Line Of Apsides Research Articles

The Orbit of Charon

The orbit of Charon has been determined from 60 images of the Pluto–Charon system acquired with the Hubble Space Telescope Wide Field and Planetary Camera between 1992 May 21 and 1993 August 18. The semimajor axis was found to be 19,636 ± 8 km, in good agreement with an older determination upon which mutual-event-based radius computations have relied, but significantly larger than two other recent determinations. Contrary to expectations based on the tidal evolution of the system, a surprisingly large eccentricity of 0.0076 ± 0.0005 was found, with the line of apsides aligned nearly along the line of sight from Earth. Approximately half of this apparent eccentricity could be due to offsets in the center of light from the center of body arising from surface albedo features on Pluto and Charon, which leaves a statistically significant portion unexplained. We propose that the remaining eccentricity is the result of a recent energetic impact. The remaining elements are generally consistent with previously determined values, though in the case of the inclination, the various determinations appear to have underestimated error bars. The systemGMderived from our data is 981.5 ± 1.1 km3sec−2. Some information on the Charon/Pluto mass ratio is present in the data, though our determination of 0.110+0.063−0.056does not improve on previous determinations, or resolve the discrepancy between them.

Apsidal motion in the eclipsing binary AS Camelopardalis

We report several new reliable times of minimum of the eclipsing binary AS Cam. Using all precise timings found in the literature, the O-C diagram is analyzed and improved values for the elements of the apsidal motion are computed. The discrepancy between observed rotational velocity of the line of apsides and the theoretically expected value still remains unresolved.

SUPERHUMPS IN CATACLYSMIC BINARIES. VIII. V1159 ORIONIS

ABSTRACT We report photometry of the cataclysmic variable V1159 Orionis for ~400 hours over 168 nights during 1992-4. The long-term light curves show that this is a dwarf nova of the SU UMa class, with normal outbursts recurring on a mean period of 4.0 days, and superoutbursts recurring on a period of 47.6 days. These periods wander slightly, as is typical of the class. High-speed photometry at minimum light, far from superoutbursts, reveals a weak photometric signal at 89.83 ± 0.10 min, which is presumably the underlying orbital period of the binary. During superoutburst, large-amplitude superhumps are observed with P=92.4 min. The superhumps appear very suddenly on the rising branch. In a few days they fade to a full amplitude of 0.1 mag and become more complex in waveform. However, they can be traced throughout the decline phase to quiescence, and even apparently succeed in enduring to the next normal eruption. In fact, we note the occasional existence of superhumps at essentially all phases of the eruption cycle--not merely at supermaxima, where they are very common and downright famous. The "positive" (P>Porb) superhumps resemble in detail the common superhumps seen in the best-known SU UMa stars, and can be reasonably interpreted as arising from an eccentric accretion disk with an advancing line of apsides. But additional subtle details are detected in V1159 Ori. In one superoutburst the frequencies of the high harmonics are slighly higher than expected, and in another they are far lower than expected. And on two occasions there appeared "negative" superhumps (P<Porb) with a period of 82.7 ± 0.2 min. We discuss these features in terms of the disk-precession model, but without any convincing resolution. Two other periodic signals, of unknown origin, were detected: rapid oscillations ("DNOs") with a period increasing from 29 to 34 s over 7 days in mid-decline from a superoutburst; and a probable signal near 8 c/day, appearing mainly in quiescence.

Simple estimation algorithm for performance-seeking controllers

that the masses ejected are smart in the sense that they have enough onboard computation and propulsion capability to effect rendezvous at high velocity. Forward proposed that incoming masses dock with a cradle that had been accelerated along the launcher up to the incoming velocity. Alternatively, a magnet-equipped spacecraft could simply land on its EML rails roughly analogous to aircraft carrier landings (the velocities are an order of magnitude higher, but electronic reactions are several orders of magnitude higher than human reactions, and the platform is stable). After landing, the spacecraft would be, essentially, a high-speed maglev rail coach. From certain orbits, a two-way EML-equipped vehicle could generate significant outward velocity without loss of reaction mass—effectively using the planet as its reaction mass. Figure 2 is a point example of this. The general bounds on this concept need to be defined, but one can imagine that, in addition to LI stationkeeping, satellites could be pushed away from planets, or planets away from the sun, without loss of reaction mass—given time and an energy source sufficient to make up for the change in potential energy and any inefficiencies. Forward briefly addressed the possibility of levitation. This might be done by rotating the line of apsides at the periapsis of the orbit of the reaction mass to make the reaction mass reintercept a stationary EML. Around planets with atmospheres, this might also be accomplished by using negative lift near periapsis. In addition, gas might be collected and brought back out to the levitating EML, provided the initial velocity was high enough.

Applicability of meteor radiant determination methods depending on orbit type

It is evident that there is no uniform method of calculating meteor radiants which would yield reliable resilts for all types of cometary orbits. In the present paper an analysis of this problem is presented, together with recommended methods for various types of orbits. Some additional methods resulting from mathematical modelling are presented and discussed together with Porter's, Steel-Baggaley's and Hasegawa's methods. In order to be able to compare how suitable the application of the individual radiant determination methods is, it is necessary to determine the accuracy with which they approximate real meteor orbits. To verify the accuracy with which the orbit of a meteoroid with at least one node at 1 AU fits the orignal orbit of the parent body, we applied the Southworth-Hawkins D-criterion (Southworth and Hawkins, Smithson Contr. Astrophys. 7, 261, 1963). D ⩽ 0.1 indicates a very good fit of orbits, 0.1 < D ⩽ 0.2 is considered to be a good fit of orbits, and D > 0.2 the fit is rather poor and the change of orbit unrealistic. The optimal methods with the smallest values of D for given types of orbits anre shown in three plots. The new mathod of retation around the line of apsides we propose is very appropriate is the region of small inclinations Hasegawa's ω-adjustment method ( Publ. Astrpn. Soc. Jpn 42, 175, 1990) has the widest application.

A period decrease in the sdB eclipsing binary system HW Vir

Observations of eclipses of HW Vir (=BD −7°3477) over a 9-yr baseline show that the period is decreasing. The overall nature of the decrease cannot yet be seen, but we briefly discuss the possible causes and rule out gravitational radiation effects, rotation of the line of apsides and mass transfer. A third body in the system could be the cause of an apparent period change, though this should be observationally testable over a few more seasons. Angular momentum loss via magnetic braking in a modest stellar wind seems the most likely possibility for the period decrease

Evidence for Accretion Disk Precession in the Cataclysmic Binary AM Canum Venaticorum

view Abstract Citations (64) References (29) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Evidence for Accretion Disk Precession in the Cataclysmic Binary AM Canum Venaticorum Patterson, Joseph ; Halpern, Jules ; Shambrook, Anouk Abstract We have found a 13.38 hr period in the helium absorption-line profiles of the cataclysmic variable AM Canum Venaticorum. The lines display blue and red troughs which alternate in depth on this period. Comparison of the data with theoretical line profiles of elliptical accretion disks suggests that this is the signature of an elliptical disk, with the line of apsides advancing slowly around the white dwarf. This interpretation of the 13.38 hr spectroscopic period as apsidal precession of the disk supports the idea that the familiar 1051 s photometric signal is the orbital frequency's precessional sideband, which is also believed to be present in the "superhumps" of dwarf novae. The exact orbital period is inferred to be 1028s.77 + _{0 }. 18. More important, this kinematic evidence for accretion disk precession in a noneruptive star strongly suggests that superhumps and tidal instabilities may be a very widespread and essentially permanent feature of the accretion disks in many CVs. The variation in the skewness of the absorption lines is best seen near line center, as expected since low velocities tend to arise in the outer disk, where tidal effects are more important. But the same periodic signal is found in the wings of the absorption lines, with a phase displaced by 120°. This unexpected phase shift may arise from a dependence of tidal lag on orbital radius in the disk. Publication: The Astrophysical Journal Pub Date: December 1993 DOI: 10.1086/173532 Bibcode: 1993ApJ...419..803P full text sources ADS | data products SIMBAD (4)

On the original distribution of the asteroids: IV. Numerical experiments in the outer asteroid belt

We assumed, in 1973, that the asteroids were the building blocks of the planets and initially were distributed approximately uniformly. We suggested that the present distribution was carved out by the perturbations of Jupiter. To test this hypothesis further, we have now integrated the orbits of 140 asteroids with 14 semimajor axes from 0.63 to 0.76 (in units where a Jupiter = 1.0) in increments of 0.01, and at 10 values of the eccentricity from 0.01 to 0.19 in increments of 0.02. The integrations extended for 1 million Jovian years (about 12 million years) unless the asteroid crossed Jupiter's orbit before then. Jupiter was in an elliptic orbit with its eccentricity varying in a 54,000-year period, and its line of apsides rotating with a 300,000-year period induced by the secular perturbations of Saturn. The integrations were confined to a plane. In the main survey, we chose the most “unstable” phases of the asteroid relative to Jupiter; i.e., the apsidal lines of the asteroid and Jupiter were separated by 180°. There are only 8 of the 8032 asteroids with reliable orbits with semimajor axes between 0.68 and 0.74. In our simulation, 64 90 (71%) of the asteroids with semimajor axes equal to or larger than 0.680 were removed. Of the 26 asteroids that remained, 16 had initial eccentricities equal to or less than 0.03. Ten of the remaining asteroids with a≥0.68 were integrated for 10 million Jovian years; 5 became Jupiter crossers and 5 remained. Including these longer integrations, 69 90 (77%) of the asteroids with a≥0.68 escaped. However, the depletion was much reduced in those cases when the initial phases caused conjunctions to occur at the asteroid's perihelion; i.e., the apsidal lines of the asteroid and Jupiter coincided. We found a strong correlation between the Lyapunov exponent and the crossing time for orbits with crossing times less than 1 million Jovian years (and for the few longer integrations). If this result extrapolates to 4.5 billion years, it would indicate that with Jupiter the only perturber, there are stable orbits where there are no asteroids today.

Aeroassisted transfer between elliptical orbits using lift control

A transfer between two elliptical orbits, using an atmospheric passage, is considered. In the atmosphere, the lift of the spacecraft is controlled to change the line of apsides of the orbit, without changing other orbital parameters. The maneuver includes three propulsive impulses to bring the spacecraft into and out of the atmosphere and to compensate for the velocity loss during the atmospheric passage. The total velocity change during this maneuver is compared to the velocity change of an optimal two-impulse, pure-propulsive maneuver and of a drag-only aeroassisted maneuver. It is shown that below a certain apsidal rotation angle, the lift-controlled maneuver is more fuel-economic than the drag-only maneuver. The lift-controlled maneuver is also more fuel economic than the pure-propulsive maneuver, provided that the lift-to-drag ratio of the spacecraft is greater than two. The limits to the rotation angle that can be achieved in a single pass are discussed. Numerical examples are presented.

The oscillation of the synodic period of the Moon: A ‘‘beating’’ phenomenon

The synodic period of the Moon (the period of the phases or the time from, say, full moon to full moon) exhibits oscillations about its mean value of 29.530 59 days which immediately suggest a ‘‘beating’’ between at least two frequencies. A Fourier analysis can provide some insight into the causes of the oscillation without the complexity of rigorous lunar theories. Such a Fourier approach is quite appropriate for undergraduate students of physics and astronomy, but, of course, is no substitute for more rigorous lunar theory. Fourier analysis suggests the periods of the beating frequencies to be 411 and 366 days. The 411-day period arises since this is the time it takes the Sun to return to a similar orientation along the line of apsides (the major axis) of the lunar orbit. The 366-day period is about a year or the time it takes the Earth to orbit the Sun. Since the lunar phases occur because of the relative orientation of the Earth, Moon, and Sun, an annual period might also be anticipated. The beat period of 3293 days is half the saros eclipse cycle period of 6585.3 days. Alternating lunar and solar eclipses are separated by the beat period. Higher frequency effects are apparent from the data, but not from the elementary Fourier approach. Thus this procedure must be used with caution in analyzing complex periodic data in astronomy.

Gyld�n systems: Rotation of pericenters

A canonical transformation in phase space and a rescaling of time are proposed to reduce a Keplerian system with a time-dependent Gaussian parameter to a perturbed Keplerian system with a constant Gaussian parameter. When the time variation is slow, the perturbation through second order in the reduced problem is conservative, and, as a result, the orbital space of the averaged system is a sphere on which the phase flow causes a differential rotation representing a circulation of the line of apsides. The flow presents two isolated singularities corresponding to circular orbits travelled respectively in the direct and in the retrograde sense, and a degenerate manifold of fixed points corresponding to the collision orbits. Normalization beyond order two does not break the degeneracy. Adiabatic invariants, which are conservative functions, may be computed from the normalized Hamiltonian evaluated here to the fourth order. Nonetheless so high an approximation gives little information because the normalizing Lie transformation depends explicitly on the time through mixed secular-periodic terms. As an application, an estimate is offered for the apsidal rotation that a second order time derivative in the mass of the sun would induce on planetary orbits. This suggests an observational method for determining the latter parameter for the solar wind, but the predicted motions are too slow for the current level of observational precision.

The motion of the line of apsides of ? phoenicis

An estimate of the period of the rotation of the line of apsides of the double-star system ζ Phe is obtained by representing the density function as a product of a normal Gaussian distribution and an associated Legendre polynomial\(\rho \left( {\bar r} \right) = \left( {1 - \bar r^2 } \right)e^{ - ^{\bar r^2 } } \).

Optimum burn scheduling for low-thrust orbital transfers

This paper describes a method for optimizing the point at which thrust should be initiated on each passage of a low-thrust, multiple finite-duration perigee-burn ascent trajectory, with the thrust vector always oriented perpendicular to nadir. The quantity being minimized is the rotation of the line of apsides. The semianalytic method developed here requires only a simple root-finding routine for the numerical portion of the solution. A perturbation solution (two-variable expansion) is used to model the flight path during the burn, yielding a burn-on position with a maximum error of approximately 2%.

Js̄bir ibn Aflah's Interesting Method for Finding the Eccentricities and Direction of the Apsidal Line of a Superior Planet

Js̄bir ibn Aflah's Interesting Method for Finding the Eccentricities and Direction of the Apsidal Line of a Superior Planet

The apsidal motion of the eccentric eclipsing binary DI Herculis - an apparent discrepancy with general relativity

view Abstract Citations (97) References (60) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS The apsidal motion of the eccentric eclipsing binary DI Herculis - an apparent discrepancy with general relativity. Guinan, E. F. ; Maloney, F. P. Abstract DI Her is an important system for studying relativistic apsidal motion because of the large masses and small fractional radii of its components, the large orbital eccentricity and its relatively short period, and the favorable orientation of its orbital plane to our line of sight producing deep eclipses. In addition, the long history of eclipse timings provides an extended baseline for studying the motion of the line of apsides. However, as shown in this study, the analysis of the eclipse timings indicates that the observed advance of the periastron is nearly one-seventh that expected from Newtonian and relativistic effects. Thus, in DI Her, we are confronted with the puzzling situation of having either an undiscovered or misunderstood classical effect present in the system, or an inconsistency with general relativity. Publication: The Astronomical Journal Pub Date: August 1985 DOI: 10.1086/113865 Bibcode: 1985AJ.....90.1519G Keywords: Apsides; Eccentric Orbits; Eclipsing Binary Stars; Relativistic Effects; Stellar Motions; Stellar Orbits; Least Squares Method; Light Curve; Minima; Orbital Elements; Radial Velocity; Relativity; Three Body Problem; Astrophysics full text sources ADS | data products SIMBAD (1) MAST (1)

Orbital equations in a weak gravitational field

With the obtainment of the Synge equations of motion in third approximation for a test particle, we determine the relativistic force in the field generated by a massive body obtained previously in terms of its potentials. Afterwards, in order to study the motion, we obtain the integral of energy and the integral of angular momentum. By means of them, the general form for the trajectory of an equatorial orbit and for the advance of its apsidal line are obtained. As we will see, the known diverse contributions for this advance appears in the general form after strong supplementary conditions on the potentials. As application, with such assumptions these contributions are derived in a unified way.

The dynamics of elliptical rings

We investigate the evolution of eccentric rings under the influence of (1) differential precession due to the planetary quadrupole moment; (2) self-gravity; (3) viscous forces due to interparticle collisions; and (4) eccentricity excitation by shepherd satellites. The principal conclusions are that: (a) Uniform precession can be enforced by self-gravity (Goldreich and Tremaine 1979b); the resulting configuration is both dynamically and secularly stable. (b) Due to viscous forces the line of apsides at the inner ring edge is not exactly aligned with the line of apsides at the outer edge; the apse shift may be detectable in the ɑ and β rings of Uranus. (c) The mean eccentricity is determined by a balance between viscous damping and excitation by shepherds. (d) We expect the dimensionless eccentricity gradient ɑΔe/Δɑ to be positive and of order unity in most eccentric rings, as observed.

Secular orbit-orbit resonance between two satellites with non-zero masses

The Rhea-Titan resonance is studied as a special case of secular orbit-orbit resonances. In earlier studies Rhea's mass has always been neglected. In order to investigate whether this approximation is valid, both masses are taken into account. It is shown that in the Rhea-Titan case the resonance is dominated by the effect of the large difference between the natural precession rates of the lines of apsides of both satellites, leading to approximations containing only one of the masses. For libration about 0 it happens to be Titan's mass, so that neglecting Rhea's mass is valid. Next, the influence of the difference between the natural precession rates on the resonance is examined, and finally it is shown that the libration period is independent of the libration amplitude.

Theory of motion of hyperion

We solve by an appropriate method the difficulty of near-commensurability, n n 1 3 4 , in the motion of Hyperion (Saturn VII) and give a first-order solution of its motion. Our result explains two interesting observed features, the regression of the apsidal line and the exclusive occurrence of apocentre C conjunction of SVII and SVI.

The path and surviving tail of a comet that fell into the sun

A satisfactory orbital solution for Comet Howard-Koomen-Michels 1979 XI is found on the assumption that the comet's line of apsides coincided with that of the Kreutz sungrazing comet group. The derived perihelion distance then shows that this is the first known case of a comet falling into the sun. A dust tail that survived the comet is studied as a particle flow phenomenon controlled by no force other than solar gravity and solar radiation pressure. The tail's outline is interpreted in terms of an onset of dust production, a peak repulsive force on the particles, and a circumsolar dustfree zone due to particle sublimation. It is shown that the surviving debris consisted mostly of absorbing, submicron size particles in hyperbolic trajectories convex to the sun and curving toward the earth. The tail width may be a product of the interaction of charged dust in the tail with a complicated structure of the coronal magnetic field.