NASA NTRS · 19780005003
An analysis was made of current heat flow data and thermal models of lunar evolution which satisfy the diverse information that has accumulated on internal processes.
Ye A Lyubimova. 1977-01-01. Heat Flow and Thermal History of the Moon. https://ntrs.nasa.gov/citations/19780005003
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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.
Analyses of lunar rocks have confirmed that the interior of the Moon has been subjected to magmatic differentiation, as has been determined by calculation of the thermal history of the Moon. However, it appears that differentiation occurred so early that it could not have been related to heating by long-lived radioactive elements, but rather indicates a high initial temperature of the Moon. The reasons for the high initial temperature remain unknown. The presence of a central, partially melted area revealed by seismic observations forces us to reject convective models of the Moon, while the dimensions of this area, together with the measured heat fluxes from the interior, serve as "boundary conditions" for any new calculations of the thermal history for a two-layered differentiated model of the Moon operative over the past 3.5 billion years. If we start with the early differentiation of the Moon and the high content of long-lived radioactive elements in it, explanation of its current thermal properties represents no difficulty. But these prerequisites themselves remain unexplained. Due to the continuing controversy concerning the true nature of the process of magmatic differentiation of the Moon, estimation of the composition of the entire Moon on the basis of analyses of surface rock remains unreliable, and use of these estimates to clarify the origin of the Moon is premature. Existing hypotheses concerning the origin of the Moon encounter dynamic difficulties, as well as difficulties with explanation of the high initial temperature, to say nothing of the difficulty involved in explaining the proposed differences in the composition of the Earth and Moon.
Among icy moons of the outer Solar System, subsurface water oceans and large collisions both seem to be common, but the impact of the latter on the presence and persistence of the former is unclear and has rarely been investigated. Here we interface a smoothed-particle hydrodynamics model to simulate collisions with a thermal-structural evolution model to simulate the evolution of moons pre-collision, post-collision and without a collision. Overall, even such large-scale collisions affect only the ocean thickness or longevity, and the presence or absence of an ocean is affected for only a part of a moon’s history. In reaccreted moons, the ocean survives the impact and becomes much thicker inside larger moons with radius near 1,000 km, whereas an ocean that would otherwise arise inside moons with radius near 500 km is absent because the collision promotes ice–rock differentiation. Our simulations have not yielded an ocean developed post-impact—whether directly via collisional or reaccretional heating or indirectly through tidal heating due to collision-induced orbital changes—in a moon that would otherwise have remained frozen. The ocean-enhancing effect is pronounced only for late disruptive impacts onto large, 1,000-km-class targets, which are unlikely in recent solar system history.