7.7.1 Spacecraft Thermal Balance

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7.7.1 Spacecraft Thermal Balance

Equation 11 is the thermal balance equation for Asterius. From left to right, the terms of Equation 11 represent solar heat input, dissipated heat, heat absorbed from the radioisotope generators, heat emitted by the spacecraft skin, and heat emitted by the radiator.

$\begin{displaymath} A_{sun}G_s\alpha+Q_W+Q_{ri}K_{ri} -AT_s^4\sigma\epsilon-A_rT_r^4\sigma\epsilon_r(1-K_L)=0 \end{displaymath}$

(11)

Symbols used in Equation 11:

Symbol Meaning

A Surface area of spacecraft

A_r Area of radiator

A_sun Projection of area illuminated by the Sun

K_L Percent of heat retained by louvers

K_ri Percent of heat absorbed by radioisotope sources

Q_ri Heat generated by radioisotope sources

Q_W Heat dissipated

T_r Temperature of the radiator

T_s Temperature of the spacecraft skin

$\alpha$ Absorptivity of the skin

$\epsilon$ Emissivity of the skin

$\epsilon_r$ Emissivity of the radiator

$\sigma$ Stefan-Boltzman constant, $5.67051\times 10^{-8}$ W/m $\ensuremath{^2}$ /K⁴

Symbol	Meaning
A	Surface area of spacecraft
A_r	Area of radiator
A_sun	Projection of area illuminated by the Sun
K_L	Percent of heat retained by louvers
K_ri	Percent of heat absorbed by radioisotope sources
Q_ri	Heat generated by radioisotope sources
Q_W	Heat dissipated
T_r	Temperature of the radiator
T_s	Temperature of the spacecraft skin
$\alpha$	Absorptivity of the skin
$\epsilon$	Emissivity of the skin
$\epsilon_r$	Emissivity of the radiator
$\sigma$	Stefan-Boltzman constant, $5.67051\times 10^{-8}$ W/m $\ensuremath{^2}$ /K⁴

The following assumptions are made when applying Equation 11.

Because Asterius will be in Earth orbit for only a short time, the albedo and infrared emission from Earth is omitted. Near Jupiter, these terms can be significant (especially Europa's albedo); however, there we are interested in the worst-case cold scenario, so they will not be considered.
Asterius can selectively absorb 5-10 percent of the waste heat from the DIPS and RTG.
The louvers can retain 90% of the heat emitted from the radiator.
Radiator emissivity is 0.8.
Asterius is modeled as a cylinder of radius 1 m, and length 4 m. After separating from the OOM, the SOM is modeled as a cylinder of radius 1 m and length 2 m.
Heat dissipated is equal to half the electric power generated.
Near Earth, Asterius' HGA will point to the Sun, to minimize sunlit area. In this case, A_sun=3.5 m $\ensuremath{^2}$ .
The skin is insulated, allowing the inside of Asterius to be 280-300 K, while the outside skin is approximately 200 K. (200 K comes from the effective emissivity equation for thermal insulation, $q=\sigma\epsilon_{eff}(T_i^4-T_o^4)$ , where q is the heat flux through the insulation. Assuming that q approximately equals the heat flux emitted by the skin ( $\sigma\epsilon T_o^4$ ), and using T_i=290 K and $\epsilon_{eff}=0.004$ [3, p. 428], then solving for T_o yields 180 K. With a 20 K margin, the skin temperature is 200 K.)

Thermal balance can be obtained anywhere in the mission if $\alpha=0.2$ , $\epsilon=0.2$ , and A_r=2.5 m $\ensuremath{^2}$ . Table 13 shows how thermal balance is obtained in different phases of the mission. Near Earth, where there is more solar heat input, the louvers are wide open, and the radioisotope heat absorption is at its minimum. Just the opposite occurs when Asterius is eclipsed, with no solar flux.

**Table 13:** Thermal Balance For Different Scenarios in the Mission
Scenario	K_L	K_ri
Solar Orbit Near Earth	0	0.05
Eclipsed by Jupiter	0.9	0.077
Daytime On Europa	0.65	0.05