## Thermal control of landers and entry probes

For obvious reasons, most electronic and other equipment on Earth function optimally at around the same temperatures as humans. To achieve correct functioning in environments where the ambient temperatures are very different requires either development of equipment that can operate in these extreme conditions, or control of the equipment's temperature, usually by largely isolating it from the environment. This latter course of action is of course impossible for some elements, such as sensors designed to measure the environmental properties themselves.

On the surface of an atmosphereless body, the thermal environment is dictated, as in deep space, by radiative balance. The difference is that there are many radiating and shadowing surfaces around. Whereas in deep space only the Sun and a (spherical) Earth need be considered and calculations can be performed by hand, the evolving thermal environment on the surface of a rotating planet generally requires more elaborate computation using time-marching numerical methods.

If we consider our spacecraft as a sphere of radius r and heat capacity mcp, then its rate of temperature change dT/dt will be given as dT

mcp â =(1 - a)nr2F + fxnr2eaT^ + f2(1 - a)(1 - A)nr2F - 4xr2eaT4 + Pi

where F is the solar flux (1340 Wm-2 at Earth) and a the reflectivity of the spacecraft (see below). The term f1 is a view factor describing how much of the sky is occupied by a nearby warm planet

where R is the radius of the planet and h the spacecraft altitude above it - this reduces to one half if the vehicle is on or near the surface, i.e. the planet occupies 2n

Surface coatings and radiation balance

steradians of solid angle seen from the spacecraft. The term Â£ is the emissivity (see below) of the spacecraft surface, a the Stefan-Boltzmann constant 5.67 X 10â8 W m ~2 Kâ4 and f2 is another view factor, describing the contribution of the reflected sunlight from the planet - if the spacecraft is over the equator at noon, or if the spacecraft is at very low altitude on the dayside, f2 = f1, but more generally f2 < f1, since the illuminated side of the planet may be obscured (i.e. the spacecraft sees a phase of the planet). The term A is the reflectivity or albedo of the planet and PI denotes any internal dissipation in the spacecraft (e.g. due to the operation of its equipment). Setting dT/dt = 0 gives the asymptotic equilibrium temperature.

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