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Advances in Astronomy
Volume 2012 (2012), Article ID 478957, 10 pages
Research Article

The Faint Young Sun Paradox: A Simplified Thermodynamic Approach

1Departamento de Física, Escuela Superior de Física y Matemáticas, Instituto Politécnico Nacional, UP Zacatenco, 07738 Mexico, DF, Mexico
2Departamento de Formación Básica, Escuela Superior de Cómputo, Instituto Politécnico Nacional, Avenida Juan de Dios Batiz s/n. Esquina M. Othón de Mendizabal UP Adolfo López Mateos, 07738 Mexico, DF, Mexico

Received 15 December 2011; Revised 16 March 2012; Accepted 15 May 2012

Academic Editor: J. P. Rozelot

Copyright © 2012 F. Angulo-Brown et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Classical models of the Sun suggest that the energy output in the early stage of its evolution was 30 percent less than today. In this context, radiative balance alone between The Sun and the Earth was not sufficient to explain the early presence of liquid water on Earth’s surface. This difficulty is called the faint young Sun paradox. Many proposals have been published to solve this paradox. In the present work, we propose an oversimplified finite-time thermodynamic approach that describes the air convective cells in the Earth atmosphere. This model introduces two atmospheric modes of thermodynamic performance: a first mode consisting in the maximization of the power output of the convective cells (maximum power regime) and a second mode that consists in maximizing a functional representing a good trade-off between power output and entropy production (the ecological regime). Within the assumptions of this oversimplified model, we present different scenarios of albedo and greenhouse effects that seem realistic to preserve liquid water on the Earth in the early stage of formation.