Dec. 20, 2008 Two researchers from the universities of Valladolid and Alicante are developing a mathematical formula to study the rotation of the moon, taking into account its structure, which comprises a solid external layer and a fluid internal core.
Their work is part of an international study, which has come up with an improved theoretical model about the orbital and rotational dynamics of the Earth and its satellite, and which the scientific community will be able to use to obtain more precise measurements in order to aid future NASA missions to the moon.
Juan J. A. Getino, from the Applied Mathematics Department of the University of Valladolid, and Alberto Escapa, from the Applied Mathematics Department of the Higher Polytechnic School of the University of Alicante, suggest in their work that the Earth and the moon should be considered as “multi-layered” systems. In order to analyse their movements, the researchers have used Hamiltonian mechanics, a kind of classical mechanics used, among other things, to study the movements of heavenly bodies in response to gravitational effects.
“The Earth can be viewed as a three-layered system, with a solid exterior mantle, a fluid intermediary layer and a solid interior nucleus,” Getino tells SINC. The researcher points out that the new proposition applies multi-layer theories to the study of the rotation and movements of the moon, as well as its interaction with the Earth.
“The end objective of this multidisciplinary study is to develop a more complete model of the movements of the moon, to make it possible to correctly interpret the increasingly precise data we have about the distance between it and the Earth,” says Alberto Escapa.
Although based in classic mechanics, the contributions of the Spanish scientists to this study of the rotational and orbital dynamics of the moon are part of a more ambitious project based on Einstein’s general theory of relativity. In fact, the study, published recently in the journal Advances in Space Research, is being led by the relativist astronomer Sergei M. Kopeikin, from the University of Missouri, United States, and also involves the participation of other researchers from the United States, Germany, Russia and China.
Escapa points out that their proposition involves “extrapolating to the moon a mathematical model that we had previously developed in order to explain the small changes within the Earth’s rotational axis”. This model helped to improve GPS navigation systems, and in 2003 led to Getino and Escapa, along with other scientists, being awarded the European Union’s Descartes Prize for Research.
Using a laser to measure the distance between the Earth and the moon
Today, the latest improvements in laser measuring system technology (Lunar Laser Ranging) enable precise measurement of the distance between the Earth and its satellite down to almost a millimetre. Work in this area started with the Apollo era programmes more than 35 years ago, when the first corner-cube reflectors (CCR) started to be installed on the lunar surface. These devices reflect rays of light emitted by various terrestrial stations, making it possible to measure the distance between the Earth and the moon.
The measurements provided by LLR are “crucial”, according to the study, both in terms of moving forward in understanding the fundamental laws of gravitational physics, but also in improving understanding of the moon’s internal structure, as well as to help in the planning of future robotic and manned missions to the moon. The relativist theoretical model, complemented by the work of the Spanish scientists, could help to bring about progress in these fields.
NASA is weighing up the possibility of incorporating the results of this modelling into its GEODYN programme, a piece of software developed in order to analyse the orbits of satellites and estimate geodesic parameters to help improve space ship navigation, and to be able to land precisely on any part of the moon.
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- Kopeikin et al. Prospects in the orbital and rotational dynamics of the Moon with the advent of sub-centimeter lunar laser ranging. Advances in Space Research, 2008; 42 (8): 1378 DOI: 10.1016/j.asr.2008.02.014
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