Note on the number and origin of apollo asteroids

Fifteen Apollo, or Earth-crossing, asteroids are now recognized, and their orbital elements tabulated here. None has been accidentally rediscovered, a circumstance that leads to the 50% probability that the total number equals or does not exceed 100 to absolute magnitude 18, or above a diameter of roughly 1 km. Physical observations, orbital characteristics, and associated meteor streams provide clues as to whether the Apollo asteroids are truly minor planets or moribund cometary nuclei. A definitive answer as to the origin of the Apollo asteroids is yet to be found, but a short discussion of the status of the problem is presented.Paper dedicated to Prof. Harold C. Urey on the occasion of his 80th birthday on 29 April, 1973.     

Dynamical equinox and analytical theory of the Sun

A concept of the dynamical equinox and its relation to the analytical form of the adopted theory of the Sun is discussed. Connection between the FK4 equinox and the dynamical equinox is determined by comparing two analytical theories of the Sun (the adopted Newcomb's theory and a new one (AT-1) constructed at the Institute of Theoretical Astronomy) with solar meridian observations made at the U.S. Naval Observatory (1911–1971). Corrections to the FK4 right ascensions, ₀ to declinations and to the angle between the equator and the ecliptic are: Secular variations in and are negligible. Large secular variations of ₀ may be explained by improvement of observational conditions after the reconstruction of the telescope pavilion in the forties.Proceedings of the Conference on Analytical Methods and Ephemerides: Theory and Observations of the Moon and Planets. Facultés universitaires Notre Dame de la Paix Namur, Belgium, 28–31 July, 1980.     

Upper bound on the mass of non-rotating neutron stars

The problem of placing an upper bound on the mass of a non-rotating neutron star is investigated under minimal assumptions on the equation of state above nuclear densities. In particular causality (dp/dq<1) is not assumed in this region. An upper bound of about five solar masses is found.Supported in part by the National Science Foundation.     

On the photometry of geostationary satellites near the equinox dates

Long-term photometric observations (on scales of half a year to one year) at different positions of geostationary satellites (GSS) relative to an observer are necessary to determine photometric, optogeometrical, and dynamic characteristics of faint GSSs needed to be identified. We propose to perform photometric measurements of GSSs during their ingress into and egress from the Earth’s shadow near the equinox dates. At the equinoxes, the GSS brightness is several magnitudes higher, making it possible to effectively use telescopes with mirror diameters of 50–70 cm. A much larger amount of information on reflective properties of an object can be derived during observation on these dates than when performing long-term observations at large phase angles.     

Phase relation between the poloidal and toroidal solar-cycle general magnetic fields and location of the origin of the surface magnetic fields

The phase relation of the poloidal and toroidal components of the solar-cycle general magnetic fields, which propagate along isorotation surfaces as dynamo waves, is investigated to infer the structure of the differential rotation and the direction of the regeneration action of the dynamo processes responsible for the solar cycle. It is shown that, from the phase relation alone, (i) the sign of the radial gradient of the differential rotation (/r) can be determined in the case that the radial gradient dominates the differential rotation, and (ii) the direction of the regeneration action can be determined in the case that the latitudinal gradient (/) dominates the differential rotation. Examining the observed poloidal and toroidal fields, it is concluded that (i) the / should dominate the differential rotation, and (ii) the determined sign of the regeneration factor (positive [negative] in the northern [southern] hemisphere) describing the direction of the regeneration action requires that the surface magnetic fields should originate from the upper part of the convection zone according to the model of the solar cycle driven by the dynamo action of the global convection.     

Predictions and observations of events and configurations occurring during the Uranian equinox

The occurrence of the Earth and Sun transits through the equatorial plane of Uranus will bring us the opportunity for observations only possible at that time: mutual events of the satellites, search for new faint satellites and measurement of the thickness of the rings.The predictions of the mutual events need a theoretical model of the motion of the satellites. The calculated occurrences of the occultations and eclipses highly depend on the model since these predictions are very sensitive to the relative positions of the satellites. A difference of 0.05 arcsec in latitude may make an event inexistent and the accuracy of the theoretical models is around 0.1 arcsec.In order to be sure of the occurrence of each event, we made the predictions using three theoretical models: the first one is GUST86 made by Laskar and Jacobson in 1986, the second is GUST06 based on the former model fitted by Emelianov on new observations and the third one is LA06 based on a brand new theory with an accuracy 10 times better than GUST and fitted on recent observations made since 1950.This comparison shows that some events predicted with one model are not predicted using another one. We try to select the events which will occur surely in order to help the observers to catch the best phenomena.The search for new satellites and the measurement of the thickness of the rings are planned by means of observations at the time of the transit of the Earth in the ring plane.     

Corrections to the lunisolar precession and the motion of the equinox from proper motions of Cepheids

Corrections to Newcomb's lunisolar precession and to motion of the equinox are evaluated from proper motions of 77 Cepheids, employing recently determined values of their distances. Results are diverse, depending on the weighting method. If the effect of the cosmic dispersion is neglected and ₀ is imposed to be 25 km/s/kpc, thenp ₁=1.1±0.2 and +e = 1.0 ± 0.1 per century in the FK4 system.Presented at IAU Colloquium No. 9, The IAU System of Astronomical Constants, Heidelberg, Germany, August 12–14, 1970.     

The use of radar observations of Near-Earth Asteroids in the determination of the dynamical equinox

Near-Earth Asteroids (NEAs) are Solar system special class objects attracting the attention of astronomical community especially during several of the last decades. To some extent the NEAs have an advantage over the minor planets of the main belt: due to close and regular approaches to the Earth the radar observations of NEAs can be obtained for the greater number of objects than for those of the main belt of the minor planets. In this paper the use of all available radar observations together with optical ones resulting in the combined data analysis solution is discussed for different problems such as the asteroid orbits and catalog orientation parameters determination. In particular the problem of the motion of the dynamical equinox in the Hipparcos reference system is considered. About 13000 radar and optical observations of 24 NEAs and main belt minor planets have been used to obtain the precise asteroid orbits, FK5 catalogue orientation parameters and the motion of the dynamical equinox from 1750 till 2000 in the Hipparcos system.     

On the relation between the ERP and the rotation vector

This paper deals with the Earth Rotation Parameters (ERP), and presents a formula to calculate the rotation vector.     

Note on secular perturbations between a retrograde body and a prograde body

Hirayama (1927) studied secular perturbations between a retrograde body and a prograde body by considering that the mean motion of the retrograde body is negative. In this paper we discuss the same problem by measuring angle variables from the departure point and keeping the mean motions positive for both the retrograde body and the prograde body, and compare the analytical solutions with numerically integrated orbits.     

A relation between solar activity and the Earth's rotation

In this paper, applying Vondrák band filter to both series of (l.o.d.) and sunspot relative number (R), we obtain variations of amplitude of 11 yr term during 1800–1985. The results show that solar cyclic signal in (l.o.d.) series is weak and unstable. The amplitude of 11 yr term in R series has long-periodic variation. The paper has briefly discussed some results about effects of solar activity on the Earth's rotation through the atmospheric motion. From the variation of (l.o.d.) obtained by band filter, we find that maxima of amplitude of annual term in (l.o.d.) occur at the same time with those of sunspot number. It implies that the angular momentum imbalance between the circulations in Southern Hemisphere and Northern Hemisphere is controlled in some way by solar activity.     

The relation between the surges and solar radio emission

The 120 limb surges which have been observed by means of Wrocaw Observatory coronagraph from September 1966 to November 1977 are investigated. The evolution of surges was compared with the radio data during the surges. A correlation between radio bursts and the surges was found, particularly with chains of type I radio bursts, which is the first reliable correlation found of these bursts with non-radio events. The type I correlation only applied for surges without accompanying flare, of which 43% are correlated with this type of radio emission. In 23 of 30 associated events the start of a surge coincided within 5 minutes with the start or an enhancement of the type I storm. If flares were present, the association was not significant.We also compared the maximum height reached by a surge with the frequencies of the radio bursts emitted at the same time and the maximum velocity of the rising surge with the frequency drift of type I chains. No such a correlation was however found.We discuss the possibility that surges are the result of a sudden energy input into the chromosphere related to the type I source in the corona.     

The relation between far-UV and visible extinctions

For directions of sufficient reddening (E(B−V)>∼0.25), there is a simple relation between the slope of the extinction curve in the far-UV and E(B−V). Regardless of direction, the far-UV extinction curve is proportional to 1/λⁿ e^{−2E(B−V)/λ} (λ in μm, n=4), in accordance with the idea that reddened stars spectra are contaminated by scattered light (Zagury, 2001b).This relation is not compatible with the standard theory of extinction which states that far-UV and visible extinctions are due to different classes of particle. In that model the two (far-UV and visible) extinctions vary thus independently according to the proportion of each type of particle.In preceding papers I have shown that the standard theory cannot explain UV observations of nebulae, and is contradicted by the UV spectra of stars with very low reddening: for how long shall the standard theory be considered as the interpretation of the extinction curve?     

A relation between Giorgilli-Galgani's and Deprit's algorithms

If \(T = \sum\nolimits_{i = 1}^\infty {\varepsilon ^i } T_i\) and \(W = \sum\nolimits_{n = 1}^\infty {n\varepsilon ^{n - 1} } W^{\left( n \right)}\) are respectively the generators of Giorgilli-Galgani's and Deprit's transformations, we show that the change of variables generated byT is the inverse of the one generated byW, ifT _i =W ⁽ⁱ⁾ for anyi. The method used is to show that the recurrence which defines the first algorithm can also be obtained with the second one.     

The relation between hot and cool loops

In order to study the origin of the hot (3 MK) corona above active regions, we compare Yohkoh/SXT X-ray images, which represent a broad temperature range above 2.5 MK, with TRACE EUV coronal images whose primary sensitivities are in the 1–2 MK range. Nearly simultaneous X-ray and EUV snapshots show that there are loops that appear similar in these images of different temperature sensitivities, but they are not exactly cospatial with each other. A significant difference is noted in the active region core, where bright loops are seen in X-ray images but not in EUV images, reflecting their high (5 MK) temperatures. In SXT time-sequence images, these loops are found to undergo repetitive minor brightenings, suggestive of their flare-like origin. This is consistent with the absence of the EUV counterparts of the X-ray loops in TRACE time-sequence images at earlier and later times. We need to revisit the validity of the assumption that coronal loops are steady.     

On the relation between resonance and instability in planetary systems

The factors which affect the linear stability of a periodic planetary orbit in the plane are studied. It is proved that planetary systems with two planets describing nearly circular orbits in the same direction are linearly stable and no perturbation exists which destroys the stability, unless a resonance of the form 1/3, 3/5, 5/7, ... among the orbits of the planets occurs. This latter resonant case is always unstable. Retrograde motion is always linearly stable. Planetary systems with three or more planets in nearly circular orbits in the same direction are proved to be unstable, in the sense that a Hamiltonian perturbation always exists which destroys the stability. The generation of instability in the case of three or more planets is not only due to the existence of resonances, as in the case of two planets, but also to the nonexistence of integrals of motion, apart from the energy and angular momentum integrals. It is also proved that planetary systems with nearly elliptic orbits of the planets are unstable.