments of inertia calculated by these formulas with experimental additional moments of inertia obtained from vacuum chamber tests of 40 spin-tunnel models indicates that formulas give satisfactory estimations of the additional moments of inertia.

MOMENTS OF INERTIA↗

NASA NTRS2000

A Determination of the Precession and Rotation-Rate of Mars from Tracking and Altimetry Data

The doppler tracking of the MGS spacecraft and the laser altimetry acquired by the MOLA instrument on MGS have been used to measure the rotation of Mars. By observing the repeating pattern of gravity anomalies and the topography the direction of the rotation axis in both inertial space and body fixed coordinates, and the rate of rotation of the planet on its axis have been derived. The tracking of MGS in orbit about Mars by stations on Earth permit the orbit of MGS to be obtained in an inertial coordinate system enabling the periodic perturbation of the MGS orbit by Mars' gravity field to be used as a sensor to detect the vector rotation of Mars under the orbit of MGS. The altimetry data acquired by MOLA on MGS permit the topography to help define the orbit of MGS about Mars in a body fixed coordinate system thus enabling the pole of rotation of the planet to be determined in a coordinate system defined by the altimetry. Together they enable the precession of the rotation axis to be observed from which the moment of inertia can be derived, changes in length of day to be measured, and a method to check for possible Mars polar motion. Tracking data on the Mariner 9, Viking 1 and 2, from the 1970's have been analyzed with MGS data obtained in the mapping orbit in 1999 to provide a new estimate of the moment of inertia.

Smith, David E.↗

NASA NTRS1990

Attitude control/momentum management of the Space Station Freedom for large angle torque-equilibrium-attitude configurations

An attitude-control and momentum-management (ACMM) system for the Space Station in a large-angle torque-equilibrium-attitude (TEA) configuration is developed analytically and demonstrated by means of numerical simulations. The equations of motion for a rigid-body Space Station model are outlined; linearized equations for an arbitrary TEA (resulting from misalignment of control and body axes) are derived; the general requirements for an ACMM are summarized; and a pole-placement linear-quadratic regulator solution based on scheduled gains is proposed. Results are presented in graphs for (1) simulations based on configuration MB3 (showing the importance of accounting for the cross-inertia terms in the TEA estimate) and (2) simulations of a stepwise change from configuration MB3 to the 'assembly complete' stage over 130 orbits (indicating that the present ACCM scheme maintains sufficient control over slowly varying Space Station dynamics).

Parlos, Alexander G.↗

NASA NTRS1977

Thermal inertia mapping - A new view of the earth

The thermal response of a substance to a time-varying surface power input is determined by its thermal inertia. Remote sensing (e.g., from satellites) can be utilized to measure this property, which is related to surface composition or to near-surface soil moisture. An algorithm is developed which relates thermal inertia to remote measurements of surface temperature and reflectance. Application to geosynchronous satellite data illustrates the contrast between irrigated and desert areas in the region north of the Gulf of California. The effect of local weather conditions (latent and sensible heat transfer to the atmosphere) must be estimated before precise values for thermal inertia can be specified.

Price, J. C.↗

NASA NTRS2007

Estimation of Cometary Rotation Parameters Based on Camera Images

The purpose of the Rosetta mission is the in situ analysis of a cometary nucleus using both remote sensing equipment and scientific instruments delivered to the comet surface by a lander and transmitting measurement data to the comet-orbiting probe. Following a tour of planets including one Mars swing-by and three Earth swing-bys, the Rosetta probe is scheduled to rendezvous with comet 67P/Churyumov-Gerasimenko in May 2014. The mission poses various flight dynamics challenges, both in terms of parameter estimation and maneuver planning. Along with spacecraft parameters, the comet's position, velocity, attitude, angular velocity, inertia tensor and gravitatonal field need to be estimated. The measurements on which the estimation process is based are ground-based measurements (range and Doppler) yielding information on the heliocentric spacecraft state and images taken by an on-board camera yielding informaton on the comet state relative to the spacecraft. The image-based navigation depends on te identification of cometary landmarks (whose body coordinates also need to be estimated in the process). The paper will describe the estimation process involved, focusing on the phase when, after orbit insertion, the task arises to estimate the cometary rotational motion from camera images on which individual landmarks begin to become identifiable.

Spindler, Karlheinz↗

NASA NTRS1972

Recent results on the mass, gravitational field and moments of inertia of the moon.

Use of Doppler tracking data from the Lunar Orbiter series of spacecraft in an analysis of the spherical harmonic coefficients of the lunar gravitational field through thirteenth degree and order. The value obtained for the mass of the moon, GM = 4902.84 cu km/sec/sec, is in good agreement with previous results and with results obtained by alternate procedures. Acceleration contour plots, derived from the gravitational coefficients, show correlations with surface features on the near side of the moon, but are of questionable validity for the far side because of the lack of direct tracking data on the far side. Based on the most recent gravitational field data, the current estimate for the polar moment of inertia of the moon is C/Ma squared = 0.4019 super + 0.004 sub - 0.002. This value indicates that the interior of the moon can be homogeneous, but some results presented strongly suggest that the moon is differentiated, with an excess of mass in the direction toward the earth.

Michael, W. H., Jr.↗

NASA NTRS1990

Interchange instability of the earth's plasmapause

The factors that affect the interchange instability of the earth's plasmapause are investigated using an extension of Richmond's (1973) procedure based on computing individual particle motions. The effects of particle inertia, centrifugal force, and gravity are estimated. A general differential equation is derived for the time variation of the perturbation potential characterizing an electrostatic ripple with no field-aligned potential drop, which can be solved as an eigenvalue problem to find the linear growth rate. Approximate analytic solutions to this equation were obtained from which it was deduced that the interchange instability is caused by the sharp change in plasma pressure at the plasmapause; its growth rate is limited by ionospheric conductivity and, for very short wavelengths, by the inertia of the magnetospheric particles.

Huang, T. S.↗

NASA NTRS2016

Inference of Surface Chemical and Physical Properties Using Mid-Infrared (MIR) Spectral Observations

Reflected or emitted energy from solid surfaces in the solar system can provide insight into thermo-physical and chemical properties of the surface materials. Measurements have been obtained from instruments located on Earth-based telescopes and carried on several space missions. The characteristic spectral features commonly observed in Mid-Infrared (MIR) spectra of minerals will be reviewed, along with methods used for compositional interpretations of MIR emission spectra. The influence of surface grain size, and space weathering processes on MIR emissivity spectra will also be discussed. Methods used for estimating surface temperature, emissivity, and thermal inertias from MIR spectral observations will be reviewed.

Earth-based telescopes↗

NASA NTRS2007

Sodium Lidar-observed Strong Inertia-gravity Wave Activities in the Mesopause Region over Fort Collins, Colorado (41 deg N, 105 deg W)

In December 2004, the Colorado State University sodium lidar system at Fort Collins, Colorado (41 deg N, 105 deg W), conducted an approximately 80-hour continuous campaign for the simultaneous observations of mesopause region sodium density, temperature, and zonal and meridional winds. This data set reveals the significant inertia-gravity wave activities with a period of approximately 18 hours, which are strong in both wind components since UT day 338 (second day of the campaign), and weak in temperature and sodium density. The considerable variability of wave activities was observed with both wind amplitudes growing up to approximately 40 m/s at 95-100 km in day 339 and then decreasing dramatically in day 340. We also found that the sodium density wave perturbation is correlated in phase with temperature perturbation below 90 km, and approximately 180 deg out of phase above. Applying the linear wave theory, we estimated the wave horizontal propagation direction, horizontal wavelength, and apparent horizontal phase speed to be approximately 25 deg south of west, approximately 1800 +/- 150 km, and approximately 28 +/- 2 m/s, respectively of wave intrinsic period, intrinsic phase speed, and vertical wavelength were also estimated. While the onset of enhanced inertia-gravity wave amplitude in the night of 338 was observed to be in coincidence with short-period gravity wave breaking via convective instability, the decrease of inertia-gravity wave amplitude after noon of day 339 was also observed to coincide with the development of atmospheric dynamical instability layers with downward phase progression clearly correlated with the 18-hour inertia-gravity wave, suggesting likely breaking of this inertia-gravity wave via dynamical (shear) instability.

mesopause region↗

NASA NTRS1974

The structure and circulation of the deep Venus atmosphere

A simple model for the structure of a nonrotating Hadley regime in an atmosphere with large thermal inertia is developed. The radiative fluxes are estimated by using a linearization about the radiative equilibrium state, and the dynamical fluxes are estimated by using scaling analysis. The requirement that differential heating by these fluxes be in balance in both the meridional and vertical directions leads to two equations for the mean static stability and meridional temperature contrast. The solution depends on two parameters: the strength of the radiative heating, as measured by the static stability of the radiative equilibrium state; and the ratio of the time it takes an external gravity wave to traverse the atmosphere to the time it would take the atmosphere to cool off radiatively. It is shown that it is not necessary to invoke convection to explain the approximate adiabatic lapse rate in the Venus atmosphere, but a greenhouse effect is necessary to explain the high surface temperatures.

Stone, P. H.↗

NASA NTRS1991

Structural design of the Large Deployable Reflector (LDR)

An integrated Large Deployable Reflector (LDR) analysis model was developed to enable studies of system responses to the mechanical and thermal disturbances anticipated during on-orbit operations. Functional requirements of the major subsystems of the LDR are investigated, design trades are conducted, and design options are proposed. System mass and inertia properties are computed in order to estimate environmental disturbances, and in the sizing of control system hardware. Scaled system characteristics are derived for use in evaluating launch capabilities and achievable orbits. It is concluded that a completely passive 20-m primary appears feasible for the LDR from the standpoint of both mechanical vibration and thermal distortions.

Satter, Celeste M.↗

NASA NTRS1993

Investigation of the role of thermal boundary layer processes in initiating convection under the NASA SPACE Field Program

The current NWS ground based network is not sufficient to capture the dynamic or thermodynamic structure leading to the initiation and organization of air mass moist convective events. Under this investigation we intend to use boundary layer mesoscale models (McNider and Pielke, 1981) to examine the dynamic triggering of convection due to topography and surface thermal contrasts. VAS and MAN's estimates of moisture will be coupled with the dynamic solution to provide an estimate of the total convective potential. Visible GOES images will be used to specify incoming insolation which may lead to surface thermal contrasts and JR skin temperatures will be used to estimate surface moisture (via the surface thermal inertia) (Weizel and Chang, 1988) which can also induce surface thermal contrasts. We will use the SPACE-COHMEX data base to evaluate the ability of the joint mesoscale model satellite products to show skill in predicting the development of air mass convection. We will develop images of model vertical velocity and satellite thermodynamic measures to derive images of predicted convective potential. We will then after suitable geographic registration carry out a pixel by pixel correlation between the model/satellite convective potential and the 'truth' which are the visible images. During the first half of the first year of this investigation we have concentrated on two aspects of the project. The first has been in generating vertical velocity fields from the model for COHMEX case days. We have taken June 19 as the first case and have run the mesoscale model at several different grid resolutions. We are currently developing the composite model/satellite convective image. The second aspect has been the attempted calibration of the surface energy budget to provide the proper horizontal thermal contrasts for convective initiation. We have made extensive progress on this aspect using the FIFE data as a test data set. The calibration technique looks very promising.

Mcnider, Richard T.↗

NASA NTRS2024

Leveraging the Gravity Field Spectrum for Icy Satellite Interior Structure Determination: The case of Europa with the Europa Clipper Mission

Understanding the interior structures of icy moons is pivotal for addressing their origins and habitability. We introduce an approach employing the gravity field spectrum as an additional constraint for the inversion of differentiated icy bodies' interior structures. After developing the general methodology, we apply it to Europa, utilizing the predicted measurement capability of NASA's Europa Clipper mission, and we prove its effectiveness in resolving key geophysical parameters. Notably, we show that using the gravity field spectrum in combination with the mass and moment of inertia of the body allows us to estimate, depending on the considered end-member interior structure, the hydrosphere thickness with 4–20 km uncertainty and reliably determine the seafloor maximum topographic range and elastic thickness to within 100–600 m and 5–15 km, respectively, together with the power–degree relationship of the seafloor topography. We also show that the proposed method allows us to determine the density of the silicate mantle and the radius of the core to within 0.25 g cc −1 and 50 km, respectively.

G. Cascioli↗

NASA NTRS1988

Random field estimation approach to multibody dynamics

The use of recursive techniques similar to random field models to factor and invert the inertia matrix of a multibody system is discussed. An equivalence is established between the composite multibody system inertia matrix and the covariance of the output of a described linear system model. Conditional mean estimation and sequential estimation problems are solved along with problems of filtering and smoothing. Formulas are developed to compute the covariance of several relevant quantities. The foregoing results are used to obtain the inverse of the composite multibody system inertia in closed form.

Rodriguez, G.↗

NASA NTRS1996

Capillary Flow in an Interior Corner

The design of fluids management processes in the low-gravity environment of space requires an accurate model and description of capillarity-controlled flow in containers of irregular geometry. Here we consider the capillary rise of a fluid along an interior corner of a container following a rapid reduction in gravity. The analytical portion of the work presents an asymptotic formulation in the limit of a slender fluid column, slight surface curvature along the corner, small inertia, and low gravity. New similarity solutions are found and a list of closed form expressions is provided for flow rate and column length. In particular, it is found that the flow is proportional to t(exp 1/2) for a constant height boundary condition, t(exp 2/5) for a spreading drop, and t(exp 3/5) for constant flow. In the experimental portion of the work, measurements from a 2.2s drop tower are reported. An extensive data set, collected over a previously unexplored range of flow parameters, includes estimates of repeatability and accuracy, the role of inertia and column slenderness, and the effects of corner angle, container geometry, and fluid properties. Comprehensive comparisons are made which illustrate the applicability of the analytic results to low-g fluid systems design.

Weislogel, Mark Milton↗

NASA NTRS2016

Center of Mass Estimation for a Spinning Spacecraft Using Doppler Shift of the GPS Carrier Frequency

A sequential filter is presented for estimating the center of mass (CM) of a spinning spacecraft using Doppler shift data from a set of onboard Global Positioning System (GPS) receivers. The advantage of the proposed method is that it is passive and can be run continuously in the background without using commanded thruster firings to excite spacecraft dynamical motion for observability. The NASA Magnetospheric Multiscale (MMS) mission is used as a test case for the CM estimator. The four MMS spacecraft carry star cameras for accurate attitude and spin rate estimation. The angle between the spacecraft nominal spin axis (for MMS this is the geometric body Z-axis) and the major principal axis of inertia is called the coning angle. The transverse components of the estimated rate provide a direct measure of the coning angle. The coning angle has been seen to shift slightly after every orbit and attitude maneuver. This change is attributed to a small asymmetry in the fuel distribution that changes with each burn. This paper shows a correlation between the apparent mass asymmetry deduced from the variations in the coning angle and the CM estimates made using the GPS Doppler data. The consistency between the changes in the coning angle and the CM provides validation of the proposed GPS Doppler method for estimation of the CM on spinning spacecraft.

Spacecraft↗

NASA NTRS2016

Center of Mass Estimation for a Spinning Spacecraft Using Doppler Shift of the GPS Carrier Frequency

Estimation↗

NASA NTRS2018

Virtual Sensors Determined Through Machine Learning

We propose a method that increases the capability of a conventional sensor/instrument, transforming it into an enhanced virtual sensor/instrument. This paper focuses on a virtual thermal IR sensor based on a conventional visual (RGB) sensor. The estimation of thermal IR images can enhance the ability of terrain classiﬁcation, which is crucial for autonomous navigation of rovers. The estimate in IR from visual band has inherent limitations, as these are different bands, yet correlations between visual/RGB and thermal IR images exist, as different terrains, which visually may appear different, also have different thermal inertia. We developed a deep learning-based algorithm that estimates thermal IR images from RGB images of terrains, providing the feasibility of the idea with average 1.21 error [degree].

Kurazume, Ryo↗