A new photographic method for mapping lunar eclipse shadow

A new photographic method suitable for digital processing of a two-dimensional density distribution of lunar eclipse shadow has been developed and it has been applied to the observation of the eclipse of December 30, 1982. The principle of this method is to extract the terrestrial shadow by utilizing immediate post- or pre-eclipse full Moon image as a reference template. The uncertainties of the obtained shadow maps in density and position are mostly 0.03–0.05 and 10–15 respectively. Iso-density contours of the penumbra have revealed unknown systematic deviations from a geometrical (concentric) shadow model in terms of their directions of center and radii of curvature. A density map of the umbra has shown very irregular shapes of isophotoes and density variation in the outer umbra has been proved to be consistent with the optical depth measurement of the stratosphere performed in the same period of time with lidars and aircrafts. Geographic consideration of the shadow terminator on the Earth suggests that the remnant aerosols above the northern Pacific and northern Europe flown up by a Mexican volcano 8 months ago prior to this eclipse will be mainly responsible for the formation of such variation of density in the outer penumbra.On leave from Tokyo Astronomical Observatory as Visiting Scientist (from 28 Aug. 1984 to 27 Aug. 1985).     

Orbital evolution of giant comet-like objects

We investigated by numerical integrations the long-term orbital evolution of four giant comets or comet-like objects. They are Chiron, P/Schwassmann-Wachmann 1 (SW1), Hidalgo, and 1992AD (5145), and their orbits were traced for 100–200 thousand years (kyr) toward both the past and the future. For each object, 13 orbits were calculated, one for the nominal orbital elements and other 12 with slightly modified elements based on the rms residual of the orbit determination and on the number of observations. As past studies indicate, their orbital evolution is found to be very chaotic, and thus can be described only in terms of probability. Plots of the semi-major axis (a) and perihelion distance (q) of the objects treated here seem to cross each other frequently, suggesting a possibility of their common evolutionary paths. About a half of all the calculated orbits showedq- ora-decreasing evolution. This indicates that, at least on the time scale in question, the giant comet-like objects are possibly on a dynamical track that can lead to capture from the outer solar system. We could hardly find the orbits with perihelia far outside the orbit of Saturn (q>15 AU). This is perhaps because the evolution of the orbits beyond Saturn is so slow that substantial orbital changes do not take place within 100–200 kyr.     

Statistical nature of perihelion passages of long-period comets

The distributions of annual flux and time interval of perihelion passages of long-period comets are examined statistically. The former is found to be well represented by the Poisson distribution, while the latter by the exponential one. This means that the perihelion passages of long-period comets are an almost random phenomenon, at least within the time scale of a few hundred years, even if the samples are affected by observational selection and/or the effect of physical disruption.     

CCD surface photometry of an outburst of P/Schwassmann-Wachmann 1 comet

We have observed an outburst of P/Schwassmann-Wachmann 1 (SW1) on 25–26 July 1987 using a CCD imager with R-band filter. The total brightness increased from 15.5 mg (25d) to 14.4 mag (26d) during tabout 24 hrs. The southward elongated coma of 25 was detected. The radial surface brightness (B) profiles are plotted against apparent distance p from the nucleus. The logarithmic derivative k = d ln B/d ln p for the inner coma is found to have steepened from k = –1.40 (25d) to k = –1.69 (26d), whereas that for the outer coma showed no appreciable change (k = –1.19 ~ –1.22). The ellipticity of the isophotal contour of the inner coma increased about 15% fro 25d to 6d. It is concluded that the scale of this outburst was smaller than the typical ones whose magnitude change is 5–8 mag. From recent findings on the outburst natur eof SW1 including ours, a working model of the nuclues is proposed.     

Invisible comets on evolutionary track of short-period comets

We systematically surveyed the orbits of short-period (SP) comets that show a large change of perihelion distance (q) between 1–2 AU (visible comets) and 4–5 AU (invisible comets) during 4400 years. The data are taken from Cosmo-DICE (Nakamura and Yoshikawa 1991a), which is a long-term orbital evolution project for SP comets. Recognizing that q is the most critical element for observability of comets, an invisibility factor (f), defined as the ratio of unobservable time span to observable span during 4400 years, is calculated for each of the large-q-change comets. A detection limit for each comet is obtained from the heliocentric distance at discovery and/or the absolute magnitude at recent apparitions. A mean f value for 35 SP comets with 2.9 J (J is the Tisserand's invariant) is found to be 19.8. This implies that for each visible SP comet of this J-range, at every epoch of time, there exist about 20 invisible comets near the capture orbits by Jupiter, under the assumptions of steady-state flux and ergodicity for the SP-comet population.     

Orbital evolution of long-period comets I. Trivariate Monte Carlo simulation

The mean orbital evolution of long-period comets for 16 representative initial orbits to short-period comets is calculated by a Monte Carlo method. First, trivariate perturbation distributions of barycentric Kepler energy, total angular momentum, and its z component in single encounters of comets with Jupiter are obtained numerically. Their characteristics are examined in detail and the distributions are found to be simple, symmetric, and easy to handle. Second, utilizing these distributions, we have done trivariate Monte Carlo simulations of the orbital evolution of long-period comets, with special emphasis on high-inclination orbits. About half of the 16 initial orbits are traced up to 5000 returns. For each of these orbits, the mean values of semimajor axis, perihelion distance, and inclination; their standard deviations, survival, and capture rates; as well as time scales of orbital evolution are calculated as functions of return number. Survival rates of the initial orbits with high inclination (～90°) and small perihelion distance (～1–2 AU) have been found to be only two or three times smaller than those of the main-source orbits of short-period comets established quantitatively by Everhart. The time scales of orbitsl evolution of the former, however, are nearly 10 times longer than the latter. There is a general trend that, for smaller perihelion distance, the survival efficiency becomes higher. The results of this paper should be considered a basis for a succeeding paper (Paper II) in which the physical lifetime of comets will be determined, and a comparison with the orbital data will be done.