Line Of Apsides Research Articles

HR 7551 : A NEW SUPERGIANT ECLIPSING BINARY.

ABSTRACT A photometric and spectroscopic investigation of the spectroscopic binary HR 7551, which belongs to spectral type B0.5 Ib and thus has an evolved primary component, is presented. Spectroscopic data taken from the measurements of Plaskett and Pearce (1931) made in the 1920s and spectrograms obtained with the 2-m telescope at Ondrejov from 1978-1980 are used to determine radial velocities which indicate a binary period of 13.374 days, and spectroscopic elements indicating a strongly eccentric orbit and the possible rotation of the line of apsides in the 50 year interval. UVB photometry has confirmed the existence of primary and secondary eclipses, with times in good agreement with the spectroscopy. The presence of secondary lines, which appears probable, would indicate a value of M1 sin i-cubed of 26.9 solar masses, M2 sin i-cubed of 13.5 solar masses, and a sin i of 56.6 x 10 to the 6th km, with an inclination close to 90 deg. The secondary thus appears to be of the same spectral type as the primary, and the system does not appear to be affected yet by mass transfer.

On the motion of the apsidal line in interacting binary systems

On the motion of the apsidal line in interacting binary systems

Co-Apsidal Autonomous Terminal Rendezvous in Mars Orbit

The autonomous (or unmanned) Mars Orbit Rendezvous may be divided into four phases: approach, terminal, station-keeping, and docking. The paper outlines a feasible concept for the terminal rendezvous phase. A co-apsidal terminal rendezvous technique is described which utilizes the advantages of aligning the lines of apsides of two coplanar elliptic orbits of slightly different periods but of the same apoapsis distance. An initial maneuver nulling the inclination between the orbits is followed by another maneuver to align the two lines of apsides. A proper phasing maneuver is then executed at the coapsidal point, and the final rendezvous maneuver is performed at the same coapsidal point to complete the terminal rendezvous transfer. Cases are formulated in order of complexity with a view to illustrate the basic ideas of this technique. Pertinent calculations are also presented.

Secular Post‐NEWTONian Effects for the Restricted Three‐Body Problem in TREDER'S Dynamics with Induced Inertia

AbstractIn the framework of TREDER'S dynamics, in which according to the MACH‐EINSTEIN‐doctrin the inertial masses are induced by the gravitational interaction with the particles of the cosmos, we calculate the secular post‐NEWTONian effects for the restricted three‐body problem. The dominant secular post‐NEWTONian variation of nodes and apsides is shown to be the same as in EINSTEIN'S theory of gravitation. The formulation of the gravodynamics in the HERTZian configuration space allows – as in General Relativity – the explanation of the effect as an “geodetic precession” of the lines of nodes and apsides.

Secular resonance, solar spin down, and the orbit of Mercury

A mechanism capable of accounting for the large mean eccentricity (0.175) and inclination (7°.2) of Mercury is discussed. Provided the gravitational field of the rapidly rotating primordial Sun had a sufficiently large second degree harmonic (i.e., J 2 ≳ order 10 −3), subsequent solar spin down would drive the orbit of Mercury through two secular resonances with Venus, one involving the precession of the line of apsides, the other one involving the regression of the nodal line. Resonance passage generates contributions to the eccentricity and inclination that are proportional to the square root of the characteristic solar spin down time. We find that an initial solar rotation l period of P ≲ 5 1 2 hr guarantees passage through resonance and that a spin down time of τ = Ω|dΩ/dt| −1 of order 10 6 years could have produced the observed eccentricity and inclination. Such a primordial rotation rate is comparable to the measured rotations of very young stars and the spin down time appears consistent with the time scale derived for magnetic braking of the Sun's rotation by an intense solar wind during a T-Tauri stage of solar evolution.

Poisson equations of rotational motion for a rigid triaxial body with application to a tumbling artificial satellite

Differential equations are derived for studying the effects of either conservative or nonconservative torques on the attitude motion of a tumbling triaxial rigid satellite. These equations, which are analogous to the Lagrange planetary equations for osculating elements, are then used to study the attitude motions of a rapidly spinning, triaxial, rigid satellite about its center of mass, which, in turn, is constrained to move in an elliptic orbit about an attracting point mass. The only torques considered are the gravity-gradient torques associated with an inverse-square field. The effects of oblateness of the central body on the orbit are included, in that, the apsidal line of the orbit is permitted to rotate at a constant rate while the orbital plane is permitted to precess (either posigrade or retrograde) at a constant rate with constant inclination.

Minor planets and comets in libration about the 2:1 resonance with Jupiter

view Abstract Citations (30) References (27) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Minor planets and comets in libration about the 2:1 resonance with Jupiter. Franklin, F. A. ; Marsden, B. G. ; Williams, J. G. ; Bardwell, C. M. Abstract We examine the orbits of minor planets in a search for objects librating about the 2:1 mean-motion resonance with Jupiter. Some 30 candidates are found among the Palomar-Leiden Survey and other unnumbered minor planets. Although almost all the orbits are very uncertain, there does seem to be an indication that librators of low orbital eccentricity do exist, contrary to the hypothesis by Giffen. We also tabulate data describing 12 comets that are temporarily librating about the 2:1 resonance. Finally, we present a discussion of what are apparently 'apocentric' librations. This type of libration, of which we find seven representatives among the numbered minor planets, can occur only for sufficiently small eccentricity. For such bodies, the role of Jupiter's eccentricity is vital; it is associated with a continuing alternation between apocentric libration and an oscillation of the line of apsides. Publication: The Astronomical Journal Pub Date: September 1975 DOI: 10.1086/111806 Bibcode: 1975AJ.....80..729F Keywords: Asteroids; Comets; Jupiter (Planet); Librational Motion; Orbital Elements; Planetary Orbits; Circular Orbits; Eccentric Orbits; Resonance; Saturn (Planet); Tables (Data); Lunar and Planetary Exploration full text sources ADS |

Two-body problem with slowly decreasing mass

Evolution of the orbital elements of a two-body system with slowly decreasing mass according to Jeans' mode is described by a non-linear, non-autonomous system of differential equations. In general the system contains one stationary solution (e=1,f=π), for which an instability criterion is derived. For example the stationary solution is unstable for all Jeans-Eddington functionsm n (t) with 1≦n≦3 which characterize the loss of mass. Furthermore, it is possible to describe the quantitative behaviour ofE+ω,e anda for arbitrarym(t) in a large number of cases. In the case of the Jeans-Eddington functions we find that the amplitude of the oscillations ine is monotone decreasing with time ifn>3 and it is monotone increasing with time ifn<3. By comparing these analytical results with the numerical calculations of Hadjidemetriou we explain the rapid rotation of the line of apsides which occurs if the initial value ofe is nearly-circular.

Photometric orbit and apsidal motion of the eclipsing binary V 477 Cygni

The photometric orbit of V 477 Cygni is determined from 1548 photoelectric observations made at Castel Gandolfo. The orbital eccentricity is found to be 0·302 and the period of rotation of the line of apsides about 349 years.

The Persian "Observation" of the Solar Apogee in CA. A. D. 450

Previous articleNext article No AccessThe Persian "Observation" of the Solar Apogee in CA. A. D. 450David PingreeDavid Pingree Search for more articles by this author PDFPDF PLUS Add to favoritesDownload CitationTrack CitationsPermissionsReprints Share onFacebookTwitterLinkedInRedditEmail SectionsMoreDetailsFiguresReferencesCited by Journal of Near Eastern Studies Volume 24, Number 4Oct., 1965Erich F. Schmidt Memorial Issue. Part Two Article DOIhttps://doi.org/10.1086/371827 Views: 3Total views on this site Citations: 3Citations are reported from Crossref Copyright 1965 The University of ChicagoPDF download Crossref reports the following articles citing this article:S. Mohammad Mozaffari Holding or Breaking with Ptolemy's Generalization: Considerations about the Motion of the Planetary Apsidal Lines in Medieval Islamic Astronomy, Science in Context 30, no.11 (Apr 2017): 1–32.https://doi.org/10.1017/S0269889717000011José Chabás, Bernard R. Goldstein Ibn al-Kammād’s Muqtabis zij and the astronomical tradition of Indian origin in the Iberian Peninsula, Archive for History of Exact Sciences 69, no.66 (Aug 2015): 577–650.https://doi.org/10.1007/s00407-015-0158-8Arkadiusz Sołtysiak Ancient Persian Skywatching and Calendars, (Jul 2014): 1901–1906.https://doi.org/10.1007/978-1-4614-6141-8_198

Explorer 10 plasma measurements

Plasma measurements were made with a detector aboard the Explorer 10 satellite, launched on a highly elongated elliptical trajectory with the line of apsides about 33° to the antisolar direction. Magnetic field measurements were also carried out on Explorer 10 by the Goddard Space Flight Center of NASA. A plasma moving with a velocity of about 300 km sec−1 was first observed when the satellite reached a distance of about 22 earth radii. During the rest of the observations (which terminated about 40 hours later, at a distance of 42 earth radius, periods in which substantial plasma fluxes were recorded alternated with shorter periods in which the plasma flux was below or just above the detection limit. There was a striking correlation between the plasma flux and the magnetic field: in the absence of plasma the magnetic field direction was nearly radial from the earth, whereas in the presence of plasma, the field was irregular and generally formed large angles with the earth-satellite direction. The plasma probe did not provide accurate information on the direction of the plasma flow, but placed the direction within a ‘window’ of about 20° by 80°. This window includes the direction pointing radially away from the sun. The flux densities of the positive ions (presumably protons) corresponding to the observed currents were of the order of a few times 108 cm−2 sec−1. They fluctuated over a range of about a factor of 2 during the periods when plasma was observed.

SATELLITE LIFETIMES UNDER THE INFLUENCE OF CONTINUOUS THRUST, ATMOSPHERIC DRAG, AND PLANET OBLATENESS

Approximate analytic solutions are obtained for the lifetimes of satellites in either circular or elliptical orbits under the influence of continuous tangential thrust, atmospheric drag, and planet oblateness. The cases treated are those in which the satellite mission requires the perigee of the orbit to remain within fixed bounds in altitude and position. For circular orbits it is found that, to increase greatly the useful life time over the nonthrusting case, an almost perfect matching of thrust to drag is required. Two solutions are obtained for elliptical orbits. The first requires that the thrust level over each revolution be the value needed to hold the perigee fixed. Extremely low thrust levels are found over most of the lifetime while increases in lifetime on the order of 30% over the nonthrusting case result. The second case considers thrusting at a constant level over a symmetrical arc about perigee; the length of the arc for each cycle being determined by the condition that the perigee remain fixed. Greatly increased lifetimes over the nonthrusting case and the preceding case are obtained with low mass consumption and small thrust-to-drag ratios. Expressions for the forces required to provide a secular change of the line of nodes, the line of apsides, and the inclination including the effect of planet oblateness are given and several examples are calculated.

The be Spectrum Variable HD 20336.

The spectrum of HD 20336 has been studied on more than 300 spectrograms taken between 1903 and 1961, of whIch 261 were measured for radial velocities of absorption and emission features Conspicuous variation of the ratio V/R of the hydrogen emissions occurred from 1903 to 1937. A fairly regular period of about 4 5 years was adhered to from 1916 to 1931. Before and after that interval the cycles were appreciably longer. About 1937, variation practically ceased and had not yet resumed in 1961 The bright lines weakened appreciably in 1933, but bright Ha and H were still present in 1961 Displacements of the hydrogen emissions and their central absorptions accompanied the variations V/R, with amplitudes up to 110 km/sec. The correlation of phenomena was of the usual type, with maxima of both V/R and velocity approximately coincident in time. Helium absorption lines often appeared double or triple. Their displacements and structures showed no correlation with hydrogen velocfties and structures In this respect HD 20336 differed from Aquarii. In spite of the apparent regularity from 1916 to 1931, a binary-star interpretation appears very improbable. As in the much less regular Be variable Aquarii, the preferred model is an equatorial "shell" of elliptical outline whose line of apsides rotates slowly.

Reply to Comment on the Termperature Distribution in a Spinning Sphere During Atmospheric Entry

ther, the directions of these components have a degree of invariance in tha t one component remains normal to the radius vector and the other component remains normal to the line of apsides. Where this property has been noted in the literature its derivation has been accomplished by geometry in which little use is made of terms that are physically familiar in orbit mechanics. Also, no inferences seem to have been made that there is any practical application which takes advantage of the invariance of these two velocity components. To illustrate these invariant velocity components, designated Vk and Vp (Fig. 1), assume a two-body conic trajectory, either elliptic or hyperbolic, where

Location of Focal Points of Ellipses

O in talks or published articles (1,2), one notes gross errors in the location of the focal points of ellipses. Through some psychological orientation toward circular symmetry, engineers and scientists alike are apt to place the focus near the center of curvature despite a distance error that may amount to 100 per cent. I t is the intention here to suggest simple checks, which the editor, or any reader, can make on the spot. Scientists sometimes excuse their carelessness in locating the focus on the grounds that it does not upset the validity of the theory they are expounding. While the pure mathematician is entitled to a measure of poetic license, it would be straining the bounds of tolerance, for example, to accept an error of 100 per cent in the perigee distance of an orbit. Engineers can fall into the same error, e.g., in a blackboard talk concerning parabolic reflector-type antennas. In this case, the slip is usually corrected before it gets into print, thanks to the shop drawings made for the design and test of the prototype. Without going into the mathematics of ellipses, let us consider methods of locating the focus. One of the properties of the ellipse is illustrated in Fig. 1, where FB, the distance from the focus to an extremity B of the minor diameter, equals the semi-major axis PO. Location of the focal point F may be made simply, as follows. Placing the edge of a strip of paper along the line of apsides (major diameter), mark off on the strip the perigee and apogee points P and A. Fold the paper in two, superposing P and A. Now crease to locate the center 0 of the ellipse. With the paper still folded, superpose the P and A points on B, holding in place by the point of a pencil. Rotate the other end 0 until it crosses the axis at the point F. Mark the focal point F. Thus, in a few seconds, one has checked whether the author calculated or guessed at the position of F. A further useful check is as follows. Draw a vertical line through F intersecting the ellipse at E. The line segment FE is the semilatus rectum P, which is the radius of curvature of

Attempted Interpretations of V/R Variation in Be Spectra.

view Abstract Citations References Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Attempted Interpretations of V/R Variation in Be Spectra. McLaughlin, Dean B. Abstract pulsating model for V/R variation (McLaughlin, 1931, Publ. Am. Astron. Soc. 7, 31; 1933, Proc. Natl. Acad. Sci. 19, 44) does not account satisfactorily for some details of the observations. In particular, it fails to yield the large shifts of emission lines in the same direction as the central absorption. Where the absorption varies in strength (as in ~ Mon A) it is weakest at the phase predicted for maximum strength by the rotating-pulsating model. The very large motions implied for cycles of over 1000 days are difficult to admit. Attempts were made to account for the variations by means of a rotating atmosphere subject to intermittent expansion that is alternately accelerated and retarded. Qualitative agreement is obtained only with artificial assumptions that do not appear physically justifiable. Again the shifts of emission lines are not satisfactorily represented. All the observed phenomena do appear explicable by rotation of the line of apsides of elliptical rings of gas, as originally suggested by Struve (1931, A strophys. J. 73' 94). Periastron at the receding node gives maximum positive velocity of both em ission and absorption, associated with V/R> 1. Periastron at approaching node yields V/R ~ 1 and negative shifts of emission and absorption. Weakest shell absorption in p Mon A corresponds to presentation of periastron towards the observer, since higher angular velocity then produces a minimum of density. The phase at which this occurs is consistent with an advancing periastron. According to M. Johnson (1958, Liege Symposium 7, 219), observed V/R "periods" are dynamically consistent with this hypothesis. Publication: The Astronomical Journal Pub Date: 1960 DOI: 10.1086/108122 Bibcode: 1960AJ.....65R.350M full text sources ADS |

On rotating ring orbits in galaxies

If ω is the angular velocity of circular motions in a stellar system depending on the distance R from the centre, and κ is the frequency of oscillation in the radius vector for an orbit in the equatorial plane which differs slightly from a circular orbit, we may show that in a coordinate system of angular speed the orbit in question is a closed oval, in the first approximation an ellipse, with two opposite vertices and with its centre in the centre of the system. The conditions are illustrated in Fig. 1, when AA is the apsidal line of an orbit. The expression for κ is where A is Oort's constant of differential rotation. If the distribution of matter in the stellar system may be approximated by a sum of concentric spheroids with one and the same plane of symmetry, the density increasing with decreasing dimensions of the spheroids, we should expect κ = 2ω close to the centre, whereas in the outermost regions we must expect that κ approaches to ω. It is therefore likely that ω – ½κ does not change appreciably within the system. Fig. 2 gives the run of κ, ω, and ω – ½κ for the galactic system according to the values of ω given by Kwee, Muller, and Westerhout [2]. In this case ω – ½κ changes very slowly with R. A relative orbit has a quite important property, if ω – ½κ is constant in the interval of R covered by the orbit. In this case, if the centre of gravity of a cloud of free particles follows the orbit, and if the velocity dispersion is small, the particles will pursue orbits which differ only slightly from each other and from the central orbit, but on the other hand there will in general be considerable differential motions along the central orbit. This orbit is therefore the curve in space along which a cloud of free particles tends to disperse. The process is similar to the dispersion of the meteoric particles of a comet along its orbit.

Apsidal Motion for an Early Main-Sequence Model.

view Abstract Citations (22) References (4) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Apsidal Motion for an Early Main-Sequence Model. Härm, R. ; Rogerson, J. Abstract The effective polytropic index, which determines the rate of advance of the line of apsides, is computed for a Cowling-type stellar model with pure electron-scattering opacity in the envelope. The low value of n = 2.63 found for this model strongly suggests that the onset of electron scattering as an opacity factor in early B-star binaries may be reponsible for their observed low effective polytropic indices. For comparison, the analysis was also carried out for a Cowling-type model with Kramers' opacity. Publication: The Astrophysical Journal Pub Date: March 1955 DOI: 10.1086/146005 Bibcode: 1955ApJ...121..439H full text sources ADS |

THE ORIENTATION OF THE LINES OF APSIDES OF SPECTROSCOPIC BINARIES

THE ORIENTATION OF THE LINES OF APSIDES OF SPECTROSCOPIC BINARIES

The orbital elements and apsidal motion of AR Cassiopeiae.

view Abstract Citations (4) References Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS The orbital elements and apsidal motion of AR Cassiopeiae. Petrie, R. M. Abstract Orbital elements for this eclipsing binary system have been determined at five epochs covering an interval of thirty-four years. The earliest orbit is based upon 67 spectrograms obtained at the Allegheny Observatory in 1908-9. The mean values of the fixed elements are as follows: e = 0.247 .oo6, K = 55.4 km/sec 0.3, V = -13.8 " 1.0. The anomalistic period is found to be 6d066522 0d000003 Spectrophotometric measures of line intensities yield the spectral type of the primary star, which is B4, while its spectroscopic absolute magnitude is - 1.3. The values of ~ show that the line of apsides is advancing, the observed values being, Mean Date 1909 6?o 3?2 1935 23.8 8.4 1935 30.2 4.5 1941 33.2 4.8 1943 36.3 3.8 From the above values it is found that w is well represented by a linear relation as follows: = -I?72 ~ o?872(t - 1900.0), and from this the period of apsidal motion is found to be 413 years. Dominion A strophysical Observatory, Victoria, B. C. Publication: The Astronomical Journal Pub Date: June 1944 DOI: 10.1086/105787 Bibcode: 1944AJ.....51...22P full text sources ADS | data products SIMBAD (1)