Fred A. Franklin

On the original distribution of the asteriods. I.

Abstract The depletion of an initially uniform distribution of asteroids extending form Mars to Saturn, caused by the gravitational perturbations of Jupiter and Saturn, is calculated by numerical integration of the asteroid orbits. Almost all (about 85%) the asteroids between Jupiter and Saturn are ejected in the first 6000 years Most of the asteroids between the 2 3 Jupiter resonance (4.0 A.U.) and Jupiter are ejected in the first 2400 years with the exception of the stable librators (e.g., the Hilda group). Interior to the 2 3 resonance the depletion was small, and interior to the 1 2 resonance (3.3 A.U.) no asteroids were ejected in the first 2400 years.

Saturn's rings - A survey.

Abstract In this review paper we first discuss the dimensions of major ring features and of the disk of the planet. We then summarize the observed photometric parameters, and because frozen H 2 O appears to be a major ring constituent, we compare the appropriate photometric properties of various forms of snow with those of the ring. We examine several ring models, noting certain characteristics that any model should supply. In our view, a physical means of accounting for the observed ring thickness of ∼2 km is a prime requirement. There appears to be one model that presents no clear observational or theoretical inconsistency. Finally, we list certain problems whose solutions should broaden our knowledge of the ring system.

An explanation of the light curve of Iapetus

Abstract This paper seeks a simple explanation for the large-amplitude (∼ 2 mag) periodic light curve of Saturns satellite Iapetus, which, as the light curve shows, apparently rotates synchronously. We point out that the mean densities of Saturns satellites increase from ∼ 1 gm cm −3 for the innermost to ∼ 3 gm cm −3 for Iapetus, a fact suggesting that frozen H 2 O, now quite certainly established as a major constituent of Saturns rings, forms a much larger fraction of the inner satellites than of the outer. We thus assume that Iapetus was once covered by a thin ice or snow layer, which, we show, has been more subject to erosion by meteoroidal bombardment on the “leading” hemisphere of the satellite in its orbit than on the “trailing” one. If the “initial” ice layer was ∼ 1 m thick and the interplanetary meteoroidal density has not changed much during most of the age of the solar system, then erosion by meteoroidal bombardment would produce the currently observed light curve and also account for the similar colors of the bright and faint hemispheres if the bare surface has sufficiently low reflectivity.

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

Abstract 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., J2 ≳ 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 106 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 Suns rotation by an intense solar wind during a T-Tauri stage of solar evolution.

On the azimuthal brightness variations of Saturn's rings

Abstract We present a simple, semiquantitative explanation that accounts both for the presence of the azimuthal brightness variations in Saturns ring A and for their absence in ring B. Our explanation avoids any ad hoc reliance on albedo variations and/or synchronous rotation of ring particles. Instead, it requires only some degree of self-gravitation between nearby orbiting bodies. A bias in the particle distribution and corresponding photometric effects are thereby produced—the latter corresponding very closely to the variations observed in ring A. Their absence in ring B is primarily a consequence of the higher optical thickness and decreasing importance of self-gravitation in that ring.

A dynamical model for the radial structure of Saturn's rings

Abstract In this paper we inquire whether the major positional features of Saturns ring can be explained by perturbations associated with the planets satellites. We assume a simple but observationally consistent model in which the ring is composed of a single layer of particles, and we further suppose that the system has evoted to a state in which collisions between particles may be ignored. Under these conditions, we find that only gravitational forces and the resulting perturbations by the two satellites Mimas and Titan suffice for a rather complete description of the ring system.

On predicting long-term orbital instability : a relation between the Lyapunov time and sudden orbital transitions

In three examples representative of Solar System dynamics, we find that the Lyapunov time, T L (i.e., the inverse of the Lyapunov exponent) and the time for an orbit to make a sudden transition T C are strongly correlated. The relation between the two times is T C ∞T L b , with b≅1.8. The first example examines asteroid orbits interior to Jupiter; the sudden transition occurs when the asteroid makes a close approach to Jupiter, which occurs close to the time when the asteroids orbit crosses Jupiters orbit

Photometry of Saturn's satellites: The opposition effect of Iapetus at maximum light and the variability of Titan

Abstract We present photometry, V and ( B - V ), of Iapetus at six western elongations (the phase of maximum brightness) that span a range in solar phase, α, from ≈6° to 0.12 mag ( V ), is present. We make a few cautious remarks about the possible relevance of the use of this result to interpret the phase curve of Saturns ring. We also give a few measures of Rhea and Hyperion, at α ≊ 0.3° , and more of Titan, which indicate that the latter has been anomalously bright during much of 1973 and 1974, sometimes by nearly 0.1 mag ( V ).

Predictions of mutual phenomena of the Galilean satellites in 1990–1992

Abstract An extended search shows that 200 observable eclipses and occultations of Galilean satellites occur between November 1990 and March 1992. This Note tabulates quantities needed to obtain light curves of these events, excluding only those occuring less than 2 Jovian radii from the planets center and/or with Jupiter and the Sun separated by less than about 25°. Since observations are quite short and are easy to incorporate into other photometric programs, we urge an active effort so as to provide accurate astrometric data for the Galileo Mission and to look for changes in Ios mean motion. For infrared observers interested in volcanism, there are a few moderately long occultations of Io.

Mutual phenomena of Jupiter's five inner satellites in 1979

Abstract In this paper, we first predict eclipses and occultations of the Galilean satellites in 1979 and find that, although circumstances are generally poor, about 75 events are observable. We have then made a special point of including 40 eclipses of J5 (Amalthea) by the Galilean satellites in the hope that both visual and far-infrared light curves can be obtained—the former giving accurate astrometric information for J5, and the latter possibly bearing on its surface stucture or composition.