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Planetary motion zero-rank effects numerical integration, using Hill secular perturbation method and trace of dyadics
Planetary orbit change in major axis, eccentricity and inclination induced by passing star and calculated with central limit theorem
Integration of equations of planetary peturbations in rectangular coordinates
Hill method of secular perturbations and determination of zero-rank effects in nonsingular vectorial elements of motion of planets, comets, and satellites
In an investigation of the properties of the quasi-geostrophic Eliassen-Palm (EP) flux for planetary-scale motions, particular attention is given to the relation between the EP flux divergence and the meridional flux of eddy potential vorticity, and the relations between the EP flux, group velocity, and the zonal mean refractive index in the Wentzel-Kramers-Brillouin-Jeffreys limit. This latter diagnostic has appeared in a number of different forms as that quantity whose gradient determines the refraction of group velocity paths or EP flux trajectories. The question is considered which, if any, of these forms holds for planetary scale motions. In this investigation, a planetary-scale motion is formally defined to be one for which Burger's (1958) quasigeostrophic theory is appropriate.
An unusual insect-like vehicle designed for planetary surface exploration is made the occasion for a discussion of control concepts in path selection, hazard detection, obstacle negotiation, and soil sampling. A control scheme which actively articulates the pitching motion between a single-loop front module and a dual loop rear module leads to near optimal behavior in soft soil; at the same time the vehicle's front module acts as a reliable tactile forward probe with a detection range much longer than the stopping distance. Some optimal control strategies are discussed, and the photos of a working scale model are displayed.
Studies of planets in binary star systems are especially important because it was estimated that about half of binary stars are capable of supporting habitable terrestrial planets within stable orbital ranges. One-planet binary star systems (OBSS) have a limited analogy to objects studied in atomic/molecular physics: one-electron Rydberg quasimolecules (ORQ). Specifically, ORQ, consisting of two fully stripped ions of the nuclear charges Z and Z′ plus one highly excited electron, are encountered in various plasmas containing more than one kind of ion. Classical analytical studies of ORQ resulted in the discovery of classical stable electronic orbits with the shape of a helix on the surface of a cone. In the present paper we show that despite several important distinctions between OBSS and ORQ, it is possible for OBSS to have stable planetary orbits in the shape of a helix on a conical surface, whose axis of symmetry coincides with the interstellar axis; the stability is not affected by the rotation of the stars. Further, we demonstrate that the eccentricity of the stars’ orbits does not affect the stability of the helical planetary motion if the center of symmetry of the helix is relatively close to the star of the larger mass. We also show that if the center of symmetry of the conic-helical planetary orbit is relatively close to the star of the smaller mass, a sufficiently large eccentricity of stars’ orbits can switch the planetary motion to the unstable mode and the planet would escape the system. We demonstrate that such planets are transitable for the overwhelming majority of inclinations of plane of the stars’ orbits (i.e., the projections of the planet and the adjacent start on the plane of the sky coincide once in a while). This means that conic-helical planetary orbits at binary stars can be detected photometrically. We consider, as an example, Kepler-16 binary stars to provide illustrative numerical data on the possible parameters and the stability of the conic-helical planetary orbits, as well as on the transitability. Then for the general case, we also show that the power of the gravitational radiation due to this planet can be comparable or even exceed the power of the gravitational radiation due to the stars in the binary. This means that in the future, with a progress of gravitational wave detectors, the presence of a planet in a conic-helical orbit could be revealed by the noticeably enhanced gravitational radiation from the binary star system.
Three transiting circumbinary planets (Kepler-16 b, Kepler-34 b, and Kepler-35 b) have recently been discovered from photometric data taken by the Kepler spacecraft. Their orbits are significantly non-Keplerian because of the large secondary-to-primary mass ratio and orbital eccentricity of the binaries, as well as the proximity of the planets to the binaries. We present an analytic theory, with the planet treated as a test particle, which shows that the planetary motion can be represented by the superposition of the circular motion of a guiding center, the forced oscillations due to the non-axisymmetric components of the binary's potential, the epicyclic motion, and the vertical motion. In this analytic theory, the periapse and ascending node of the planet precess at nearly equal rates in opposite directions. The largest forced oscillation term corresponds to a forced eccentricity (which is an explicit function of the parameters of the binary and of the guiding center radius of the planet), and the amplitude of the epicyclic motion (which is a free parameter of the theory) is the free eccentricity. Comparisons with direct numerical orbit integrations show that this analytic theory gives an accurate description of the planetary motion for all three Kepler systems. We find that all three Kepler circumbinary planets have nonzero free eccentricities.
The radar measurements phase of the lunar studies involving reflectivity and topographic mapping of the visible lunar surface was ended in December 1972, but studies of the data and production of maps have continued. This work was supported by Manned Spacecraft Center, Houston. Topographic mapping of the equatorial regions of Mars has been carried out during the period of each opposition since that of 1967. The method comprised extended precise traveling time measurements to a small area centered on the subradar point. As measurements continued, planetary motions caused this point to sweep out extensive areas in both latitude and longitude permitting the development of a fairly extensive topographical map in the equatorial region. Radar observations of Mercury and Venus have also been made over the past few years. Refinements of planetary motions, reflectivity maps and determinations of rotation rates have resulted.
We present the MOA Collaboration light-curve data for the planetary microlensing event OGLE-2015-BLG-0954, which was previously announced in a paper by the KMTNet and OGLE Collaborations. The MOA data cover the caustic exit, which was not covered by the KMTNet or Optical Gravitational Lensing Experiment (OGLE) data, and they provide a more reliable measurement of the finite source effect. The MOA data also provide a new source color measurement that reveals a lens-source relative proper motion of μ {sub rel} = 11.8 ± 0.8 mas yr{sup −1}, which compares to the value of μ {sub rel} = 18.4 ± 1.7 mas yr{sup −1} reported in the KMTNet-OGLE paper. This new MOA value for μ {sub rel} has an a priori probability that is a factor of ≳100 times larger than the previous value, and it does not require a lens system distance of D {sub L} < 1 kpc. Based on the corrected source color, we find that the lens system consists of a planet of mass 3.4{sub −1.6}{sup +3.7} M{sub Jup} orbiting a 0.30{sub −0.14}{sup +0.34} M{sub ⊙} star at an orbital separation of 2.1{sub −1.0}{sup +2.2} au and a distance of 1.2{sub −0.5}{sup +1.1} kpc.
Planetary motion and heat loss during rotation analyzed using energy and motion equations
It is shown that the magnetohydrodynamic conditions of the Venus ionosphere near the terminator favor convection of a magnetic field rather than diffusion. Consequently, any planetary magnetic field which Venus may possess will be strongly affected by the global antisunward flow of the ionosphere which has been revealed by the Pioneer-Venus retarding potential analyzer. The magnetic flux from an internal magnetic field will accumulate in the night hemisphere. Details of the structure and dynamics of such accumulations depend on particular details of the magnetic field source and the time-dependent plasma flow pattern, but a simple interpretation of observational data yields a magnetic dipole moment of 7 x 10 to the 20th cu cm directed along the planet spin vector.
Interplanetary space is pervaded by a supersonic 'solar wind' plasma; five planets, in addition to the earth, have magnetic fields of sufficient strength to form the cometlike cavities called 'magnetospheres'. Comparative studies of these structures have indicated the specific environmental factor that can result in dramatic differences in the behavior of any pair of magnetospheres. Although planetary magnetospheres are large enough to serve as laboratories for in situ study of cosmic plasma and magnetic field behavior effects on particle acceleration and EM emission, much work remains to be done toward relating magnetospheric physics results to the study of remote astrophysical plasmas.
Ephemeris magnetic tape system for predicting Moon and planetary motions and positions
A method of solution of the equations of planetary motion is described. It consists of the use of numerical general perturbations in orbital elements and in rectangular coordinates. The solution is expanded in Fourier series in the mean anomaly with the aid of harmonic analysis and computerized series manipulation techniques. A detailed application to the relativistic motion of the planet Mercury is described both for Schwarzschild and isotropic coordinates.
The tumbling motion of vehicles entering planetary atmospheres is analyzed. A differential equation governing the tumbling motion, its arrest, and the subsequent oscillatory motion is obtained and identified as the equation for the fifth Painleve transcendant. An approximate analytical solution for the transcendant is derived. Comparisons with results obtained from numerical integration of the exact equations of motion indicate that the solution for the angle-of-attack history is sufficiently accurate to be of practical use.
Equations and charts are presented which permit rapid estimation of propulsion system performance requirements for some typical deep space missions. The simplicity results from use of gravity-free equations of motion, which are shown to yield good approximations to trip times obtained with solar gravity and planetary motion included. The agreement is satisfactory for missions that do not enter or depart from low orbits about the major planets. A number of advanced propulsion concepts for which performance estimates are available are compared with respect to their capability for fly-by, rendezvous, and round-trip planetary missions. Based on these estimates, the gas-core nuclear fission rocket and the pulsed fusion rocket yield the fastest trip times to the near planets. For round trips to Jupiter and beyond, the controlled fusion rocket shows progressively superior capabilities. Several propulsion concepts based on use of impinging laser beams are found to be noncompetitive with the other advanced concepts for deep space missions.
The study of exoplanets (planets orbiting other stars) is revolutionizing the way we view our universe. High-precision photometric data provided by the Kepler Space Telescope (Kepler) enables not only the detection of such planets, but also their characterization. This presents a unique opportunity to apply Bayesian methods to better characterize the multitude of previously confirmed exoplanets. This paper focuses on applying the EXONEST algorithm to characterize the transiting short-period-hot-Jupiter, HAT-P-7b (also referred to as Kepler-2b). EXONEST evaluates a suite of exoplanet photometric models by applying Bayesian Model Selection, which is implemented with the MultiNest algorithm. These models take into account planetary effects, such as reflected light and thermal emissions, as well as the effect of the planetary motion on the host star, such as Doppler beaming, or boosting, of light from the reflex motion of the host star, and photometric variations due to the planet-induced ellipsoidal shape of the host star. By calculating model evidences, one can determine which model best describes the observed data, thus identifying which effects dominate the planetary system. Presented are parameter estimates and model evidences for HAT-P-7b.