Capture Orbits Research Articles

Kaonic hydrogen - past puzzles

The experimental study of low energy kaon–nucleon interactions began in the ’50s when accelerators reached an energy at which kaons could first be produced in the laboratory. Hydrogen-, deuterium-, and helium-filled bubble chambers were used to study both negative and positive kaon scattering and absorption reactions. Where available, beams of negative kaons were stopped in targets ranging from helium to carbon – and later up to uranium – for the purpose of studying the X-rays resulting from the de-excitation of the kaon from a high capture orbit down to the lowest orbit reached. The energy of this lowest orbit of these so-called exotic atoms was shifted in energy and absorption-broadened by the kaon–nucleus strong interaction. Hence, the X-ray spectrum could be used to measure both the shift and width of this lowest level. X-ray intensity ratios of the feeding transition to this lowest transition could also be used to deduce the absorption width of the higher level. However, in the late ’70s, no experimental data yet existed for the simplest and most fundamental of these – the exotic kaonic hydrogen isotopes – for reasons discussed below. The optical model theory of exotic hadronic atoms relating low-energy scattering data to shifts and widths was well developed for pions in the ’60s by the Ericsons [1], thus the formalism for kaons, which are also spinless particles, was put in place. Knowing the shift and width, the complex scattering length could then be deduced and compared with scattering data. Physicists embroiled in the excitement of both the experiments and the theoretical underpinnings prepared many excellent reviews. They do far better justice to this period of kaonic hydrogen pre-history than would I. The reader is referred to Burhop [2] and the references therein for the early period up to the late ’60s, and to Seki and Wiegand for kaonic and other exotic atom data up to the mid-’70s [3]. Chris Batty reviewed both theory and experimental results on a broad range of exotic atoms in the late ’70s (and updated it recently [4]). H. Poth [5] provided a valuable compilation of hadronic atom data in 1979. A bibliography of exotic atoms from 1939 to 1982 was produced by Dezso Horvath and Richard Lambrecht [6] in 1984. The state of theory up to the early ’80s has been well presented by Florian Scheck [7].

Mercury sun-synchronous polar orbiter with a solar sail

An innovative mission MESSAGE (MErcury Solar Sailing Advanced Geoscience Exploration) is proposed where a solar sail spacecraft of about 240kg total mass delivers a limited but highly valuable science payload to a sun-synchronous Mercury orbit in 312 years. Corresponding operation near the terminator offers favorable thermal and remote sensing conditions for the considered instruments. Since Mercury is still the poorest explored and least known planet of the inner solar system, there is a high level of scientific interest for further exploration. Science objectives and a potential payload package of about 20 kg for the proposed solar sail mission considering the special orientation and geometry of a sun-synchronous orbit about Mercury will be discussed. Determination of the elemental composition of the Hermian surface with respect to major rock forming elements and volatiles could be carried out by a gamma-ray spectrometer. In the current mission architecture the spacecraft will be launched into an Earth escape trajectory with a relatively low-cost launch option such as TAURUS or ROCKOT with upper stages. The sail is used as a transportation means for the interplanetary transfer, for orbit capture upon Mercury arrival, and subsequent adjustment of a sun-synchronous orbit about the planet near the terminator. Due to Mercury's 3:2 spin-orbit coupling the eccentric polar orbit of 200 km × 6350 km altitude with periapsis above the north pole will allow complete coverage of the planet's surface within two Mercury years. Optimized interplanetary trajectories as well as simulations of the orbit about Mercury will be shown. A conceptual design of the spacecraft including the deployment concept of the square sail of an estimated size of about 86m × 86m and its support structure will be presented. The lightweight booms are proposed to be manufactured of carbon fibre reinforced plastic profiles that can be stored on a central hub prior to deployment. Possible sail film materials, coatings and folding concepts will be discussed. In a more advanced scenario two identical solar sails could be launched in a stacked configuration by a Med-Lite to realize a dual sun-synchronous Mercury orbiter mission.

The Role of Chaos in the Circularization of Tidal Capture Binaries. II. Long-Time Evolution

view Abstract Citations (81) References (28) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS The Role of Chaos in the Circularization of Tidal Capture Binaries. II. Long-Time Evolution Mardling, Rosemary A. Abstract We examine the long-time dynamical evolution of binaries formed by tidal capture using a self-consistent normal mode analysis. An efficient method for handling very long period orbits is developed which allows us to examine the highly eccentric phase following capture. We start with an adiabatic analysis and show that the orbital eccentricity performs a random walk between the initial eccentricity (≥ 1) and some nonzero minimum value. The existence of a minimum eccentricity in turn restricts the maximum tidal energy the system is capable of acquiring. We then examine dissipative systems by introducing an artificial mode damping mechanism and show that tidal capture binaries go through two distinct phases. Following capture is a short violent chaotic phase during which the dynamical behavior is as described by the adiabatic analysis. Huge tides are raised, and the tidal luminosity is likely to be large if nonlinear dissipative processes are efficient. Given that the binary survives this phase, it must dissipate a prescribed amount of energy before it enters the second phase during which the orbital behavior is no longer chaotic and the orbital eccentricity varies quasi-periodically. During this long quiescent phase, the tides are small and the binary circularizes only via dissipative processes. The prescribed energy loss and the eccentricity at the beginning of this phase depend on the periastron separation at capture. For example, for equal mass stars with an initial periastron separation of 3 stellar radii, the system starts this phase with an eccentricity of 0.8. For such a system, the quiescent circularization phase is estimated to be at least 107 yr, in contrast to a circularization time predicted by the standard model of 10 yr (McMillan, McDermott, & Taam 1987). Since capture orbits are chaotic, there exists the possibility of a binary returning to an unbound state. We show that the majority of tidal capture binaries are stable against self-ionization. We discuss the various destructive processes which the stars must be stable against during the chaotic phase in order to enter the quiescent phase intact. We also discuss the implications for the formation of low-mass X-ray binaries and related objects and the role of tidal capture binaries in globular cluster evolution. Publication: The Astrophysical Journal Pub Date: September 1995 DOI: 10.1086/176179 Bibcode: 1995ApJ...450..732M Keywords: CELESTIAL MECHANICS; STELLAR DYNAMICS; CHAOS; GALAXY: GLOBULAR CLUSTERS: GENERAL; STARS: BINARIES: CLOSE; STARS: PULSARS: INDIVIDUAL ALPHANUMERIC: PSR 2127+11C; X-RAYS: STARS full text sources ADS | data products SIMBAD (2) Related Materials (1) Part 1: 1995ApJ...450..722M

Mercury orbiter with a solar sail spacecraft

A mission to Mercury is discussed, where a solar sail spacecraft with a total mass of about 500 kg delivers a scientific payload of approximately 50 kg to an orbit about Mercury. As knowledge of this planet is very limited, a Mercury orbiter mission is proposed by scientists since many years. The solar sail, a deployable light-weight structure, is used for spiraling to Earth escape, for interplanetary transfer, and orbit capture upon Mercury arrival, while flight times of moderate length are still possible. This strategy allows very low Earth departure and Mercury arrival energies, and can significantly reduce the total mass to be delivered by the Earth-based launch system in comparison to conventional missions using chemical propulsion. Therefore, a low-cost launch option may be considered. Moreover, a sun-synchronous orbit about Mercury can be accomplished with the sail, bearing considerable advantages for the spacecraft's thermal environment and suitable conditions for remote sensing. Solar sails are promising future low-cost transportation systems and may also be used across a wide range of other planetary missions.

Motions close to escapes in the rhomboidal four body problem

In this work we study escape and capture orbits in the planar rhomboidal 4-body problem in a level of constant negative energy. There are only two different values of the masses here. By using numerical analysis, we show certain transversal intersections of the invariant manifolds of parabolic orbits. We then introduce Symbolic Dynamics when the mass ratio is small, and when it is close to one. In the first case the escapes or captures predominate in the direction of one of the diagonals of the rhombus, while in the second case we find solutions escaping or being captured in the direction of both possible diagonals.

Capture orbits and melnikov integrals in the planar three-body problem

The separatrix between bounded and unbounded orbits in the three-body problem is formed by the manifolds of forward and backward parabolic orbits. In an ideal problem these manifolds coincide and form the boundary between the sets of bounded and unbounded orbits. As a mass parameter increases the movement of the parabolic manifolds is approximated numerically and by Melnikov's method. The evidence indicates that for positive values of the mass parameter these manifolds no longer coincide, and that capture and oscillatory orbits exist.

Classes of orbits in the main problem of satellite theory

We consider the main problem in satellite theory restricted to the polar plane. For suitable values of the energy the system has two unstable periodic orbits. We classify the trajectories in terms of their ultimate behavior with respect these periodic orbits in: oscillating, asymptotic and capture orbits. We study the energy level set and the existence and properties of the mentioned types of motion.

Heteroclinic Phenomena in the Isosceles Three-Body Problem

When two of the three particles have equal masses, the three-dimensional three-body problem has a subsystem consisting of motions for which the configuration of the particles is always an isosceles triangle. This subsystem has only two degrees of freedom. Geometrical methods are used to construct an invariant set containing a variety of periodic orbits which exhibit close approaches to triple collision and wild changes of configuration. Furthermore, orbits heteroclinic between these periodic orbits as well as oscillation and capture orbits are found. The whole invariant set is described using symbolic dynamics.

Parabolic orbits in the planar three body problem

It is not known whether there exist oscillatory and capture orbits in the planar 3-body problem. Sitnikov [6] proved such orbits exist for the restricted 3-body problem. Alekseev [I] extended this work and related it to the existence of homoclinic orbits. McGehee and Easton ]3] studied a model problem closely related to the planar 3-body problem and proved the existence of oscillatory and capture orbits near certain orbits biasymptotic to an invariant 3-sphere. The goal of this paper is to construct an invariant 3-sphere “at infinity” in the planar 3-body problem and to prove that the stable and unstable manifolds of this sphere are Lipschitz manifolds. To complete the study of oscillatory and capture orbits one must investigate the way in which the stable and unstable manifolds of the 3-sphere intersect each other. This is a difficult question which is not treated here. However, using methods of Melnikov and using one of the masses as a perturbation parameter such an investigation might be possible. The stable manifold theorem which is proven here is not standard since the invariant 3-sphere is not hyperbolic. Geometric methods of McGehee [ 4 ] are extended and applied to obtain the theorem. A special case of the system of equations that we study has the form J, =x: dY)lX, + E,(x, Y)L f, = 4 dY>l-x* + E,(x, Y)L (0.1) 4’ =

Gravitational wave scattering

We consider scattering of gravitational radiation incident axially on Kerr black holes. A Jeffreys-Wentzel-Kramers-Brillouin formulation applied to a combination of the Teukolsky-Press and Chandrasekhar-Detweiler formalisms allows the integration for relatively large frequencies $|M\ensuremath{\omega}|$. Many interesting structures arise in the resultant cross sections. These include glories, dips in the cross section "due to" geometrical-optics orbits near the capture orbits, preferential polarization of the scattered wave, and very strong backward scattering when the conditions for superradiance hold.

Secular changes in Jovian eccentricity: Effect on the size of capture orbits

The model of dynamic capture proposed by Bailey based on the elliptic restricted three-body problem is examined in the light of eccentricity variations in the orbits of the primaries. It is found that good agreement between theory and observations for the case of the outer satellites of Jupiter is obtained when the current orbital eccentricity of Jupiter is used, but this agreement does not follow from most past conditions. The current orbits do fall within the predicted limits. The implication for a purely capture origin for these satellites is discussed.

Horseshoe and Trojan orbits associated with Jupiter and Saturn

view Abstract Citations (58) References (15) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Horseshoe and Trojan orbits associated with Jupiter and Saturn Everhart, Edgar Abstract Numerical experiments with orbits of small inclination in the Jupiter-Saturn region find many examples of orbits associated with either Jupiter or Saturn that are horseshoe-shaped in the frame revolving with the planet-sun line. In several cases, the Saturn horseshoe patterns persisted indefinitely, one lasting at least 368 000 yrs. The libration periods varied between 700 and 2200 yrs, depending on the amplitude of the excursion. Longer periods, to 20 000 yrs, were accompanied by variations in eccentricities and perihelia of objects in such orbits at Saturn's distance. The Jupiter horseshoes had shorter periods and seemed to be less stable than those associated with Saturn. Trojan orbits with either planet were found about as often as the horseshoe orbits. Many orbits librating at multiples or submultiples of the planet's period are found here, and most of these can be considered as generalized horseshoes of various orders. However, a few examples are of a new pattern that is best described as a generalized Trojan libran. . Also found were a number of near-circular orbits in two belfs between Jupiter and Saturn with lifetimes of the order of 100 000 yrs, and some satellite capture orbits. Publication: The Astronomical Journal Pub Date: May 1973 DOI: 10.1086/111421 Bibcode: 1973AJ.....78..316E full text sources ADS |

Origin and evolution of the earth-moon system

The origin and evolution of the Earth-Moon system is studied by comparing it to the satellite systems of other planets. The normal structure of a system of secondary bodies orbiting around a central body depends essentially on the mass of the central body. The Earth with a mass intermediate between Uranus and Mars should have a ‘normal’ satellite system that consists of about half a dozen satellites each with a mass of a fraction of a percent of the lunar mass. Hence, the Moon is not likely to have been generated in the environment of the Earth by a normal accretion process as is claimed by some authors. Capture of satellites is quite a common process as shown by the fact that there are six satellites in the solar system which, because they are retrograde, must have been captured. There is little doubt that the Moon is also a captured satellite, but its capture orbit and tidal evolution are still incompletely understood. The Earth and the Moon are likely to have been formed from planetesimals accreting in particle swarms in Kepler orbits (jet streams). This process leads to the formation of a cool lunar interior with an outer layer accreted at increasingly higher temperatures. The primeval Earth should similarly have formed with a cool inner core surrounded in this case by a very strongly heated outer core and with a mantle accreted slowly and with a low average temperature but with intense transient heating at each individual impact site.

On the ultimate behavior of orbits with respect to an unstable critical point I. Oscillating, asymptotic, and capture orbits

This work concerns an analytic autonomous Hamiltonian system of differential equations with two degrees of freedom which admits and unstable equilibrium point. More specifically, the eigenvalues corresponding to the equilibrium point include one real pair and one imaginary pair and so we know (by a theorem of A. Liapunov) that passing through the equilibrium point there is an invariant two dimensional manifold on which all solutions are periodic. Furthermore, the level surfaces of the Hamiltonian function are invariant three dimensional manifolds which, for appropriate values of that function, contain exactly one of these periodic solutions. Our aim is to study the orbits on such a level surface. The nature of the work is most easily described in terms of the following example: consider two bowls connected by a trough so that, when inverted they look like two mountains with a pass between. The differential equations are taken to be those describing the motion of a point mass sliding without friction on this “double bowl”. The Hamiltonian function is the sum of the potential energy, i.e. the height in the bowl, and the kinetic energy, also obtained as usual. Since the kinetic energy is positive, fixing the value of the Hamiltonian function corresponds to limiting the height to which the mass can go. Our problem concerns the case where the mass can go high enough to get from one bowl to the other with just a little room to spare. Having fixed on an appropriate level surface (of the Hamiltonian function) we first study the behavior of orbits near the equilibrium point, which in the example above, corresponds to the saddle point in the trough connecting

Low Energy Transit Orbits in the Restricted Three-Body Problems

Low Energy Transit Orbits in the Restricted Three-Body Problems

π−Capture byHe3and the Two-Nucleon Capture Model

The rates of capture of ${\ensuremath{\pi}}^{\ensuremath{-}}$ mesons by ${\mathrm{He}}^{3}$ leading to the final states $d+n$ and $p+n+n$ are calculated using a phenomenological two-nucleon Hamiltonian for the capture interaction $\ensuremath{\pi}\mathrm{NN}\ensuremath{\rightarrow}\mathrm{NN}$, obtained previously by Eckstein from an analysis of the experimental data on the inverse process of one-pion production in nucleon-nucleon collisions. Both $S$- and $P$-orbit captures are considered and it is shown that $P$-orbit capture does not compete with the $P\ensuremath{\rightarrow}S$ radiative transition. The radiative capture rate ${W}_{\ensuremath{\gamma}}$ (for final state ${\mathrm{H}}^{3}$+$\ensuremath{\gamma}$) is computed in terms of the photoproduction amplitude of Chew, Goldberger, Low, and Nambu and is used to deduce the nucleonic absorption rate ${W}_{\mathrm{abs}}={W}_{d}+{W}_{p}$ from the ratio $\frac{{W}_{\mathrm{abs}}}{{W}_{\ensuremath{\gamma}}}$ measured experimentally. The agreement between calculation and experiment for ${W}_{\mathrm{abs}}$ is satisfactory. Our conclusion is that the form of close pair correlations in nuclei is essentially the same as that for the "free" nucleon-nucleon interaction and is comparatively insensitive to the presence of other nucleons.

The Distribution of Hydrogen in the Telluric Hydrogen Corona.

view Abstract Citations (29) References (7) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS The Distribution of Hydrogen in the Telluric Hydrogen Corona. Johnson, Francis S. Abstract The distribution of hydrogen in the telluric hydrogen corona is calculated by identifying the components of a fictitious hydrostatic distribution which are actually present in the real atmospheric distribution. The components which are clearly present are the captive ballistic orbits and the escaping ballistic orbits which originate near the base of the exosphere. The components which are clearly absent are the hyperbolic orbits which originate in space; these consist of two groups, those which do not intersect the base of the exosphere and which return to space and those which intersect the base of the exosphere and which are capture orbits. Trapped elliptic orbits, or satellite orbits, may or may not be present, but near the earth they are probably occupied. Each of these components can be evaluated as an explicit portion of a hydrostatic distribution, and the distribution calculated from the hydrostatic distribution in a straightforward manner. Calculations are presented for temperatures of 10000 and 15000 K. Publication: The Astrophysical Journal Pub Date: March 1961 DOI: 10.1086/147072 Bibcode: 1961ApJ...133..701J full text sources ADS |

Pion-momentum spectrum from K− absorption in helium

The pion-momentum spectrum from K−-absorption stars in helium is calculated in the impulse approximation. The kaon is assumed to be pseudoscalar and to be captured from the 1s state. A final state consisting of free particles is used. The effect of final bound states is considered and taken into account phenomenologically. All final-state interactions are neglected. It is shown that the shape of the momentum spectrum is determined mainly by kinematics,i.e., the shapes and position of the spectral peaks are quite insensitive to detailed dynamical assumptions such as the nature of the K parity and capture orbit. The effect of final-state interactions is discussed.