Counterglow from the Earth-Moon libration points

Results from the OSO-6 Rutgers Zodiacal Light Analyzer experiment show photometric perturbations above the background in the anti-Sun line of sight. Sixteen successive lunations were examined, and the accumulated perturbations show a maximum value in the direction of the L₄ and L₅ Earth-Moon libration points. This is interpreted as a counterglow from a cloud of particles at the libration points. The average brightness of these libration clouds is 20 S₁₀ Vis. The average angular size of the libration clouds is approximately 6 degrees. Their position varies from one lunation to the next, within an ellipsoidal zone centered on the libration point direction, with its semi-major axis, of approximately 6 degrees, nominally in the ecliptic and its semi-minor axis, of approximately 2 degrees perpendicular to the ecliptic. The position of these clouds with respect to the Lagrangian L₄ and L₅ points, is towards the Moon in the northern summer and away from the Moon in the northern winter.     

Position and velocity sensitivities at the triangular libration points

The model of the circular restricted problem of three bodies is used to investigate the sensitivity of the third body motion when it is given a positional or velocity deviation away from the L₄ triangular libration point. The x-axis is used as a criteria for defining the stability of the third body motion. Poincaré's surfaces of section are used to compare the regions of periodic, quasi-periodic and stochastic motion to the trajectories found using the definition of stability (not crossing the x-axis) defined in this study. Values of the primary/secondary mass ratios () ranging from 0 to the linear critical value 0.038521... are investigated. Using this new form of stability measure, it is determined that certain values of are more stable than others. The results of this study are compared, and found, to give agreeable results to other studies which investigate commensurabilities of the long and short period terms of periodic orbits.     

Periodic rotations of a rigid body located at the libration point

Periodic rotations of a rigid body close to the flat motions were found. Their orbital stability was investigated. Analysis was done up to second order of the small parameter. It was proved that solutions found are orbitally stable except of the third order resonance case. This resonance do not appear if terms up to the first order of small parameter are considered only.     

Global sensitivity to velocity errors at the libration points

The global effects on non-linear stability are investigated at and around the triangular libration points. The model of the circular restricted problem of three bodies is used, considering the Earth and the Moon as the primaries. Areas of the initial conditions in the configuration space leading to stability with zero initial velocity around the equilibrium points are compared to stable areas in the phase space with variable initial velocity and zero initial deviations at the equilibrium points. The behavior of the system concerning errors due to initial conditions in the configuration space is studied for 6 years and the effects of initial velocity errors are considered for 7.73 years.Paper presented at the 1981 Oberwolfach Conference on Mathematical Methods in Celestial Mechanics.     

A Hopf variables view on the libration points dynamics

This study analyzes a recently discovered class of exterior transfers to the Moon. These transfers terminate in retrograde ballistic capture orbits, i.e., orbits with negative Keplerian energy and angular momentum with respect to the Moon. Yet, their Jacobi constant is relatively low, for which no forbidden regions exist, and the trajectories do not appear to mimic the dynamics of the invariant manifolds of the Lagrange points. This paper shows that these orbits shadow instead lunar collision orbits. We investigate the dynamics of singular, lunar collision orbits in the Earth–Moon planar circular restricted three-body problem, and reveal their rich phase space structure in the medium-energy regime, where invariant manifolds of the Lagrange point orbits break up. We show that lunar retrograde ballistic capture trajectories lie inside the tube structure of collision orbits. We also develop a method to compute medium-energy transfers by patching together orbits inside the collision tube and those whose apogees are located in the appropriate quadrant in the Sun–Earth system. The method yields the novel family of transfers as well as those ending in direct capture orbits, under particular energetic and geometrical conditions.     

A novel algorithm for generating libration point orbits about the collinear points

This paper presents a numerical algorithm that can generate long-term libration points orbits (LPOs) and the transfer orbits from the parking orbits to the LPOs in the circular-restricted three-body problem (CR3BP) and the full solar system model without initial guesses. The families of the quasi-periodic LPOs in the CR3BP can also be constructed with this algorithm. By using the dynamical behavior of LPO, the transfer orbit from the parking orbit to the LPO is generated using a bisection method. At the same time, a short segment of the target LPO connected with the transfer orbit is obtained, then the short segment of LPO is extended by correcting the state towards its adjacent point on the stable manifold of the target LPO with differential evolution algorithm. By implementing the correction strategy repeatedly, the LPOs can be extended to any length as needed. Moreover, combining with the continuation procedure, this algorithm can be used to generate the families of the quasi-periodic LPOs in the CR3BP.     

Non-linear stability around the triangular libration points

The configuration space around the triangular libration points in the Earth-Moon system is partitioned according to the stability of the motion. The regions aroundL ₄ andL ₅ are established where particles placed with zero initial velocity will librate. The complexity of the partitioning is revealed.     

A search for forward scattering of sunlight from lunar libration clouds

An attempt to determine the radiance of forward scattered sunlight from particles in lunar libration regions was made with the white light coronagraph on Skylab. The libration regions could not be distinguished against the solar K + F coronal background; an upper limit to the libration cloud radiance is determined to be $\text{2·5 × 10}{}^{\mathrm{?11}}\text{B}{}_{\mathrm{?}}$, where $\text{B}{}_{\mathrm{?}}$ is the mean radiance of the solar disk. Employing a model of the particle composition and size distribution which has been proposed for the interplanetary medium, we determine upper limits for the density enhancements in the libration region from the upper limit of the forward scattered radiance presented herein. Similarly, the actual spatial density enhancement is calculated using the earlier observations of the libration region backscattered radiance (Roach, 1975). Enhancements of a factor of 10²–10³ are thus determined, depending upon material composition and size distribution used. By combining the forward and backscatter observations, it is possible to eliminate from consideration clouds whose power law particle size distribution exponent k is 2·5 and complex index of refraction m is 1·33?0.05i and 1·50?0.05i (i.e. absorbing ice and quartz particles, respectively). Finally, the radiance contrast of a possible model libration cloud is calculated with respect to the K- and F-corona/zodiaal light background and is shown to be a maximum in the vicinity of solar elongation angle ～30 deg.     

Numerical orbits near the triangular lunar libration points

The behavior of a test particle placed at a triangular libration point of the Earth-Moon system is calculated using Newton's equations for the four-body problem, with arbitrarily chosen initial conditions. If the orbits of the massive bodies have their real eccentricities, then the test particle leaves the vicinity of the libration point in three years, much faster than if the orbits were circular. Very small particles are affected by solar radiation pressure, and may leave even faster.     

A dynamical equivalent to the equilateral libration points of the earth-moon system

Consider the Earth-Moon-particle system as a Restricted Three Body Problem. There are two equilateral libration points. In the actual world system, those points are no longer relative equilibrium points mainly due to the effect of the Sun and to the noncircular motion of the Moon around the Earth. In this paper we present the problem as a perturbation of the RTBP and we look for the dynamical equivalent of L _4,5. It turns out to be a quasiperiodic orbit. It is obtained for a simplified model but the procedure to obtain it is general and can be carried out with an additional computational effort.     

A search for infrared stellar objects in Vela

In a search for infrared excess objects near the galactic plane, a star field of 28.5 square degrees in Vela has been measured on UK Schmidt plates R4272 and 14183 with the Cosmos machine at Royal Observatory, Edinburgh. The magnitude limit is around 20 in R and around 19 in I. 131 infrared excess objects with colour index R-I > 2.5 are discovered in the field, and 3 red stellar objects have been identified as the optical counterparts of IRAS point sources.     

A search for unique objects in nearby galaxies

A list of 171 stars in the galaxy M33 is presented. The stars could be considered as candidates for unique objects, such as SS 433, S Dor, P Cyg stars and possibly new kinds of peculiar objects. All these stars have been selected on the basis of the similarity to SS 433, free from interstellar absorption: OB star with strongH emission or with HeII 4686 and CIII, NIII 4630 - 4660 emission lines; a hot star inside a supernovae remnant or radio nebula. The variability of these stars has been used as an additional criterion of the selection. It is important to carry out spectral observations of the presented stars, which will allow us to select stars with intrinsicH emission.     

Conditions for the linear stability of libration points and effects of drag on the linear stability of triangular libration points in the restricted three-body problem

A number of criteria for linear stability of libration points in the perturbed restricted three-body problem are presented. The criteria involve only the coefficients of the characteristic equation of the tangent map of the libration points and can be easily applied. With these criteria the effect of drag on the linear stability of the triangular libration points in the classical restricted three-body problem is investigated. Some of Murray et al.'s results are improved.     

Solar and planetary destabilization of the Earth-Moon triangular Lagrangian points

In the restricted circular three-body problem, two massive bodies travel on circular orbits about their mutual center of mass and gravitationally perturb the motion of a massless particle. The triangular Lagrange points, L₄ and L₅, form equilateral triangles with the two massive bodies and lie in their orbital plane. Provided the primary is at least 27 times as massive as the secondary, orbits near L₄ and L₅ can remain close to these locations indefinitely. More than 2200 cataloged asteroids librate about the L₄ and L₅ points of the Sun-Jupiter system, and five bodies have been discovered around the L₄ point of the Sun-Neptune system. Small satellites have also been found librating about the L₄ and L₅ points of two of Saturn's moons. However, no objects have been discovered around the Earth-Moon L₄ and L₅ points. Using numerical integrations, we show that orbits near the Earth-Moon L₄ and L₅ points can survive for over a billion years even when solar perturbations are included, but the further addition of the far smaller perturbations from other planets destabilize these orbits within several million years. Thus, the lack of observed objects in these regions cannot be used as a constraint on Solar System formation, nor on the tidal evolution of the Moon's orbit.     

Photographic observations of the cloud in the neighbourhood of libration point L 5 of the Earth-Moon system

The paper contains results of three-colour photographic observations of positions and brightness of the cloud in the vicinity of the Earth-Moon libration point L₅. The real character of the images obtained is confirmed by an agreement of their positions on different plates exposed at the same time. The colours of the cloud obtained are essentially different from those of the counterglow. The clouds appeared to be much redder than the counterglow, which may indicate that the particles constituting them are of different nature than those causing the counterglow.     

A proposed search of the solar neighborhood for substellar objects

The Infrared Astronomical Satellite (IRAS) program will produce an extremely sensitive all-sky survey over the wavelength region 8 to 120 μm when the mission is flown in 1982. These data will provide a novel opportunity to detect planetary-sized objects having masses <0.08M_⊙ or near our solar system. The improved detection limit of the IRAS will greatly increase the volume of space searched for such objects as compared with previous optical and infrared studies.     

A search program for objects in the vicinity of the Earth

Using a Super-Schmidt camera installed at the Cesco Observatory we are developing a program conducted to detect asteroids (especially members of the Aten Group) and comets approaching the Earth. The search strategy is based on simulations of the population of objects in this kind of orbits.     

Stability of the libration points of a rotating triaxial ellipsoid

The problem of stability of the equilibrium points (the libration points) in the problem of motion of a mass point in the neighbourhood of a rotating triaxial ellipsoid is investigated in the strict sense.In the plane of parameters, depending on the form and dynamical characteristics of the ellipsoids, the regions of stability and instability of the libration points are obtained.It is shown that the libration points of the ellipsoids, the form and dynamical characteristics of which are close to the planets of the solar system, are stable.

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On the collinear libration points in the photo-gravitational three-body problem

The existence of the three-parametric family of the collinear-libration points in the photo-gravitational three-body problem (differing from the classical one by the addition to the gravitational field the light repulsion force-field) is proved. The number and situation of these points are determined with respect to the system parameters. Their stability to a first approximation is investigated. It is shown that oppositly to the classical problem the internal collinear libration-points may be stable in some domain of parameter-space.     

A search for natural satellites of Mercury

We present the results of an imaging survey of Mercury's Hill sphere in search for objects dynamically bound to the planet, motivated by the existence of hermeocentric orbits that have been shown to be stable over 5 Myr or more. A six-day survey of Mercury's apparent vicinity from 6 to 140 Mercury radii, with full coverage between 19 and 73 Mercury radii, was performed with the Nordic Optical Telescope using ALFOSC in the R-band. The deepest limiting magnitude of 18.6 at a signal-to-noise-level of 3 corresponds to a hermeocentric object size of 0.5 km, while the brightest limiting magnitude corresponds to a size of 1.6 km. While two suspected sources were found, no hermeocentric objects could be confidently identified.