On cooling
One of the first initial and guttural reactions to learning of startups’ pursuing in-orbit compute is, “Satellites are in a vacuum in space, how will you keep the computers cool?” In reality, keeping things warm in satellites can be just as big of a struggle as keeping them cool. Satellites will commonly have resistive heaters placed in critical areas because this temperature drop can be so extreme.
If we view our satellite as a system, there is only one method of heat transfer to and from the external environment: radiation. Inside the satellite, conduction occurs through the structure and components, and convection can occur within closed fluid systems such as heat pipes or pumped coolant loops. Aluminum-ammonia heat pipes are a staple of satellite thermal control. These pipes are sealed aluminum tubes filled with ammonia; their internal structure enables ammonia to vaporize at the hot end, travel to the cold end, condense, and return; passively equalizing temperatures wherever the heat pipe contacts the satellite. These are called constant conductance heat pipes, and they are a completely passive means to redistribute heat within the satellite.
A completely passive system means that our deep-space-facing radiator will never be hotter than our Sun-facing solar cells under steady-state conditions. If the Sun is constantly inputting more energy than we radiate away, how can we hope to keep the satellite cool? The heat capacity of the satellite’s components allows it to act like a thermal battery, dampening temperature swings, but ultimately, thermal equilibrium is set by the balance between absorbed solar power and radiated heat.
Stefan-Boltzmann law
Q=ϵσAT⁴
Q = Heat out
ϵ = emissivity
σ = Stefan-Boltzmann constant, 5.67 x 10⁻⁸ W/m²/K⁴
A = Radiator surface area
Take a satellite in SSO LEO that uses 1 kW of power and rejects it to space. It has 30% efficient GaAs solar cells and is hit by 1350 W/m² from the Sun.
0.3 x 1350 W/m² = 405 W/m²
1000 W / 405 W/m² = 2.47 m²
If our electronics safely run at 60°C (or 333K, slightly above Earth ambient), then we can find the area of the radiator we can use inside our build.
Q = 1000 W/m²
ϵ = 0.9, a very reasonable emissivity for white paint or black anodizing
σ = Stefan-Boltzmann constant, 5.67 x 10⁻⁸ W/m²/K⁴
Rearranging these, we get…
A = Q / (ϵ x σ x T⁴) = 1000 W/m² / (0.9 x 5.67 x 10⁻⁸ W/m²/K⁴ x 333⁴)
A = 1000 / 627.6
A = 1.6 m²
In other words, to keep our systems cooled to 60°C, we need 1.6 m² of radiator for every 2.47 m² of solar panel on our satellite.
On energy
Solar energy is abundant. Terrestrially, we are limited by the amount of solar energy we can take in due to atmospheric attenuation as the Sun approaches the horizon and the periods of eclipse when the Sun passes beneath the horizon of our solar site. In space, there are certain orbits that allow us to never, or at least seldom, fall behind the shadow of the Earth. Obviously, there is no atmosphere to contend with while in orbit, either.
On Earth, the Sun generates around 1000 W/m² at high noon. In the sunniest geographies, this is normally distributed across a day to reach at most 8 kWh/m² per day. In orbit, the amount of energy is 1340 to 1440 W/m² depending on the solar activity and distance from the Sun, but averages 1360 W/m².
Sun-synchronous, low Earth orbits are defined by being at an altitude of 600-900 km from sea level, and an inclination of 97-99°. Orbits with the preceding characteristics have local solar times which will be similar on every pass, making this a popular trajectory for observation satellites, as photos taken of one location will be under the same lighting conditions. Adding another criterion to the orbit, a local time descending node, or LTDN, describes the position of the orbit relative to the position of the Sun/Earth. A LTDN of 0600 or 1800 describes a satellite which is hugging the terminator line and constantly exposed to the Sun in either dawn or dusk. If the satellite was not in SSO, its LTDN would change as the orbit continued.
By placing a satellite inside of a dawn-dusk orbit, we expose it to constant sunlight. This allows us to experience sunlight 24 hours a day, 7 days a week.
1360 W/m² x 24 hours = 32.640 kWh/m² per day
This means we have four-fold the amount of solar energy available to us compared to terrestrial sites.
