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NASA NTRS1991

The earth's equatorial principal axes and moments of inertia

The earth's equatorial principal moments of inertia are given as A and B, where A is less than B, and the corresponding principal axes are given as a and b. Explicit formulas are derived for determining the orientation of a and b axes and the difference B - A using C(22) and S(22), the two gravitational harmonic coefficients of degree 2 and order 2. For the earth, the a axis lies along the (14.93 deg W, 165.07 deg E) diameter, and the b axis lies perpendicular to it along the (75.07 deg E, 104.93 deg W) diameter. The difference B - A is 7.260 x 10 to the -6th MR2. These quantities for other planets are contrasted, and geophysical implications are discussed.

Liu, H. S.↗

NASA NTRS1991

Sub-milliarcsecond determination of pole position using Global Positioning System data

The determination of pole-position variations from the analysis of 23 days of Global Positioning System (GPS) data continuously collected with a globally distributed, 21-station network is discussed. The comparison of the estimated pole positions from these data with results from 11 very long baseline interferometry (VLBI) experiments conducted during this same interval yields weighted root-mean-square differences about the mean differences of 0.5 mas for both X- and Y-pole position estimates from an analysis using single-day arcs, and 1.0 and 0.8 mas from an analysis using three weekly multiday arcs. These results are of sufficient quality that GPS could provide an alternative technique to VLBI and satellite laser ranging for regular monitoring of high-time-resolution variations in the position of the earth's rotation axis.

Herring, Thomas A.↗

NASA NTRS1992

The semiannual variation of great geomagnetic storms and the postshock Russell-Mcpherron effect preceding coronal mass ejecta

Recent results indicate that the intense southward interplanetary magnetic fields (IMFs) responsible for great storms can reside in the postshock plasma preceding the driver gas of coronal mass ejections (CMEs) as well as in the driver gas itself. It is proposed here that strong southward fields in the postshock flow result from a major increase in the Russell-McPherron polarity effect through a systematic pattern of compression and draping within the ecliptic plane. Differential compression at the shock increases the Parker spiral angle and, consequently, the azimuthal field component that projects as a southward component onto earth's dipole axis. The resulting prediction is that southward fields in the postshock plasma maximize at the spring (fall) equinox in CMEs emerging from toward (away) sectors. This pattern produces a strong semiannual variation in postshock IMF orientation and may account at least in part for the observed semiannual variation of the occurrence of great geomagnetic storms.

Crooker, N. U.↗

NASA NTRS1997

The In-Orbit Battery Reconditioning Experience On Board the Orion 1 Spacecraft

The Orion 1 spacecraft is a three-axis stabilized geostationary earth orbiting commercial communications satellite which was launched on November 29, 1994 aboard an Atlas II launch vehicle. The power subsystem is a dual bus, dual battery semi-regulated system with one 78 Ampere-hour nickel-hydrogen battery per bus. The batteries were built and tested by Eagle Picher Industries, Inc., of Joplin, MO and were integrated into the spacecraft by its manufacturer, Matra Marconi Space UK Ltd. This paper presents the results obtained during the first four in-orbit reconditioning cycles and compares the battery performance to ground test data. In addition, the on-station battery management strategy and implementation constraints are described. Battery performance has been nominal throughout each reconditioning cycle and subsequent eclipse season.

Hoover, S. A.↗

NASA NTRS1995

Planetary-Induced Nutation of the Earth: Direct Terms

Small torques by the planets can alter the direction of the Earth's rotation axis in space. These direct planetary-induced nutations have been computed using a numerical technique. 62 nutation terms with periods between 0.2 and 883 yr are presented. The maximum,nutation is 0.5 marcsec. Also given are planetary-induced rates and accelerations of precession and obliquity.

Williams, James G.↗

NASA NTRS1993

Three dimensional eye movements of squirrel monkeys following postrotatory tilt

Three-dimensional squirrel monkey eye movements were recorded during and immediately following rotation around an earth-vertical yaw axis (160 degrees/s steady state, 100 degrees/s2 acceleration and deceleration). To study interactions between the horizontal angular vestibulo-ocular reflex (VOR) and head orientation, postrotatory VOR alignment was changed relative to gravity by tilting the head out of the horizontal plane (pitch or roll tilt between 15 degrees and 90 degrees) immediately after cessation of motion. Results showed that in addition to post rotatory horizontal nystagmus, vertical nystagmus followed tilts to the left or right (roll), and torsional nystagmus followed forward or backward (pitch) tilts. When the time course and spatial orientation of eye velocity were considered in three dimensions, the axis of eye rotation always shifted toward alignment with gravity, and the postrotatory horizontal VOR decay was accelerated by the tilts. These phenomena may reflect a neural process that resolves the sensory conflict induced by this postrotatory tilt paradigm.

NASA Program Space Physiology and Countermeasures↗

NASA NTRS2015

Individual Global Navigation Satellite Systems in the Space Service Volume

Besides providing position, navigation, and timing (PNT) to terrestrial users, GPS is currently used to provide for precision orbit determination, precise time synchronization, real-time spacecraft navigation, and three-axis control of Earth orbiting satellites. With additional Global Navigation Satellite Systems (GNSS) coming into service (GLONASS, Beidou, and Galileo), it will be possible to provide these services by using other GNSS constellations. The paper, "GPS in the Space Service Volume," presented at the ION GNSS 19th International Technical Meeting in 2006 (Ref. 1), defined the Space Service Volume, and analyzed the performance of GPS out to 70,000 km. This paper will report a similar analysis of the performance of each of the additional GNSS and compare them with GPS alone. The Space Service Volume, defined as the volume between 3,000 km altitude and geosynchronous altitude, as compared with the Terrestrial Service Volume between the surface and 3,000 km. In the Terrestrial Service Volume, GNSS performance will be similar to performance on the Earth's surface. The GPS system has established signal requirements for the Space Service Volume. A separate paper presented at the conference covers the use of multiple GNSS in the Space Service Volume.

Beidou↗

NASA NTRS1995

Planetary-Induced Nutation of the Earth - Direct Terms

Small torques by the planets can alter the direction of the Earth's rotation axis in space. These direct planetary-induced nutations have been computed using a numerical technique. 55 nutation terms with periods between 0.2 and 243 yr are presented. The maximum nutation is 0.5 milliarcseconds. Also given are planetary-induced rates and accelerations of precession and obliquity.

Planetary-Induced↗

NASA NTRS2004

Compact Optoelectronic Compass

A compact optoelectronic sensor unit measures the apparent motion of the Sun across the sky. The data acquired by this chip are processed in an external processor to estimate the relative orientation of the axis of rotation of the Earth. Hence, the combination of this chip and the external processor finds the direction of true North relative to the chip: in other words, the combination acts as a solar compass. If the compass is further combined with a clock, then the combination can be used to establish a threeaxis inertial coordinate system. If, in addition, an auxiliary sensor measures the local vertical direction, then the resulting system can determine the geographic position. This chip and the software used in the processor are based mostly on the same design and operation as those of the unit described in Micro Sun Sensor for Spacecraft (NPO-30867) elsewhere in this issue of NASA Tech Briefs. Like the unit described in that article, this unit includes a small multiple-pinhole camera comprising a micromachined mask containing a rectangular array of microscopic pinholes mounted a short distance in front of an image detector of the active-pixel sensor (APS) type (see figure). Further as in the other unit, the digitized output of the APS in this chip is processed to compute the centroids of the pinhole Sun images on the APS. Then the direction to the Sun, relative to the compass chip, is computed from the positions of the centroids (just like a sundial). In the operation of this chip, one is interested not only in the instantaneous direction to the Sun but also in the apparent path traced out by the direction to the Sun as a result of rotation of the Earth during an observation interval (during which the Sun sensor must remain stationary with respect to the Earth). The apparent path of the Sun across the sky is projected on a sphere. The axis of rotation of the Earth lies at the center of the projected circle on the sphere surface. Hence, true North (not magnetic North), relative to the chip, can be estimated from paths of the Sun images across the APS. In a test, this solar compass has been found to yield a coarse estimate of the North (within tens of degrees) in an observation time of about ten minutes. As expected, the accuracy was found to increase with observation time: after a few hours, the estimated direction of the rotation axis becomes accurate to within a small fraction of a degree.

Christian, Carl↗

NASA NTRS1992

Long-term orbital and spin dynamics of Mars

This review of the long-term dynamical behavior of Mars covers secular variations of the orbit, oscillations of the obliquity, and polar wandering. Calculations of the large-scale obliquity oscillations of Mars are updated using the most recent orbit theory and contrasted with the earth. The motion for Mars is characterized by about 100,000-yr oscillations driven by differential spin axis and orbit plane precession rates during which the obliquity may change by as much as about 20 deg. The possible role of spin-orbit secular resonances to the spin axis histories of the earth and Mars is also considered. Numerical integrations of the equations of motion indicate that Mars may have passed through resonance as little as 5 Myr ago and that obliquities approaching about 45 deg could have been achieved during such an event.

Ward, William R.↗

NASA NTRS1998

Using Sequential Earth Images to Determine the Orientation of a Satellite at L1

This paper introduces a method for determining the three-axis attitude (orientation) of a spacecraft from a sequence of Earth images taken while in orbit about the stationary Lagrange point between the Earth and the sun (LI). Two axes of information can be obtained simply by monitoring the Earth's position within the field-of-view of the camera. The third axis is obtained by correlating sequential Earth images in such a way as to detect the flow of the features within the Earth's disk over time. When taken correctly, this measurement is perpendicular to the Earth's spin axis and, consequently, locates the Earth's spin axis within the images. This is equivalent to determining the orientation of the spacecraft about the instrument's boresight. Actual data from the Galileo spacecraft is used to test the algorithms outlined in this paper.

Houghton, Martin B.↗

NASA NTRS1990

Contamination control of the Cryogenic Limb Array Etalon Spectrometer

The cleanliness requirements of the Cryogenic Limb Array Etalon Spectrometer (CLAES) are described and the control program is assessed with particular emphasis given to the effects of particulate interference. The use of the CLAES is reviewed, and off-axis scatter from the earth is identified as an important noise source. Since the CLAES altitude of interest causes a low-altitude detection of 0.2 deg above the earth's surface, straylight controls are important in the development of the instrument. The development of off-axis rejection and the particulate-cleanliness level are evaluated in terms of those required for a certain BRDF. The control plan is described, and procedures are outlined including cleaning methods and facilities. The modeling predictions and procedural controls are found to effectively satisfy requirements for low scatter levels and out-of-field view-rejection by maximizing straylight control and allowing a margin against noise-equivalent radiance.

Steakley, B. C.↗

NASA NTRS1990

Is the earth's dipole actually inclined with respect to the rotation axis?

Planetary exploration by deep space probes in recent years has shown that the dipole moment of some magnetized planets has a surprisingly large inclination angle with respect to the rotation axis. Applying the method developed for the source surface magnetic field of the sun (a spherical surface of 2.5 solar radii), it is suggested that the main dipole of the earth and the magnetized planets may actually be axial (the magnetic moment being parallel or antiparallel to the rotation axis), and that two or three smaller dipoles near the core surface could be responsible for the apparent inclination of the main dipole. In formulating a dynamo theory of the planetary magnetic field, such a possibility should be considered, as well as the inclined dipole case.

Akasofu, S.-I.↗

DOE OSTI2020

Earth as an Exoplanet. I. Time Variable Thermal Emission Using Spatially Resolved Moderate Imaging Spectroradiometer Data

Among the more than 4000 exoplanets known today, some terrestrial planets have been detected in the so-called habitable zone of their host stars and their number is expected to increase in the near future, energizing a drive to understand and interpret the eagerly awaited wealth of data to identify signs of life beyond our solar system. So far, Earth remains the best and only example of a habitable (and inhabited) world. Although, it seems extremely unlikely that any other exoplanets will be true Earth twins, it is important to explore and understand the full range of spectral signatures and variability of Earth in order to inform the design of future instruments and missions, and understand their diagnostic power as well as potential limitations. In this work we use Earth observation data collected by the MODIS instrument aboard the Aqua satellite. The complete data set comprises 15 years of thermal emission observations in the 3.66–14.40 μm range for five different locations on Earth (Amazon Rainforest, Antarctica, Arctic, Indian Ocean, and the Sahara Desert). We then determine flux levels and variations as a function of wavelength and surface type (i.e., climate zone and surface thermal properties) and investigate whether periodic signals indicating Earth’s tilted rotation axis can be detected. Our findings suggest that (1) viewing geometry plays an important role when thermal emission data is analyzed as Earth’s spectrum varies by a factor of three and more depending on the dominant surface type underneath; (2) typically strong absorption bands from CO 2 (15 μm) and O 3 (9.65 μm) are significantly less pronounced and partially absent in data from the polar regions implying that estimating correct abundance levels for these molecules might be challenging in these cases; and (3) the time-resolved thermal emission spectrum encodes information about seasons/planetary obliquity, but the significance depends on the viewing geometry and spectral band considered.

79 ASTRONOMY AND ASTROPHYSICS↗

NASA NTRS2000

Space Elevators: Building a Permanent Bridge for Space Exploration and Economic Development

A space elevator is a physical connection from the surface of the Earth to a geo-stationary orbit above the Earth approximately 35,786 km in altitude. Its center of mass is at the geo-stationary point such that it has a 24-hour orbit, and stays over the same point above the equator as the Earth rotates on its axis. The structure is utilized as a transportation and utility system for moving payloads, power, and gases between the surface of the Earth and space. It makes the physical connection from Earth to space in the same way a bridge connects two cities across a body of' water. The space elevator may be an important concept for the future development of space in the latter part of the 21th century. It has the potential to provide mass-transportation to space in the same way highways, railroads, power lines, and pipelines provide mass-transportation across the Earth's surface. The low energy requirements for moving payloads up and down the elevator make it one of only a few concepts that has the potential of lowering the cost to orbit to less than $10 per kilogram. This paper will summarize the findings from a 1999 NASA workshop on Space Elevators held at the NASA Marshall Space Flight Center (MSFC). The workshop was sponsored by the Advanced Projects Office in the Flight Projects Directorate at MSFC, and was organized in cooperation with the Advanced Space Transportation Program at MSFC and the Advanced Concepts Office in the Office of Space Flight at NASA Headquarters. New concepts will be examined for space elevator construction and a number of issues will be discussed that has helped to bring the space elevator concept out of the realm of science fiction and into the realm of possibility. In conclusion, it appears that the space elevator concept may well he possible in the latter part of the 21st century if proper planning and technology development is emphasized to resolve key issues in the development of this advanced space infrastructure concept.

Smitherman, David V., Jr.↗

NASA NTRS1997

Topography of the Moon from the Clementine Lidar

Range measurements from the lidar instrument carried aboard the Clementine spacecraft have been used to produce an accurate global topographic model of the Moon. This paper discusses the function of the lidar; the acquisition, processing, and filtering of observations to produce a global topographic model; and the determination of parameters that define the fundamental shape of the Moon. Our topographic model: a 72nd degree and order spherical harmonic expansion of lunar radii, is designated Goddard Lunar Topography Model 2 (GLTM 2). This topographic field has an absolute vertical accuracy of approximately 100 m and a spatial resolution of 2.5 deg. The field shows that the Moon can be described as a sphere with maximum positive and negative deviations of approx. 8 km, both occurring on the farside, in the areas of the Korolev and South Pole-Aitken (S.P.-Aitken) basins. The amplitude spectrum of the topography shows more power at longer wavelengths as compared to previous models, owing to more complete sampling of the surface, particularly the farside. A comparison of elevations derived from the Clementine lidar to control point elevations from the Apollo laser altimeters indicates that measured relative topographic heights generally agree to within approx. 200 in over the maria. While the major axis of the lunar gravity field is aligned in the Earth-Moon direction, the major axis of topography is displaced from this line by approximately 10 deg to the cast and intersects the farside 24 deg north of the equator. The magnitude of impact basin topography is greater than the lunar flattening (approx. 2 km) and equatorial ellipticity (approx. 800 m), which imposes a significant challenge to interpreting the lunar figure. The floors of mare basins are shown to lie close to an equipotential surface, while the floors of unflooded large basins, except for S.P.-Aitken, lie above this equipotential. The radii of basin floors are thus consistent with a hydrostatic mechanism for the absence of significant farside maria except for S.P.-Aitken, whose depth and lack of mare require significant internal compositional and/or thermal heterogeneity. A macroscale surface roughness map shows that roughness at length scales of 10(exp 1) - 10(exp 2) km correlates with elevation and surface age.

Smith, David E.↗

NASA NTRS1984

Secular rotational motions and the mechanical structure of a dynamical viscoelastic earth

A survey is presented of analytical methods for computing the linear responses of the rotational axis of a layered viscoelastic earth to surface loading. Theoretical research in this area is first summarized, and the differences between the mechanical boundary conditions to be applied at the interface separating the upper and lower mantles for an adiabatically and chemically stratified mantle are discussed. Some examples of polar wander and secular variation of the spin rate from glacial excitation are presented for various types of chemical and viscosity stratifications. The effects of an artificial density jump at the base of the lithosphere in models are examined, and certain issues concerning the fluid tidal Love number for different types of density stratification are addressed. The meaning of effective plate thickness over geological time scales for rotational dynamics is discussed.

Yuen, D. A.↗

NASA NTRS1973

Geodetic reference systems for long period studies in earth physics

A simple system of reference axes is defined for possible use in high precision geodetic studies over long periods of time for programs in earth physics. The proposed system is based on the gravitational and dynamic characteristics of the axis of rotation and the earth's center of mass as defined instantaneously at a given epoch. Techniques are outlined for its continuous representation over time intervals of significance for studies in earth physics. The relationship between the proposed system and the representation of extra-terrestrial objects using the celestial sphere concept is also discussed.

Mather, R. S.↗