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190 MEMS and Microstructures in Aerospace Applications

intermediately controlled by altering a radiation’s surface solar absorptivity or
infrared emissivity. Mechanical devices such as pinwheels, louvers, or shutters
that can be ‘‘opened or closed’’ to view space may be used to achieve such effective
changes in absorptivity or emissivity.
The major heat sources in the heat transfer process for a spacecraft of
space include solar radiation, Earth radiation, reflected radiation (albedo), and
internally generated heat. Spacecrafts reject heat by radiation to space, mainly
through its designated radiator surfaces. The law for conservation of energy
describes heat that is received, generated, and rejected by a spacecraft with the
following equation:
dT 4
MC p ¼ aA p ðS þ E a Þþ « E A p E r «AsT þ Q int (9:7)
dt
where M: mass (kg)
1
C p : heat capacity (W sec kg 1 K )
T: temperature (K)
t: time (sec)
a: spacecraft surface solar absorptivity
2
A p : surface area for heat absorption (m )
2
S: solar flux (~1353 W m )
2
E a : Earth albedo (~237 W m )
« E : Earth surface emissivity
2
E r : Earth radiation (~50 W m )
«: spacecraft surface infrared emissivity (0 « 1)
2
A: surface area for heat radiation (m )
4
s: Stefan–Boltzmann constant (s ¼ 5.67 10 8 Wm 2 K )
Q int : internal heat generation (W).
For a spacecraft to reach thermal equilibrium in space, the rate of energy absorption
or generation and radiation must be equal. At thermal equilibrium, the spacecraft
heat balance is at a steady state and the derivative term dT/dt on the left hand side of
Equation (9.7) becomes zero. If one simplifies the situation and assumes that the
spacecraft receives solar radiation as the only heat source, the heat balance equation
(9.7) at steady state is reduced to the following equations:

Q ¼ 0 ¼ aA p S « AsT 4 (9:8)
1 = 4 1 = 4 1 = 4
A p S a
T ¼ (9:9)
A s «
According to Equation (9.9), for a fixed spacecraft orientation and thermal
exposure, surface temperature becomes a function of surface properties only.
Therefore, spacecraft surface is proportional to 1/4 power of the ratio of a and «;
¼
that is, T ¼ f [(a/«) ]. By properly selecting surface materials, spacecraft thermal

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