An equation of state at subnuclear densities

An equation of state for cold matter above white dwarf densities is evaluated. The gas is considered to be a mixture of degenerate neutrons, protons and electrons combined with nuclei of one type (that is only oneA andZ value). We derive the equilibrium equations for the mixture and calculate the number densities as well as theA andZ of the nucleus. Finally we calculate an equation of state, which smoothly goes over to that of a neutron, proton electron gas mixture at a density of 5×10¹³ g/cm³.     

Roughness of the lunar soil

In situ measurements at the lunar surface at millimeter resolution by the Apollo astronauts have been analyzed. Several statistical parameters have been determined for the landing site. The surface roughness has been found to be very nearly gaussian. The root-mean-square slopes have been obtained over scales between 0.5 mm and 5 cm. They steadily decrease with increasing scale length from 58° to 2° and are in reasonable agreement with radar-measured values. The autocorrelation coefficient of the height distribution has also been obtained. It has a scale-length of 0.7 mm.Adjunct Professor at the University of Massachusetts.Visiting Scholar at the University of Massachusetts.     

Structure and dynamics of the Bok globule B335

CO maps of the Bok globule B335 are presented and used to derive its density profile, mass distribution, and rotational velocity structure. It is found that the cloud is in nearly hydrostatic equilibrium with a density profile that varies roughly as r^?1 in the core and r^?3 in the envelope. The observed rotation is unimportant in the force balance at the present stage of evolution.     

Environmental changes on Yugorski Peninsula, Kara Sea, Russia, during the last 12,800 radiocarbon years

New pollen and radiocarbon data from an 8.6-m coastal section, Cape Shpindler (69°43′N; 62°48′E), Yugorski Peninsula, document the latest Pleistocene and Holocene environmental history of this low Arctic region. Twelve AMS ¹⁴C dates indicate that the deposits accumulated since about 13,000 until 2000 radiocarbon years BP. A thermokarst lake formed ca. 13,000–12,800 years BP, when scarce arctic tundra vegetation dominated the area. By 12,500 years BP, a shallow lake existed at the site, and Arctic tundra with Poaceae, Cyperaceae, Salix, Saxifraga, and Artemisia dominated nearby vegetation. Climate was colder than today. Betula nana became dominant during the Early Preboreal period about 9500 years BP, responding to a warm event, which was one of the warmest during the Holocene. Decline in B. nana and Salix after 9500 years BP reflects a brief event of Preboreal cooling. A subsequent increase in Betula and Alnus fruticosa pollen percentages reflects amelioration of environmental conditions at the end of Preboreal period (ca. 9300 years BP). A decline in arboreal taxa later, with a dramatic increase in herb taxa, reflects a short cold event at about 9200 years BP. The pollen data reflect a northward movement of tree birch, peaking at the middle Boreal period, around 8500 years BP. Open Betula forest existed on the Kara Sea coast of the Yugorski Peninsula during the Atlantic period (8000–4500 years BP), indicating that climate was significantly warmer than today. Deteriorating climate around the Atlantic–Subboreal boundary (ca. 4500 years BP) is recorded by a decline in Betula percentages. Sedimentation slowed at the site, and processes of denudation and/or soil formation started at the beginning of the Subatlantic period, when vegetation cover on Yugorski Peninsula shifted to near-modern assemblages.     

Pre-perihelion CCD photometry of Comet 1995 01 (Hale-Bopp)

Systematic CCD photometry of Comet 1995 O1 (Hale-Bopp) began in early August 1995 shortly after its discovery (IAU Circular 6187) and continued until mid-November 1996. The light curve derived from a 34″ square centered on the nucleus shows clearly and objectively how the inner regions of the comet brightened during this 15 month period. Possible connections between sudden brightenings and reported outbursts are investigated. During the interval August–December 1995, the magnitude of the comet showed strong evidence of a periodicity of 20±5 days with a full amplitude of approximately 0.20 mag. It is noteworthy that this result spans both the period of 18 days suggested by Sekanina (1995, 1996) and the “superperiod” of 22±2 days reported by Jorda et al. (1997). However, in 1996 neither this periodicity nor any other could be detected with certainty in the photometric data.     

Automated,closed form integration of formulas in elliptic motion

In some perturbation theories it is possible to avoid expansion of the perturbations in powers of the eccentricity, obtaining results in closed form by using the true or eccentric anomaly instead of the mean anomaly. This paper describes an algorithm (which has been programmed for the 6600 computer using the formula manipulation system TRIGMAN) for automatically performing the integrals which arise in these theories.     

Ionospheric conditions

A general analysis of ionospheric conditions has been made in the light of possible ionic reactions occurring in the upper atmosphere. Data obtained on various parameters, such as ionic production and recombination, show that precise knowledge of the spectral distribution of solar radiation is needed and that other experimental determinations on dissociative recombinations are required.

The ionic complexity of the ionosphere is underlined by describing how the atomic ions O⁺ and N⁺ react with N₂, O₂ and NO molecules. The behavior of the molecular ions N⁺₂, O⁺₂and NO⁺depends on a group of simultaneous processes involving charge transfers and ionatom interchanges which are more important than dissociative recombinations. The altitude distribution of ions is exemplified by discussing the relative importance of various loss coefficients in the D-, E- and F-regions. It is seen that molecular nitrogen ions are subject to important charge transfer processes, that nitric oxide ions are always final products destroyed only by dissociative recombination. Additionally, the entire production of atomic oxygen ions is related to the photoionization of molecular nitrogen. Some information is also given on possible anomalies in the ratio of O⁺₂ and NO⁺ densities in the lower ionosphere. From the lack of sufficient experimental information on ionic processes it is shown that a precise analysis of ionospheric behavior remains highly speculative.     

Optimal low-thrust takeoff from an orbit about an oblate planet

Future space missions to the outer planets may depend upon the use of low-thrust propulsion systems. As these planets are decidedly oblate, the question of the effect of that oblateness on a low-thrust trajectory is of some interest. In this paper the problem of optimal energy increase is attacked under the assumption that the coefficients for the second zonal harmonic, i.e.,J ₂, and the nondimensional thrust acceleration are the same order of magnitude. Using a two variable asymptotic expansion technique, a near optimal control program is generated and the first order uniformly valid approximation for the corresponding trajectory is obtained. Tangential thrust is shown to be a good near-optimal thrust program even in the presence of oblateness effects. The optimal control program is found to be oscillatory and quite similar to the optimal control for energy increase in an inverse square gravitational field.This research was supported by the National Aeronautics and Space Administration under Grant NGR-23-005-329.     

An improved lunar moment of inertia determination: a proposed strategy

The current error of 0.0025 on the lunar homogeneity parameterI/MR ² is dominated by the uncertainties in theC ₂₀ andC ₂₂ gravity harmonics. This error level is equivalent to a 4.20 gm cm^–3 density uncertainty for a lunar interior model having a core 300 km in radius. Covariance analyses are performed using Doppler data from the relay satellite of the proposed Lunar Polar Orbiter mission to determine an optimum reduction strategy which obtains an order of magnitude improvement in the gravity estimates. Error studies show the long-arc reduction method obtains results which are an order of magnitude more accurate than the short-arc technique. The nominal 4000 km circular orbit of the relay satellite is very sensitive to the unmodeled effects of gravity harmonics of degree 5 through 9. Results from this orbital geometry indicate that it may not be possible to achieve the desired order of magnitude accuracy improvement. A modified orbit having the identical orbital conditions as the nominal one, but with a larger semi-major axis of 7000 km is studied. Results show the desired order of magnitude improvement can be achieved when a complete fourth degree and order model and some fifth and sixth degree terms are estimated while considering the unmodeled effects of the remaining harmonics through degree and order eight. Studies also show a 50% additional improvement inC ₂₂ can be achieved if differential differenced Doppler is also processed with the direct Doppler. The improved uncertainty inI/MR ² reduces the core density error from 4.20 gm cm^–3 to 0.1 gm cm^–3 for the case of a lunar density model having a 300 km core radius.Contribution #2885 of the Division of Geological and Planetary Sciences, California Institute of Technology, Pasadena, California 91125, U.S.A.