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NASA NTRS2026

Beyond Melting: Amorphous Bonding for Joining and Consolidation

Crystallization may be the hidden constraint in thermoplastic composite manufacturing. It requires tightly controlled cooling, induces residual stresses through shrinkage, and introduces path-dependent behavior that complicates predictive modeling yet remains essential for structural performance. This work asks: can bonding be achieved without relying on melt-driven crystallization? To address this, thin (5–20 μm) polyetherimide (PEI) interlayers are pre-healed to slow-cooled polyaryletherketone (PAEK) in two contexts. The first, Thermabond®, is sub-melt joining of low melt-PAEK laminates. Results show that bond quality is governed primarily by processing (i.e., adequate healing and film handling) rather than modest changes in interlayer thickness. This concept is then extended to laminate-scale manufacturing through an architecture known as OATMEAL (Out-of-autoclave Amorphous/semicrystalline Thermoplastic Material for Energy-efficient Aerospace-grade Laminates). PEI is healed to carbon fiber reinforced polyetheretherketone (PEEK) at the prepreg and excess PEI is then ablated from the surface. Crystallinity is developed off-line during prepreg fabrication, while subsequent consolidation occurs below the melt temperature to preserve it. Cross-ply warpage experiments show that, contrary to intuition, repeated amorphous interfaces reduce global curvature by lowering the effective stress lock-in temperature and eliminating crystallization shrinkage from the lamina response. Correspondingly, laminate behavior is accurately predicted using classical laminate theory (CLT) with a single effective stress-free temperature, whereas conventional CF/PEEK requires accounting for crystallization-driven effects. By decoupling interfacial healing from crystallization, OATMEAL enables sub-melt consolidation, reduces energy consumption by up to 75%, and increases manufacturing throughput by fivefold. These results demonstrate that amorphous bonding is not only a joining strategy, but a pathway to more predictable and scalable thermoplastic composite manufacturing.

solidification↗

NASA NTRS2018

Initial Jitter Analysis of Lynx, a Proposed Future Large Astrophysics Facility

Lynx is an X-Ray telescope large-mission concept for consideration in NASA's 2020 Astrophysics Decadal Survey. A conceptual structural design is evolving that leverages the success and lessons learned from Chandra and that takes into account unique needs of Lynx. Space optics systems require extreme stability. Any motion in-service (thermal effects, structural dynamics, etc.) impacts performance. An initial analysis was performed to predict the first-cut dynamic responses, jitter, at two selected points on the Lynx observatory. One point is on the Lynx X-ray Mirror Assembly (LMA) and the other, on the focal plane Integrated Science Instrument Module (ISIM). Relative motion between these two points was predicted along with vibration spectra. This information will be used in upcoming analyses of the LMA and the ISIM.

J Brent Knight↗

NASA NTRS1977

Magnetic and Dielectric Properties of Lunar Samples

The dielectric properties of lunar soil and rock samples show a systematic character when careful precautions are taken to ensure there is no moisture present during measurement. The dielectric constant (K) above 10 5 Hz is directly dependent on density according to the formula K = (1.93 ± 0.17) p where p is the density in g/cc. The dielectric loss tangent is only slightly dependent on density and has values less than 0.005 for typical soils and 0.005-0.03 for typical rocks. In addition to a density dependence, the loss tangent appears to be directly related to the metallic ilmenite content. These results are in good agreement with the results of the Surface Electrical Properties Experiment carried on Apollo 17. It showed a surface layer of dielectric constant 3.8 and a loss tangent of 0.008. This is presumed to be a layer of compact soil about 7 m thick, overlying a medium with a dielectric constant of roughly 7.5 and a loss tangent interpreted to be 0.035, The medium is presumed to be bedrock. These results are compatible with seismic results. The magnetic properties of lunar samples can be used to study the distribution of metallic and ferrous iron which shows systematic variations from soil-type to soil-type and a general tendency to increasing Fe°/Fe** distribution in the more highly rewelded breccias. The other magnetic characteristics can also be used to determine the distribution of grain sizes. There are a number of ways of interpreting the origin of the stable remanent magnetization in lunar samples, but several lines of evidence suggest that it is of thermal origin and was acquired at a time when the igneous rocks and breccias cooled from above 800°C in the presence of an ancient field.

D W Strangway↗

NASA NTRS2025

Operational Correction for the Temperature Dependence of A Class of Hyperspectral Radiometers

The correction for temperature response of optical radiometers implies access to their working temperature (i.e., either the internal or ambient one with the radiometers in thermal equilibrium). With specific reference to a class of widely used hyperspectral radiometers lacking a thermistor to measure the internal temperature, this work investigated the potential for operational corrections relying on the ambient temperature derived from the radiometer dark digital counts. With the objective to keep within approximately 1% the uncertainty for radiometric corrections in the 400–800-nm spectral range, findings showed the applicability of the method for ambient temperatures higher than approximately 30°C. The alternative use of an ambient temperature proxy, determined from the air temperature incremented by a few degrees Celsius, was shown a valid solution to constrain the uncertainty of radiometric corrections to within 1% over the entire 0°–40°C interval.

Giuseppe Zibordi↗

NASA NTRS1964

Performance of Solar Reflectors When Applied to Storage of Cryogenic Propellants in Space

An analysis was performed to determine the effectiveness of solar reflectors in reducing heat transfer through the insulation of cryogenic fuel tanks located in deep space. A solar reflector, as used herein, is defined as a surface having a ratio of absorptance with respect to solar radiation to hemispherical emittance (α/ϵ) less than 1.0. This analysis considers the effect of surface coatings with α/ϵ values varying from 0.1 to 1.0 when applied to the external surfaces of bulk insulation or multifoil insulation. Results were obtained in terms of heat leak to two cryogenic propellants, liquid hydrogen and liquid oxygen, when stored at Mars, Earth, and Mercury orbital distances from the sun. The results show that, with sufficiently good insulation and low heat leaks to the propellant, α/ϵ is a reasonable criterion of merit for these coatings, but that, at larger heat leaks, consideration of ϵ (or α) is necessary. It was observed that selective finishes of α/ϵ = 0.1 on a given amount of bulk insulation material can reduce the heat leak to 40 to 55 percent of the heat leak obtained when gray finishes are considered. Or, for equivalent heat leaks, a reduction in bulk insulation material thickness of about one-half is possible with high-quality selective finishes (α/ϵ = 0.1) compared with flat reflectors. Larger benefits may be achieved from selective finishes painted on foils; the analysis shows that heat leak may be reduced tenfold for surfaces with an α/ϵ of 0.1 compared with gray surfaces. Again, consideration of equivalent heat leaks indicates that the use of approximately 10 times fewer foils of emissivity 0.05 is possible when spectrally selective surfaces are employed. The present state of the art in achieving such surfaces is also briefly reviewed.

Propellant Storage↗

NASA NTRS1977

A Survey of Lunar Rock Types and Comparison of the Crusts of Earth and Moon

The principal known types of lunar rocks are briefly reviewed, and their chemical relationships discussed. In the suite of low-KREEP highland rocks, Fe/(Fe + Mg) in the normative mafic minerals increases and the albite content of normative plagioclase decreases as the total amount of normative plagioclase increases, the opposite of the trend predicted by the Bowen reaction principle. Lunar highland samples analyzed are uniformly distributed in this sequence, in which normative plagioclase contents range from ~ 40 percent to ~ 100 percent. The distribution of compositions of rocks from terrestrial layered mafic intrusives is substantially different: here the analyses fall in several discrete clusters (anorthositic rocks, norites, granophyres and ferrogabbros, ultramafics), and the chemical trends noted above are not reproduced. It is suggested that the observed trends in lunar highland rocks could be produced by crystal fractionation in a deep global surface magma system if (1) plagioclase tended to float, upon crystallization, and (2) the magma was kept agitated and well mixed (probably by thermal convection) until crystallization was far advanced and relatively little residual liquid was left. When such a system was finally immobilized, the Fe-, Na-rich residual liquid would produce Fe-rich mafic minerals in the upper levels of the system, but could not much alter the composition of abundant calcic plagioclase. Conversely, the same liquid would produce sodic plagioclase deep in the sequence, but could not much alter the composition of abundant magnesian mafic minerals. After the crustal system solidified, but before extensive cooling had developed a thick, strong lithosphere, mantle convection was able to draw portions of the lunar anorthositic crust down into the mantle in a manner analogous to the present-day behavior of the terrestrial mantle and crust. At depth, the crustal material was heated; KREEP-rich norite was extracted by partial melting and erupted at the surface as a lava, analogous to terrestrial andesite eruptions.

John A Wood↗

NASA NTRS1990

Space Environments and their Effects on Space Automation and Robotics

Automated and robotic systems will be exposed to a variety of environmental anomalies as a result of adverse interactions with the space environment. As an example, the coupling of electrical transients into control systems, due to EMI from plasma interactions and solar array arcing, may cause spurious commands that could be difficult to detect and correct in time to prevent damage during critical operations. Spacecraft glow and space debris could introduce false imaging information into optical sensor systems. The presentation provides a brief overview of the primary environments (plasma, neutral atmosphere, magnetic and electric fields, and solid particulates) that cause such adverse interactions. The descriptions, while brief, are intended to provide a basis for the other papers presented at this conference which detail the key interactions with automated and robotic systems. Given the growing complexity and sensitivity of automated and robotic space systems, an understanding of adverse space environments will be crucial to mitigating their effects.

Henry B Garrett↗

NASA NTRS2002

Proceedings of the 36th Aerospace Mechanisms Symposium

The Aerospace Mechanisms Symposium (AMS) provides a unique forum for those active in the design, production, and use of aerospace mechanisms. A major focus is the reporting of problems and solutions associated with the development and flight certification of new mechanisms. Organized by the Mechanisms Education Association, the National Aeronautics and Space Administration and Lockheed Martin Space Systems Company (LMSSC) share the responsibility for hosting the AMS. Now in its 36th year, the AMS continues to be well attended, attracting participants from both the United States and abroad. The 36th AMS, hosted by the Glenn Research Center (GRC) in Cleveland, Ohio, was held May 15, 16, and 17, 2002. During these three days, 32 papers were presented. Topics included deployment mechanisms, tribology, actuators, pointing and optical mechanisms, International Space Station mechanisms, release mechanisms, and test equipment. Hardware displays during the supplier exhibit gave attendees an opportunity to meet with developers of current and future mechanism components.

Boesiger, Edward A.↗

NASA NTRS2026

Improvement of Odor Control for the UWMS Hard-Sided Fecal Canister and the Alternate Fecal Canister

On longer range exploration missions, the mass and volume of critical hardware and consumables required to support crew will pose a big stowage challenge. This includes the hardware for the collection and storage of human metabolic solid waste. The amount of stowage needed for this hardware both before (empty) and after (full) use will be a significant burden on the overall spacecraft habitable volume, layout, and design. To help with this challenge, the National Aeronautics and Space Administration (NASA) Mars Campaign Office (MCO) Logistics Reduction (LR) Portfolio has developed a collapsible canister for the collection and containment of fecal deposits. The Alternate Fecal Canister (AFC) is a collapsible alternative to the exploration toilet Hard-sided Fecal Canister (HFC). The AFC in its empty state has a volumetric benefit to smaller vehicles on longer missions. The current designs for HFC and AFC were tested with human fecal material for odor containment at White Sands Test Facility (WSTF) where the tests on both were unsuccessful. The source of the lack of containment was isolated to a gasket used on both HFC and AFC. The gasket used was found to be open cell in design. This paper provides a summary of the materials selection and testing process to identify a replacement gasket material with the intention to replace the gaskets on both existing units as well as incorporate it into the designs going forward for future builds for exploration. Details will be provided on the design of the canisters interface with the odor bacteria lid which led to the selection of the thickness of the desired replacement. Finally, the paper will provide an update on the testing in advance of a return to WSTF for final testing and detail plans to complete testing and perform a demonstration on ISS with UWMS.

Toilet↗

NASA NTRS1995

Analysis of Gas Absorption to A Thin Liquid Film in the Presence of A Zero-Order Chemical Reaction

The paper presents a detailed theoretical analysis of the process of gas absorption to a thin liquid film adjacent to a horizontal rotating disk. The film is formed by the impingement of a controlled liquid jet at the center of the disk and subsequent radial spreading of liquid along the disk. The chemical reaction between the gas and the liquid film can be expressed as a zero-order homogeneous reaction. The process was modeled by establishing equations for the conservation of mass, momentum, and species concentration and solving them analytically. A scaling analysis was used to determine dominant transport processes. Appropriate boundary conditions were used to solve these equations to develop expressions for the local concentration of gas across the thickness of the film and distributions of film height, bulk concentration, and Sherwood number along the radius of the disk. The partial differential equation for species concentration was solved using the separation of variables technique along with the Duhamel's theorem and the final analytical solution was expressed using confluent hypergeometric functions. Tables for eigenvalues and eigenfunctions are presented for a number of reaction rate constants. A parametric study was performed using Reynolds number, Ekman number, and dimensionless reaction rate as parameters. At all radial locations, Sherwood number increased with Reynolds number (flow rate) as well as Ekman number (rate of rotation). The enhancement of mass transfer due to chemical reaction was found to be small when compared to the case of no reaction (pure absorption), but the enhancement factor was very significant when compared to pure absorption in a stagnant liquid film. The zero-order reaction processes considered in the present investigation included the absorption of oxygen in aqueous alkaline solutions of sodiumdithionite and rhodium complex catalyzed carbonylation of methanol. Present analytical results were compared to previous theoretical results for limiting conditions, and were found to have very good agreement.

S Rajagopalan↗

NASA NTRS2026

Improvement of Odor Control for the UWMS Hard-Sided Fecal Canister and the Alternate Fecal Canister

ECLSS↗

NASA NTRS2026

Investigation of Bipropellant Plume-Induced Contamination Effects on Coverglass Materials

Contamination and degradation of external spacecraft materials by unburned and partially combusted species from bipropellant thruster plumes has long been observed as a key component of the induced space environment. Space shuttle flight experiments and returned flight hardware from the International Space Station (ISS) have both experienced microscopic impact features induced by high-velocity thruster plume droplets. Analytical results have shown that droplet impingement angle relative to a receiving surface plays a key role in the surface damage. Although impacts with normal impingement angles contribute more severely to surface degradation than highly oblique angles, surface effects at higher impingement angles should not be dismissed. Thruster plume-induced materials degradation is a complex phenomenon that depends on a variety of parameters, including but not limited to material type, system temperature and pressure, plume composition, and thruster firing specifications such as number of pulses, pulse duration, and sample distance from the thruster. For space applications, attaining the vacuum pressure and temperature conditions necessary for flight-like plume expansion and exposure conditions is not a trivial task. The German Aerospace Center (Deutsches Zentrum für Luft- und Raumfahrt, DLR) is a facility uniquely capable of simulating such conditions. Test coupons were exposed to bipropellant thruster firings under high vacuum at the DLR facility. Percent area coverage (PAC) and droplet size distributions were evaluated for the uncoated and coated solar array coverglass materials over a range of impingement angles (0̊ to 75̊). A post-test imaging workflow was developed that aimed to quantify changes in sample surface morphology obtained from scanning electron microscopy (SEM) images using the Image Processing and Analysis in Java (ImageJ) tool; an opensource image processing software. The goal was to create a framework through which to evaluate the effect of bipropellant-induced PAC and droplet size distribution on solar array coverglass optical transmission losses. Understanding this relationship is important because optical transmission losses are known to lead to current reduction in solar power generation systems. In addition to the development of surface characterization workflows, valuable lessons learned as they pertain to future investigations and experiments will be discussed. The authors hope that sharing these lessons will facilitate more utilization of DLR’s unique capabilities as well as open the conversation for how best to address experimental characterization of flight-like plume expansion and its impacts on materials surface degradation effects.

Gateway↗

NASA NTRS2026

Tracing the Source of Carbon Oxides on the Large Moons of Uranus

The Uranian moons Ariel, Umbriel, Titania, and Oberon are enriched in CO 2 mixed with CO, but the origin(s) of these carbon oxides, be they primarily native or radiolytic, remain(s) uncertain. Using data collected by NIRSpec on the James Webb Space Telescope (JWST), we measured the spectral signature of CO 2 and other carbon oxides to help disentangle these hypotheses. Through comparison to laboratory data, we find that many of the detected spectral features are consistent with CO 2 ice, including 12 CO2 scattering peaks (4.15–4.26 μm), multilobe 13 CO 2 bands (4.35–4.43 μm), and CO 2 biphonon and triphonon modes (4.80–5.25 μm). Our measurements show that CO 2 and CO are concentrated on the trailing hemispheres of the inner moons Ariel and Umbriel, potentially supporting a radiolytic production hypothesis, consistent with prior ground-based results. However, many of the identified spectral features are only observed in thick crystalline ice deposits measured in the laboratory, which may be difficult to form via radiolysis of carbon-bearing material mixed in icy regoliths. Similarly, the data exhibit weak 4.02 and 4.40 μm bands, hinting at the presence of carbonate minerals and 13 CO 2 clathrates, respectively, possibly formed in the interiors of these moons. Furthermore, JWST has revealed that CO 2 is widespread at Uranus, present in its system of rings, ring moons, and irregular satellites, consistent with its largest moons accreting CO 2 and other carbon oxides from the Uranian subnebula. We conclude that exposed carbon oxides are potentially native, with their surface distributions shaped by charged particle irradiation and seasonal sublimation–condensation cycles.

Ice spectroscopy↗

NASA NTRS1992

Ruled and holographic experiment (AO 138-5)

The AO 138-5 experiment has been designed, via the French Cooperative Payload (FRECOPA) experiment with the aim to study the optical behavior of different diffraction gratings submitted to space vacuum long exposure and solar radiation. Samples were rules and holographic gratings, masters or replica, and some additional control mirrors with various coatings. The experiment was located on the B3, trailing edge of the Long Duration Exposure Facility (LDEF) and has been protected against atomic oxygen flux. The experienced thermal cycling has been evaluated from -23 C to 66 C during the flight, 34,000 orbits. The analysis has been focused on the triple point characterization including light efficiency, wavefront flatness quality and stray light level. Tests were conducted on control mirrors and gratings loaded but not exposed to cosmic dust or solar irradiations. They did not show any significant variations. Solar exposure has damaged the coating reflectivity in the ultraviolet region, the degradation is higher with the gratings, in terms of efficiency. However, wavefront flatness quality and stray light level tests revealed no additional changes.

Francis Bonnemason↗

NASA NTRSDate not supplied

NASA's Small Spacecraft and Distributed Systems: Development and Demonstration of Technologies Enabling Swarms and New Spacecraft Platforms with AI and Edge Computing

NASA’s Small Spacecraft & Distributed Systems (SSDS) within the Research and Technology Mission Directorate (RTMD) expands U.S. capability to execute unique missions through targeted investment, rapid development, and flight demonstration of small spacecraft technologies applicable to exploration, science and the commercial space sector. SSDS strategically invests in technology development and on-orbit demonstrations executed across NASA, other government agencies, industry, and academia. The program’s University SmallSat Technology Partnerships initiative awards academic researchers with the opportunity to collaborate with NASA to mature innovative technology. Capabilities aligned with RTMD’s technology shortfalls and interests - power, processing, propulsion, sensors, communications, autonomous navigation, architectures, and advanced applications like artificial intelligence (AI), machine learning, and edge computing - are prioritized in SSDS investments. These investments enable distributed, autonomous, and cooperative small spacecraft systems that support swarm missions extending beyond low Earth orbit into cislunar and deep space. This paper highlights representative SSDS flight demonstrations that mature these capabilities to enable a future operational infrastructure needed to support sustained exploration of the Moon and beyond. SSDS’s investment strategy emphasizes rapid development and on-orbit demonstration to validate spacecraft technologies required for swarms and distributed mission architectures. The Starling swarm technology demonstration mission exemplifies this approach by advancing distributed spacecraft autonomy, cooperative operations, and space situational awareness. Extended flight testing and ongoing studies of next generation swarm configurations and on-orbit space traffic monitoring and management continue to inform future swarm designs. DiskSat’s four-spacecraft demonstration mission represents SSDS’s strategic vision to expand the design space for future small spacecraft through its commitment to advance novel platform concepts that can impact how science is performed on orbit. Continuing to invest in future platforms, the notional PY12 concept is a 12-spacecraft swarm hosting neuromorphic processors and is envisioned as an on-orbit testbed for AI, edge computing, and positioning, navigation and timing technologies. SSDS also invests in single-spacecraft technology demonstrations that underpin the success of future swarm missions and accelerate the availability of validated technologies across the small spacecraft ecosystem. Examples of such demonstrations include Pathfinder Technology Demonstrator-3 (PTD-3), which performed high-rate optical communications; PTD-R, which demonstrated a camera capable of simultaneous ultraviolet and short-wave infrared optical sensing; and CAPSTONE, the Cislunar Autonomous Positioning System Technology and Operations Navigation Experiment, which validated autonomous navigation in cislunar space. Collectively, SSDS-funded demonstrations advance capabilities across swarms and illustrate a coordinated investment strategy to mature high-impact technologies required for autonomous, distributed, and cooperative small spacecraft systems for low Earth orbit, cislunar, and deep space applications. Technology demonstrations strengthen SSDS partnerships with industry, academia, and other government agencies, and promote small spacecraft community adoption of capabilities required to close technical gaps for swarm missions.

Jan Stupl↗

NASA NTRS2026

Development and Validation of a High-Vacuum Thermal Conductivity Testbed for Aerospace Interface Materials

Thermal Interface Materials (TIMs) are critical components in spacecraft thermal management systems, where thermal performance is strongly influenced by vacuum conditions, interface contact resistance, and layered metallic joint behavior. However, manufacturer-reported thermal conductivity values are often derived under idealized conditions and may not accurately represent performance within operational aerospace applications. To address this limitation, the Testbed for Advanced Interface Materials in Vacuum (TAIMV) was developed as a modular vacuum-compatible thermal conductivity characterization platform capable of evaluating aerospace-relevant TIM configurations under both ambient and high-vacuum environments. The testbed was derived from the ASTM C1044-16 guarded hot plate methodology and incorporates interchangeable layers of stainless steel coupon geometries, independently controlled main and guard heaters, embedded resistance temperature detectors (RTDs), thermocouples, multi-layer insulation (MLI), and a temperature-controlled cold plate to characterize through-thickness thermal gradients across layered interfaces. In the current configuration, interface compression is limited to the nominal contact pressure generated by the experimental stack assembly. Initial experimental campaigns were conducted at ambient pressure and below 1×10-5 torr for vacuum cases using multiple interface materials including Braycote 601EF and Krytox-based greases across a range of thermal operating conditions. In parallel, a coupled numerical Python thermal model was developed to predict temperature distribution throughout the stack while accounting for conduction, radiation, and parasitic heat transfer pathways and effective interface resistance effects. Experimental measurements and numerical predictions showed consistent thermal trends across multiple operating conditions and environmental states. Results also revealed measurable differences between ambient and vacuum thermal behavior, demonstrating the importance of interface resistance, parasitic heat transfer mechanisms, and stack geometry in determining effective thermal performance within layered thermal interfaces. The presented work establishes a foundation for future thermal model correlation efforts and expanded characterization of aerospace thermal interface materials under representative environmental conditions. Future work will focus on the integration of a load cell system to enable controlled pressure-dependent characterization of thermal interface materials under compressive loading. This capability will allow investigation of the influence of contact pressure on effective thermal conductivity, interface resistance, and thermal performance within layered aerospace thermal interfaces under representative operational conditions.

Thermal Development Testing↗

NASA NTRSDate not supplied

Evaluating Crystallinity in Thermoplastic composites

Polymer matrix composites (PMCs) offer many benefits for the aerospace industry due to their potential for weight reduction when compared to metal or ceramic based materials. Most PMCs currently in flight use thermoset matrices, however, thermoplastic resins are being explored as alternatives due to their ability to be remelted, which is of particular interest due to the potential for in-situ repair and manufacturing required in space. Most thermoplastic resins are semicrystalline polymers. The properties of semicrystalline thermoplastics are largely influenced by their crystallinity, which can vary due to many factors including thermal treatments, environmental conditions, and mechanical deformation. Monitoring the crystallinity of thermoplastic composites is key to ensuring these materials reliably meet the high demands required by space exploration. This talk discusses the use of multiple techniques such as Polarized Light Optical Microscopy and Fourier-Transform Infrared Spectroscopy to characterize the crystallinity in various thermoplastic composites, including carbon fiber reinforced PMCs and novel bio-based Martian and Lunar regolith composites designed for in-situ manufacturing. This work aims to provide the fundamental data necessary to understand the effects of crystallinity on thermoplastic PMCs, which is key to advancing their use in space applications.

Thermoplastics↗

NASA NTRS1977

Calculations of the Moon's Thermal History at Different Concentrations of Radioactive Elements, Taking Into Account Differentiation on Melting

Calculations of the thermal history of the moon were carried out by solving the thermal conductivity equation for the case in which the heat sources are the long-lived radioactive elements Th, U, and K 40 . The concentrations of these elements were adjusted to give four variations of the heat flow: 1.35 x 10 -8 and 0.91 x 10 -6 cal cm -2 s -1 (I and I**), 0.61 x 10 -6 (variant II, the terrestrial mixture of Lyubimova and Starkova), and 0.236 x 10 -6 (variant III, the chondrite model of Urey and MacDonald). In the same calculations, we considered layering of the differentiated material with transport to the surface of the radioactive elements after the temperature of the layer rose to 200 K above the melting temperature, which is considered in five variants that differ in the amount of transported radioactive elements: 100 percent ( n = 1), 80 percent n = 0.8), 40 percent, 20 percent ( n = 0.6, 0.4, 0.2). During fusion the heat capacity and heat conductivity were changed. We considered two variants of an initially cold (273 K) and hot (900 K) Moon. Calculations show that the interior of the Moon was heated to melting during the first 0.7 to 2.3 x 10 9 years. The maximum fusion involved practically the entire Moon to a distance from 15 to 45 km beneath the surface, and started 3.5 to 4.0 x 10 9 years ago (I, I**), or 2.5 to 3.0 x 10 9 years ago (II, III) and continued for 1 to 2 x 10 9 years. Today the Moon is cooling. The current thickness of the solid crust is from 150 to 200 km and the heat flow exceeds the stationary value 1.5 fold. Apparently the most realistic variant is II (terrestrial mixture) for an initially hot Moon, and gives, regardless of the moderate concentration of radioactive elements, a heat flow of 0.9 to 0.95 x 10 -6 cal cm -2 s -1 , which agrees with the radioastronomical measurements of Troitsky and Krotikov and with the Apollo 15 data.

O I Ornatskaya↗