A modification of Herrick's solution of the two-body problem for all cases
Transcendental functions and Kepler equation modifications in two body problem
Goodyear, W. H.↗
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How to assemble a Keplerian processor
Computer program for two body problem literal series expansions using Kepler functions with Bessel and Poisson series operation
Broucke, R.↗
Tests of the equivalence principle and gravitation theory using solar system bodies
The M sub g/M sub i ratio (ratio of body acceleration to gravitation field) of celestial bodies was measured. Deep probes of the post-Newtonian structure of gravitational theories are indicated. Kepler's third law is considered for the Sun-Jupiter system.
Nordtvedt, K., Jr.↗
Lunar gravity derived from long-period satellite motion, a proposed method
A method was devised to determine the spherical harmonic coefficients of the lunar gravity field. The method consists of a two-step data reduction and estimation process. Pseudo-Doppler data were generated simulating two different lunar orbits. The analysis included the perturbing effects of the L1 lunar gravity field, the earth, the sun, and solar radiation pressure. Orbit determinations were performed on these data and long-period orbital elements were obtained. The Kepler element rates from these solutions were used to recover L1 lunar gravity coefficients. Overall results of the experiment show that lunar gravity coefficients can be accurately determined and that the method is dynamically consistent with long-period perturbation theory.
Ferrari, A. J.↗
Bistatic-radar investigation
A bistatic-radar study during the Apollo 15 flight is reviewed, with the orbiting command module as one terminal. Bistatic-radar slopes are compared to geological maps of Copernicus and Riphaeus mountain regions and Kepler region. Basic theory is discussed, including the radar echoes composed of the sum of the reflections from the moon area that is mutually visible from the spacecraft and earth. A signal receiving system and data processing system are outlined schematically.
Howard, H. T.↗
The VLBI time delay function for synchronous orbits
The VLBI is a satellite tracking technique that to date was applied largely to the tracking of synchronous orbits. These orbits are favorable for VLBI in that the remote satellite range allows continuous viewing from widely separated stations. The primary observable, geometric time delay is the time difference for signal propagation between satellite and baseline terminals. Extraordinary accuracy in angular position data on the satellite can be obtained by observation from baselines of continental dimensions. In satellite tracking though the common objective is to derive orbital elements. A question arises as to how the baseline vector bears on the accuracy of determining the elements. Our approach to this question is to derive an analytic expression for the time delay function in terms of Kepler elements and station coordinates. The analysis, which is for simplicity based on elliptic motion, shows that the resolution for the inclination of the orbital plane depends on the magnitude of the baseline polar component and the resolution for in-plane elements depends on the magnitude of a projected equatorial baseline component.
Rosenbaum, B.↗
Eleventh order resonance terms in the geopotential from the orbit of Vanguard 3
The orbit of Vanguard 3 (1959-7A) is strongly resonant with 11th order and odd degree terms in the geopotential. It affords an excellent opportunity to determine a significant linear constraint between these terms. Tracking data on this satellite (in the form of mean Kepler elements) are analyzed over a 3 1/2 year period in the early 1960's, which ends with the orbit having just passed through perfect commensurability. The eccentricity and inclination show the deep resonance variations (up to 0.0002 in e and .02 deg in i) with great clarity. Previous and current geopotential solutions fail to explain these perturbations.
Wagner, C. A.↗
The 15th order resonance on the decaying orbit of TETR-3
The orbit of TETR-3 (1971-83B), inclination: 33 deg, passed through resonance with 15th order geopotential terms in February 1972. The resonance caused the orbit inclination to increase by 0.015 deg. Analysis of 48 sets of mean Kepler elements for this satellite in 1971-1972 (across the resonance) has established strong constraints for high degree, 15th order gravitational terms (normalized). This result combined with previous results on high inclination 15th order and other resonant orbits suggests that the coefficients of the gravity field beyond the 16th degree are significantly smaller than Kaula's rule.
Wagner, C. A.↗
Profiles of emission lines in Be stars. II - Interpretation of the long-period V/R variation.
Investigation of the long-period V/R variation in some Be stars studied by McLaughlin (1966) and others, based on the assumption that the variation is caused by the apsidal motion of an elliptical ring in which the emitting atoms revolve around the star according to Kepler's laws of motion. The results indicate that the behavior of the V/R variation depends upon both the eccentricity and the lateral extent of the gaseous ring. However, if the ring is narrower than a certain limit, the dependence on the width is negligible. In such a case, the eccentricity of the ring can be determined by the observed amplitude of the V/R variation. Based on this model, the radial-velocity curves of both emission edges and central absorption are derived. It is found that they all have the same amplitude, which also depends on the eccentricity, and that all are changing in phase with the V/R variation.
Huang, S.-S.↗
Mars gravity derived from the long-period motion of Mariner 9
The spherical harmonic coefficients in the Mars gravity field are determined using a two-stage filtering process. In the first stage, a weighted least-squares orbit determination processor is applied to Mariner 9 radio data to estimate the mean Kepler elements of each orbit. A finite difference method is then used to generate orbital element rates. In the second stage, the gravity coefficients are determined using another weighted least-squares processor which fits the long period Lagrange perturbation equations to the estimated rates. The resulting gravity potential and associated equipotential surface is presented and error sources discussed. Gravity field results are applied to various physical properties of Mars, such as moments of inertia.-
Ferrari, A. J.↗
Eleventh-order geopotential resonance on the orbit of Vanguard 3
The orbit of Vanguard 3 (1959-7A) is strongly resonant with eleventh-order and odd degree terms in the geopotential. It affords an excellent opportunity to determine a significant linear constraint between these terms. Tracking data on this satellite (in the form of mean Kepler elements) are analyzed over a 3.5-year period in the early 1960s, which ends with the orbit having just passed through perfect commensurability. The eccentricity e and inclination I show the deep resonance variations (up to .0002 in e and 0.02 deg in I) with great clarity. Previous and current geopotential solutions fail to explain these perturbations. A constraint for the deep resonant terms is determined in fully normalized harmonics.
Wagner, C. A.↗
Geodetic results from ISAGEX data
Laser and camera data taken during the International Satellite Geodesy Experiment (ISAGEX) were used in dynamical solutions to obtain center-of-mass coordinates for the Astro-Soviet camera sites at Helwan, Egypt, and Oulan Bator, Mongolia, as well as the East European camera sites at Potsdam, German Democratic Republic, and Ondrejov, Czechoslovakia. The results are accurate to about 20m in each coordinate. The orbit of PEOLE (i=15) was also determined from ISAGEX data. Mean Kepler elements suitable for geodynamic investigations are presented.
Marsh, J. G.↗
ATS-5 trilateration support
The development of an L-band trilateration network capable of locating the ATS-5 satellite, determining the satellite's orbital elements, and predicting the satellite position was investigated. An automatic tone-code ranging transponder was used to compare ranging measurements and communications reliability for the VHF and L-band. The L-band transponder network, analytical techniques, and the determination of the Kepler orbit parameters are described along with the calibration procedures, operation procedures, and verification of trilateration position.
Brisken, A. F.↗
The new Martian nomenclature of the International Astronomical Union
A new nomenclature for Martian regions and topographic features uncovered by Mariner 9, as officially adopted by the International Astronomical Union, is described. About 180 craters generally of diameters greater than 100 km have been named, as well as 13 classes of topographic features designated catena, chasma, dorsum, fossa, labyrinthus, mensa, mons, patera, planitia, planum, tholus, vallis, and vastitas. In addition seven craters and the Kepler Dorsum are named on Phobos, and two craters on Deimos. Coordinates and maps of each named feature are displayed.
De Vaucouleurs, G.↗
Computer assisted expansion of 1/Delta series with Newton iteration
The Newton iteration method has been widely applied to the solution of various equations such as Kepler's equation. In this study it is used in planetary and satellite theory as a general procedure for Fourier series inversion. The method is used for the construction of the 1/Delta series either in literal form or in numerical form with small eccentricities and inclinations substituted in advance. This usually results in very compact series. With the Newton iteration procedure and a computerized series manipulation technique, the Fourier series of 1/Delta of the mutual perturbations among most natural satellites can be easily constructed.
Chao, C. C.↗
The vertical structure and thickness of Saturn's rings
The steady state thickness and vertical structure of Saturn's rings are discussed with regard to whether a collapse to a monolayer due to particle collisions may be prevented by various mechanisms. The differences between thick rings and wavy monolayers are outlined and used to show that such coherent perturbations to the rings as satellite and solar gravitational effects would produce a wavy monolayer while such dispersive mechanisms as meteoroid impact, radiation pressure, Kepler shear and radial spreading, which would produce the random particle motions necessary to maintain a thick layer, are probably insignificant. Given a typical power law distribution of particle sizes, it is found that gravitational scattering of small particles by large ones would maintain a ring thickness of several times the radius of the largest particles. A steady state ring thickness of 20 to 50 meters, derived from energy considerations, would imply a maximum particle size of a few meters.
Cuzzi, J. N.↗
A search for stellar remnants of supernovae
The slitless spectra of the stars in the central regions of six galactic supernova remnants Cas A, Kepler, Tycho, SN 1006, RCW 86, and the Cygnus Loop were obtained with the prime focus transmission gratings at the 4M telescopes on Kitt Peak and Cerro Tololo. It was found that no stellar remnant with an unusually blue or peculiar spectrum is present in any of the remnants down to the limit of m sub pg of 18.5. Except for the Cygnus Loop, the area searched in each remnant is large enough that objects with transverse velocities of 1000 km/s would be well within the field. The results are also compared with a computation of emission from gas near a neutron star and with the unpulsed emission from the Crab pulsar; in both cases upper limits were set which place constraints on a possible condensed stellar remnant.
Fesen, R. A.↗
Accuracy of gravitational physics tests using ranges to the inner planets
A number of different types of deviations from Kepler's laws for planetary orbits can occur in nonNewtonian metric gravitational theories. These include secular changes in all of the orbital elements and in the mean motion, plus additional periodic perturbations in the coordinates. The first order corrections to the Keplerian motion of a single planet around the Sun due to the parameterized post Newtonian theory parameters were calculated as well as the corrections due to the solar quadrupole moment and a possible secular change in the gravitational constant. The results were applied to the case of proposed high accuracy ranging experiments from the Earth to a Mercury orbiting spacecraft in order to see how well the various parameters can be determined.
Ashby, N.↗