The product of our project is an Java Applet which computes the flux that a site on Earth receives sunlight directly from the Sun as well as reflected from a number of mirrors in Earth orbit.
The background for this project is a study in 2004 by students of the Masters program of the International Space University in which they explored all aspects of an idea that one might use mirrors in orbit to help to heat up the waters in an atoll so that electrical power could be generated in a less expensive way.
Our applet is designed to allow to explore various configurations of such a system and its paramaters - orbital altitude, size and number of the mirrors - and to provide quantitative answers to its technical feasibility and its efficiency. It also permits to give a visual impression of the geometrical aspects of the system. Although the applet gives detailed and accurate quantitative results, is also aims to help the non-specialist user in better understanding the problems of this concept.
The SpaceMirrors Applet and its early version compute how much sunlight from the Sun can be reflected onto a spot on Earth, as a function of time of the day, the height of the mirror's orbit, and the size and number of the mirrors. A number of simplifying assumptions are used:
With a very simple model, the applet computes the time evolution of the temperature, as a result of the heating by direct and reflected sunlight and heat losses by radiation and conduction:
dT/dt = + Flux/depth - (T-T_ambient)/T_cool
Here, the user can specify the effective thickness of the water layer which is heated by the incoming flux and a time constant for heat losses. In the context of this simple model, these parameters may be thought as fitting parameters when measured temperature-time data is matched with the predictions by this simple model: The heat loss constant would be the time constant with which an initially warm body of water is left to cool down after being isolated from any heat source:
T(t) = T_ambient + (T(0)-T_ambient) exp(-t/T_cool)
Likewise, the effective thickness might be adjusted to match the observed temperature rise of the body of water. For a constant heat flux and starting from ambient temperature:
T(t) = T_ambient + Flux*T_cool/depth (1 - exp(-t/T_cool))
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