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The analysis and the FORTRAN program are presented for the determination of attitude of a spin-stabilized spacecraft. The use of telemetry data that provide information about two reference vectors and their relation to the spin is outlined. A technique for the determination of the spin-axis orientation that employs only simple calculations is described.
A general Hamiltonian function for a rotating moon in the field of the earth is expanded in terms of parameters orienting the spin angular momentum relative to the principal axes of the moon and relative to coordinate axes fixed in the orbit plane. The effects of elastic distortion are included as modifications of the moment of inertia tensor, where the magnitude of the distortion is parameterized by the Love number k sub 2.
Some preliminary mission studies are described along with the design, fabrication, and test of a breadboard model of an earth orbital, rotating gravity gradiometer with a design goal of 10 to the minus 11th power/sec sq (0.01 EU) in a 35-sec integration time. The proposed mission uses a Scout vehicle to launch one (or two orthogonally oriented) spin-stabilized satellites into a 330-km circular polar orbit some 20 days before an equinox. During the short orbital lifetime, the experiment would obtain two complete maps of the gravity gradient field with a resolution approaching 270 km (degree 75). The breadboard model of the gradiometer demonstrated a combined thermal and electronic noise threshold of 0.015 EU per data channel. The design changes needed to reduce the noise to less than 0.01 EU were identified. Variations of the sensor output signal with temperature were experimentally determined and a suitable method of temperature compensation was developed and tested. Other possible error sources, such as sensor interaction with satellite dynamics and magnetic fields, were studied analytically and shown to be small.
A photographic method was employed to record the kinematic performance of rolling elements in turbo machinery ball bearings. The 110 mm split inner ring test bearings had nominal contact angles of 26 deg and 34 deg. High speed films were taken at inner ring speeds of 4,000, 8,000 and 12,000 rpm and at thrust loads of 4,448 N and 22,240 N (1,000 and 5,000 lbs). The films were measured and this data reduced to obtain separator speed, ball speed and ball spin axis orientation.
The mission, systems, operations, ground systems, and reliability analysis of the Thor/Delta baseline design used for the Pioneer Space Probe are discussed. Tradeoff decisions concerning spin axis orientation, bus antenna design, communication system design, probe descent, and reduced science payload are analyzed. The reliability analysis is made for the probe bus mission, large probe mission, and small probe mission. Detailed mission sequences were established to identify critical areas and provide phasing of critical operation.
The requirements, trades, and design descriptions for the probe bus and orbiter spacecraft configurations, structure, thermal control, and harness are defined. Designs are developed for Thor/Delta and Atlas/Centaur launch vehicles with the latter selected as the final baseline. The major issues examined in achieving the baseline design are tabulated. The importance of spin axis orientation because of the effect on science experiments and earth communications is stressed.
A general Hamiltonian for a rotating moon in the field of the earth is expanded in terms of parameters orienting the spin angular momentum relative to the principal axes of the moon and relative to coordinate axes fixed in the orbital plane. The effects of elastic distortion are included as modifications of the moment of inertia tensor, where the magnitude of the distortion is parameterized by the Love number k2. The amplitudes of the principal periodic terms in the longitude of a point on the moon due to variations of the tide caused by the earth are discussed. A detailed derivation of the free wobble of the lunar spin axis about the axis of maximum moment of inertia is given. If the moon's rigidity is close to that of the earth there is no effect of elasticity on the rotation which can be measured with the laser ranging and, therefore, no elastic properties of the moon can be determined from variations in the rotation.
Analysis of Mariner 6 and 7 far-encounter (FE) pictures is discussed. The purpose of the studies was to devise ways to combine digital data from the full set of FE pictures so as to improve surface resolution, distinguish clouds and haze patches from permanent surface topographic markings, deduce improved values for radius, oblateness, and spin-axis orientation, and produce a composite photographic map of Mars. Attempts to measure and correct camera distortions, locate each image in the frame, and convert image coordinates to martian surface coordinates were highly successful; residual uncertainties in location were considerably less than one pixel. However, analysis of the data to improve the radius, figure, and axial tilt and to produce a composite map was curtailed because of the superior data provided by Mariner 9. The data, programs, and intermediate results are still available (1976), and the project could be resumed with little difficulty.
This paper discusses an error analysis for the Stanford Relativity experiment, designed to measure the precession of a gyroscope's spin-axis predicted by general relativity. Measurements will be made of the spin-axis orientations of 4 superconducting spherical gyroscopes carried by an earth-satellite. Two relativistic precessions are predicted: a 'geodetic' precession associated with the satellite's orbital motion and a 'motional' precession due to the earth's rotation. Using a Kalman filter covariance analysis with a realistic error model we have computed the error in determining the relativistic precession rates. Studies show that a slightly off-polar orbit is better than a polar orbit for determining the 'motional' drift.
The given review is concerned with a recent breakthrough in the investigation of polar-axis orientations and spin rates, and with the implications for the surface structure of cometary nuclei. The rotation data for twelve comets are summarized in a table. The progress achieved in the past few years has demonstrated that seemingly complex relations among observed physical and dynamical properties of comets can consistently be interpreted in terms of Whipple's (1950, 1951) model of a rotating icy-conglomerate nucleus. The nucleus, probably a few kilometers in diameter for an average comet, is believed to lose mass more or less continuously. Attention is given to the outgassing asymmetry, a formulation of the geometry of the directed ejection, and the role of rotation in cometary outbursts and splitting.
A general model is proposed which accounts for the dynamical evolution of the observed jets, envelopes and tail bands of periodic Comet Swift-Tuttle, the parent comet of the Perseid meteor stream, in terms of dust ejection from discrete active regions on the rotating nucleus. High-resolution drawings and measurements of cometary jets made upon the comet's first appearance in 1862 are used to infer a nuclear rotation period of 2.77 days, obliquity of 80 deg, and spin axis orientation with respect to the solar direction of 60 deg. The observed jets are attributed to eight discrete active regions covering not more than 1% of the cometary surface and producing bursts of duration of about 0.1 day. Calculations show that waning dust jets develop into envelopes and that old envelopes in turn become the observed tail bands. No evidence of truly violent explosions is found, and effects of active region outgassing on cometary orbital motion are negligible. Potential applications of the model to periodic Comet Halley and other comets are noted.
Spin-vector research on cometary nuclei is reviewed with emphasis on the actual determination of rotation period and spin-axis orientation. The rotation periods of 47 comets are compared with those of 41 asteroids with diameters of not more than 40 km. It is shown that the median periods for the comets is 15.0 hr as compared with 6.8 hr for the asteroids and that the preliminary distribution curve for the logarithms of the comet periods is not Gaussian and is flatter than the corresponding curve for the asteroids. Slow accumulation at low relative velocities is suggested as the cause of the longer comet rotation periods.
The present cometary activity model integrates feedback processes that involve the transport of heat, gas, and dust, as well as dust mantle development, and includes the effects of latitude, rotation, and spin axis orientation. Attention is given to the development, structural change, and distribution of dust mantles and their mutual interaction with ice surface temperature and gas and dust production. The results obtained suggest that an initially homogeneous, short period comet with a cosmic dust-to-water ice ratio, as well as typical orbit, rotation rate, and grain size distribution, would develop only a thin, less than 1 mm cyclic mantle at all points on the nucleus. Most H2O dust histories deduced from brightness data are noted to be in reasonable agreement with the model, allowing for uncertainty in radius and albedo. The exceptional case of Comet Encke is discussed.
Knowledge of the temperature distribution within comet nuclei is critical to the understanding of the state and behavior of comets. The present study is concerned with the temperature profile below the surface of the nucleus and below any dust mantle which may be present. With respect to the physics, the considered model is in some respects similar to that discussed by Weissman and Kiefer (1981, 1984). However, the new model is improved in various respects. It represents the first attempt to investigate directly the detailed nature of thermal profiles within a comet nucleus. Included in the investigation are calculations which consider the effects of variations in latitude, nucleus spin axis orientation, surface albedo, and thermal emissivity. It is shown that the application of the model, together with in situ measurements of temperatures within a cometary nucleus, could significantly constrain the range of possible subsurface physical properties.
An overview is presented for a set of simple and robust X-ray and gamma ray instruments which have both cosmic and solar objectives. The primary solar scientific objective is the study of the beaming of energetic electrons and ions in solar flares. The instrument will measure spectra and polarization of flare emissions up to 10 MeV. At X-ray energies both the directly emitted flux and the reflected albedo flux will be measured with a complement of six X-ray sensors. Each of these detectors will have a different high Z filter selected to optimize both the energy resolution and high rate capabilities in the energy band 10 to 300 keV. At energies greater than 100 keV seven 7.6 x 7.6 cm NaI and a set of 30 concentric plastic scattering detectors will record the spectra and polarization of electron bremsstrahlung and nuclear gamma rays. All of the components of the instrument are in existence and have passed flight tests for earlier space missions. The instrument will use a spinning solar oriented Scout spacecraft. The NaI detectors will act as a self-modulating gamma ray detector for cosmic sources in a broad angular band which lies at 90 degrees to the Sun-Earth vector and hence will scan the entire sky in 6 months.
Observational data obtained primarily during 1988 are analyzed and synthesized to develop a comprehensive physical model for the nucleus of Periodic Comet Tempel 2, one of the best studied members of Jupiter's family of short-period comets. It is confirmed that a previous investigation provided reliable information on the comet's spin-axis orientation, which implies and obliquity of 54 degrees of the orbit plane to the equatorial plane and which appears to have varied little - if at all - with time. This conclusion is critical for fitting a triaxial ellipsoid to approximate the figure of the nucleus.
Gravity Probe B launched in April 2004 and completed its science data collection in September 2005, with the objective of sub-milliarcsec measurement of two General Relativistic effects on the spin axis orientation of orbiting gyroscopes. Much of the technology required by GP-B has potential application in future missions intended to make precision measurements. The philosophical approach and experiment design principles developed for GP-B are equally adaptable to these mission concepts. This talk will discuss GP-B's experimental approach and the technological and philosophical lessons learned that apply to future experiments in fundamental physics. Measurement of fundamental constants to high precision, probes of short-range forces, searches for equivalence principle violations, and detection of gravitational waves are examples of concepts and missions that will benefit kern GP-B's experience.
The ARTEMIS mission, part of the THEMIS extended mission, is the first to fly spacecraft in the Earth-Moon Lissajous regions. In 2009, two of the five THEMIS spacecraft were redeployed from Earth-centered orbits to arrive in Earth-Moon Lissajous orbits in late 2010. Starting in August 2010, the ARTEMIS P1 spacecraft executed numerous stationkeeping maneuvers, initially maintaining a lunar L2 Lissajous orbit before transitioning into a lunar L1 orbit. The ARTEMIS P2 spacecraft entered a L1 Lissajous orbit in October 2010. In April 2011, both ARTEMIS spacecraft will suspend Lissajous stationkeeping and will be maneuvered into lunar orbits. The success of the ARTEMIS mission has allowed the science team to gather unprecedented magnetospheric measurements in the lunar Lissajous regions. In order to effectively perform lunar Lissajous stationkeeping maneuvers, the ARTEMIS operations team has provided orbit determination solutions with typical accuracies on the order of 0.1 km in position and 0.1 cm/s in velocity. The ARTEMIS team utilizes the Goddard Trajectory Determination System (GTDS), using a batch least squares method, to process range and Doppler tracking measurements from the NASA Deep Space Network (DSN), Berkeley Ground Station (BGS), Merritt Island (MILA) station, and United Space Network (USN). The team has also investigated processing of the same tracking data measurements using the Orbit Determination Tool Kit (ODTK) software, which uses an extended Kalman filter and recursive smoother to estimate the orbit. The orbit determination results from each of these methods will be presented and we will discuss the advantages and disadvantages associated with using each method in the lunar Lissajous regions. Orbit determination accuracy is dependent on both the quality and quantity of tracking measurements, fidelity of the orbit force models, and the estimation techniques used. Prior to Lissajous operations, the team determined the appropriate quantity of tracking measurements that would be needed to meet the required orbit determination accuracies. Analysts used the Orbit Determination Error Analysis System (ODEAS) to perform covariance analyses using various tracking data schedules. From this analysis, it was determined that 3.5 hours of DSN TRK-2-34 range and Doppler tracking data every other day would suffice to meet the predictive orbit knowledge accuracies in the Lissajous region. The results of this analysis are presented. Both GTDS and ODTK have high-fidelity environmental orbit force models that allow for very accurate orbit estimation in the lunar Lissajous regime. These models include solar radiation pressure, Earth and Moon gravity models, third body gravitational effects from the Sun, and to a lesser extent third body gravitational effects from Jupiter, Venus, Saturn, and Mars. Increased position and velocity uncertainties following each maneuver, due to small execution performance errors, requires that several days of post-maneuver tracking data be processed to converge on an accurate post-maneuver orbit solution. The effects of maneuvers on orbit determination accuracy will be presented, including a comparison of the batch least squares technique to the extended Kalman filter/smoother technique. We will present the maneuver calibration results derived from processing post-maneuver tracking data. A dominant error in the orbit estimation process is the uncertainty in solar radiation pressure and the resultant force on the spacecraft. An estimation of this value can include many related factors, such as the uncertainty in spacecraft reflectivity and surface area which is a function of spacecraft orientation (spin-axis attitude), uncertainty in spacecraft wet mass, and potential seasonal variability due to the changing direction of the Sun line relative to the Earth-Moon Lissajous reference frame. In addition, each spacecraft occasionally enters into Earth or Moon penumbra or umbra and these shadow crossings reduche solar radiation force for several hours. The effects of these events on orbit determination accuracy will be presented. In order to plan for upcoming stationkeeping maneuvers, the maneuver planning team must take the current orbit estimate, propagate it forward to the planned maneuver time, and determine the optimal maneuver to maintain the Lissajous orbit for one or more revolutions. The propagation is performed using a Runge-Kutta 7/8 integrator and typically the position and velocity uncertainty increases with propagation time, increasing the overall uncertainty of the orbit state at the maneuver execution time. The effect of orbit knowledge uncertainty on stationkeeping operations will be presented.