Lunar orbit determination in the presence of unmodeled accelerations
Artificial satellite lunar orbit calculation, representing unmodeled accelerations by first order Gauss-Markov sequence with time correlated and random components
Ingram, D. S.↗
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Surface photometry of celestial sources from a space vehicle - Introduction and observational procedures.
Consideration of the possibility of studying diffuse celestial sources of relatively low surface brightness such as the Milky Way, zodiacal light, and gegenschein from above the earth's atmosphere with equipment flown in artificial satellites. The techniques used for this purpose are reviewed, and some of the difficulties encountered in daytime observations from satellites by the use of a special photometer and polarimeter flown in the orbiting skylab observatory, OSO-6, are cited.
Roach, F. E.↗
A study of the variations in the thermosphere related to solar activity.
Densities derived from the drag of five artificial satellites and covering the time interval from 1958 to 1971 have been used to study the variations in the thermosphere arising from changes in solar activity. Exospheric temperatures derived from the densities by means of atmospheric models have been related to the 10.7-cm solar flux, in which the active-area component had been separated from the slow-varying clear-disk component by means of a relation between the flux and sunspot areas. When the day-to-day (27-day) variation is suppressed, the remaining slow temperature variation appears to be linearly related to the clear-disk flux component. If we also relate linearly the day-to-day temperature variations with the day-to-day variations of the flux, we find that the regression coefficient changes from 1 K at sunspot maximum to 2 K at low solar activity; a nearly constant coefficient is obtained by relating the temperature variations to the ratio of the active-area component to the clear-disk component of the flux.
Jacchia, L. G.↗
Dual transponder time synchronization at C band using ATS-3.
The use of artificial satellites for time synchronization of geographically distant clocks is hindered by problems due to satellite motion or equipment delay measurements. The ATS-3 satellite with its two C-band transponder channels helps solve these problems through techniques for synchronization to accuracies of tenths of microseconds. Portable cesium clocks were used to verify the accuracy of the described system.
Mazur, W. E., Jr.↗
Numerical averaging in orbit prediction.
This paper is a presentation of some useful aspects of a numerical averaging technique that has been applied with considerable success to the orbit prediction problem for artificial satellites. The method has been tested in a variety of situations wherein the satellite is subjected to combinations of perturbations for which adequate analytic theories are practically impossible. The technique provides many of the advantages of analytic averaging while retaining the ability to simulate the effects of any kind of small force that can be deterministically modeled. The theoretical basis for the method is straightforward but the details of its implementation are somewhat confusing and need some explanation. A particularly useful set of averaged equations is presented along with a description of an efficient algorithm for their solution. Examples of the advantages to be obtained by use of the method are included.
Uphoff, C.↗
Contribution to the theory of tidal oscillations of an elastic earth. External tidal potential
The differential equations of the tidal oscillations of the earth were established under the assumption that the interior of the earth is laterally inhomogeneous. The theory was developed using vectorial and dyadic symbolism to shorten the exposition and to reduce the differential equations to a symmetric form convenient for programming and for numerical integration. The formation of tidal buldges on the surfaces of discontinuity and the changes in the internal density produce small periodic variations in the exterior geopotential which are reflected in the motion of artificial satellites. The analoques of Love elastic parameters in the expansion of exterior tidal potential reflect the asymmetric and inhomogeneous structure of the interior of the earth.
Musen, P.↗
Lunar orbit determination in the presence of unmodeled accelerations
A technique for estimating the state of an artificial satellite in the presence of unmodeled accelerations is presented. The unmodeled acceleration is approximated by a first-order Gauss-Markov sequence which can be separated into a timewise-correlated component and a purely random component. Using this approximation, a sequential procedure for estimating the position, velocity, and the unmodeled acceleration is developed. The method is evaluated by reducing range-rate observations obtained by tracking the Apollo 10 and 11 spacecraft during the lunar-orbit phase of the mission. Numerical results are presented which show that the observation residual pattern lies within the observation noise standard deviation. The values of the estimated components of the unmodeled acceleration are repeatable from orbit to orbit within a given mission and from mission to mission when the same ground track is covered. Finally, the variation in the radial component of the unmodeled acceleration shows a high correlation with the reported location of the lunar surface mascons.
Ingram, D. S.↗
Computation of solar perturbations with Poisson series
Description of a project for computing first-order perturbations of natural or artificial satellites by integrating the equations of motion on a computer with automatic Poisson series expansions. A basic feature of the method of solution is that the classical variation-of-parameters formulation is used rather than rectangular coordinates. However, the variation-of-parameters formulation uses the three rectangular components of the disturbing force rather than the classical disturbing function, so that there is no problem in expanding the disturbing function in series. Another characteristic of the variation-of-parameters formulation employed is that six rather unusual variables are used in order to avoid singularities at the zero eccentricity and zero (or 90 deg) inclination. The integration process starts by assuming that all the orbit elements present on the right-hand sides of the equations of motion are constants. These right-hand sides are then simple Poisson series which can be obtained with the use of the Bessel expansions of the two-body problem in conjunction with certain interation methods. These Poisson series can then be integrated term by term, and a first-order solution is obtained.
Broucke, R.↗
Applications of radio interferometry to navigation
Radio astronomy experiments have demonstrated the feasibility of making precise position measurements using interferometry techniques. The application of this method to navigation and marine geodesy is discussed, and comparisons are made with existing navigation systems. The very long baseline technique, with a master station, can use either an artificial satellite or natural sources as position references; a high-speed data link is required. A completely ship-borne system is shown to be feasible, at the cost of poorer sensitivity for natural sources. A comparison of Doppler, delay and phase-track modes of operating a very long baseline configuration is made, as that between instantaneous measurements and those where a source can be tracked from horizon to transit. Geometric limitations in latitude and longitude coverage are discussed. The characteristics of natural radio sources, their flux, distribution on the sky, and apparent size are shown to provide a limit on position measurements precision. The atmosphere and frequency standard used both contribute to position measurement uncertainty by affecting interferometric phase.
Knowles, S. H.↗
GEODYN programmer's guide, volume 2, part 2
A computer program for executive control routine for orbit integration of artificial satellites is presented. At the beginning of each arc, the program initiates required constants as well as the variational partials at epoch. If epoch needs to be reset to a previous time, the program negates the stepsize, and calls for integration backward to the desired time. After backward integration is completed, the program resets the stepsize to the proper positive quantity.
Mullins, N. E.↗
Applications of PTTI to new techniques for determining crustal movements, polar motion, and the rotation of the earth
New extra-terrestrial techniques are discussed for geodesy and geodynamics include laser range measurements to the moon or to artificial satellites, Doppler measurements with the Transit satellite system, and both independent-clock and linked-antenna microwave interferometry. The ways in which PTTI measurements are used in these techniques will be reviewed, and the accuracies expected during the latter half of the 1970's will be discussed. At least 3 of the techniques appear capable of giving accuracies of 5 cm or better in each coordinate for many points on the earth's surface, and comparable accuracies for the earth's rotation and polar motion. For fixed stations or for sites a few hundred km apart, baseline lengths accurate to 1 cm may be achieved. Ways in which the complementary aspects of the different techniques can be exploited will be discussed, as well as how they tie in with improved ground techniques for determining crustal movements. Some recent results from the extra-terrestrial methods will be mentioned.
Bender, P. L.↗
A radio picture of the earth
A technique called passive microwave remote sensing can be used to obtain a new view of the planet earth by means of radio telescopes carried aboard artificial satellites. An important relationship between the observed radio brightness temperature and the surface conditions provides the basis for the new technique. A radio image is presented of the entire earth on the basis of Nimbus microwave-image data taken January 12-16, 1973.
Webster, W. J., Jr.↗
Issues in gravitational wave detection with space missions
Two masses freely orbiting in the solar system, separated by several astronomical units, are proposed as antennas for the detection of monochromatic gravitational radiation emitted by double stars. If one of these masses was an artificial satellite, then relative acceleration could be measured by the Doppler effect on the satellite radio signal. A highly accurate clock would have to be invented and incorporated into the tracking network in order for this plan to be feasible.
Davies, R. W.↗
Study of the decay and recovery of orbiting artificial space objects
The reentry of earth-orbiting space objects unconsumed in the atmosphere represents a potential hazard to populated areas of the earth. The Smithsonian Astrophysical Observatory has conducted a program called Moonwatch, whose purposes were to observe orbiting artificial satellites and reentries of space objects and, if possible, to recover and analyze reentered pieces. In addition, through observations of low-perigee objects, data obtained by Moonwatchers have been instrumental in defining some of the factors affecting satellite decay. The objectives of the program are presented, and the problems that enter into satellite-orbit and decay predictions are addressed. Moonwatchers contributed substantially to increasing an overall prediction capability, and some of the specific achievements over the 6-year period are cited.
Source record↗
Multistep methods of numerical integration using back-corrections
A class of linear multistep methods is proposed for the solution of the equations of motion of certain dynamical systems encountered in celestial mechanics and astrodynamics. These methods are distinguished from the classical predictor-corrector methods in that they permit 'back-corrections' of the solution to be made. As the integration advances in time, the numerical solution is corrected or improved at certain points in the past. The enhanced numerical stability of these methods allows the meaningful application of high-order algorithms. Consequently, step sizes larger than those attainable with the classical methods may be adopted, and greater overall efficiency may be realized. These methods are applied to the problem of determining the orbit of an artificial satellite, and the results are compared with those obtained using classical methods.
Feagin, T.↗
Optimal perturbation models for averaged orbit generation
Averaging techniques applied to the variation of parameters (VOP) formulation of the equations of motion are being investigated as methods for long-term prediction of artificial satellite orbits. Analytically averaged equations were compared with numerically averaged equations with respect to accuracy and efficiency for computation of zonal and nonresonant third-body perturbations. Numerically averaged equations were also evaluated for computation of long-period effects from resonant third-body, tesseral harmonic, and atmospheric drag perturbations. Guidelines will be presented for application of averaged VOP equations to a broad class of orbits.
Long, A. C.↗
Morphology of Arabidopsis grown under chronic centrifugation and on the clinostat
Morphological measurements were made on populations of Arabidopsis thaliana grown from seed for 21 days under essentially constant environmental conditions except for the influence of gravitational or centrifugal accelerations. Growth conditions were what had been proposed for experiments in an artificial satellite. Observations are reported for plants grown at normal 1-g upright or on horizontal clinostats and for plants grown on a centrifuge. Increased g-force, up to 15 times normal, was found to have significant but small effects on some morphological end points. The plants' sensitivity to the magnitude of the g-force was much less than to its vector direction. Data from centrifuge experiments were extrapolated to zero-g to predict a set of morphological characteristics of a plant developing in the satellite environment. As an alternative means of predicting properties of a zero-g plant, characteristics of plants grown on horizontal clinostats were measured. The results of these two predictive methods were not in agreement. Clinostat grown plants were morphologically distinct from upright stationary controls.
Brown, A. H.↗
The method of averages applied to the KS differential equations
A new approach for the solution of artificial satellite trajectory problems is proposed. The basic idea is to apply an analytical solution method (the method of averages) to an appropriate formulation of the orbital mechanics equations of motion (the KS-element differential equations). The result is a set of transformed equations of motion that are more amenable to numerical solution.
Graf, O. F., Jr.↗