Orbital AI Data Center: Solar and Radiator Sizing

The sizing equations are derived here from orbital geometry, conservation of electrical energy and the Stefan–Boltzmann law. NASA's Small Spacecraft Technology State of the Art (2026), chapters 3 and 7, provides power-system and thermal-control context. The reference cases test published numbers independently of this derivation.

For a circular orbit, $r=R_E+h$ and $t_o=2\pi\sqrt{r^3/\mu_E}$. In a cylindrical Earth shadow, the eclipse half angle is $\theta_e=\cos^{-1}[\sqrt{1-(R_E/r)^2}/\cos\beta]$ while $\beta<\sin^{-1}(R_E/r)$, and zero otherwise. Then $f_e=\theta_e/\pi$ with angles in radians. The implemented degree form uses a half-turn of 180°. Periods and eclipse times are converted explicitly before computing energy. See ESA Navipedia, Satellite Eclipses; Earth radius and irradiance come from NASA's Earth Fact Sheet and $\mu_E$ from JPL DE440.

The continuous bus load is $P_b=f_{aux}P_{IT}$. Eclipse delivery is $E_e=P_b t_e$. Stored energy removed is $E_s=E_e/\eta_d$ and rated pack capacity is $E_{pack}=E_s/D$. Sunlight charging needs $P_{ch}=E_s/(\eta_c t_s)$, so the array delivers $P_{SA}=P_b+P_{ch}$. Array area is $A_{SA}=P_{SA}/(S\eta_{PV}f_{array})$, using consistent W and W/m².

Peak internal waste heat is the greater of $P_b+(1-\eta_c)P_{ch}$ in sunlight and $P_b/\eta_d$ during eclipse. With no eclipse the latter mode is absent. All IT, auxiliary and battery losses become heat. Array cell inefficiency heats the solar panels, which reject it separately.

For a uniform gray radiator, $q_{net}=\epsilon\sigma(T_r^4-T_s^4)-q_{abs}$. Temperatures are converted from °C to K. With thermal factor $F_T$, total emitting area is $A_e=F_TQ_{peak}/q_{net}$. Panel footprint is $A_r=A_e/n_{faces}$. Nonpositive net rejection is blocked by a condition, never presented as a feasible size. As a derived ideal limit, $\sigma(350\,K)^4\approx851$ W/m², giving about 1,175 m² of blackbody emitting area per MW. The familiar 1,200 m²/MW shorthand excludes emissivity, absorbed radiation, bus overhead and allowances.

Assembly masses are footprint or array area times their respective kg/m² values; battery mass is rated Wh divided by pack Wh/kg. Other spacecraft mass is entered separately. Their sum times the mass factor gives estimated launch mass. Launch-only cost is mass in kg times the assumed USD/kg rate. Monetary amounts stay in USD under the unit switch.

• Continuous IT load in both sunlight and eclipse; no eclipse load shedding. Constant Sun irradiance and beta angle represent one design condition, not an annual trajectory.
• Uniform radiator temperature and emissivity. Both faces, if enabled, have the entered average environmental flux and net heat rejection. No mutual shading, Earth occultation of radiator view, fin efficiency or finite thermal conductance is calculated.
• The 3 K background is a deep-space reference. The separate 100 W/m² absorbed flux is an illustrative hot-environment allowance; replace it with a mission attitude and view-factor analysis. Do not include the same Earth IR contribution in both the background temperature and absorbed flux.
• Retained array output includes packing, pointing, operating temperature and end-of-life loss. Onboard load conversion heat belongs in the bus multiplier. Solar panel waste heat is not assigned to the server radiator.
• The 30% cell efficiency is consistent with NASA's 2026 power chapter. The 0.80 array retention, 0.95 charge and discharge efficiencies, 0.30 usable battery fraction, 180 Wh/kg pack value, 5 kg/m² radiator, 3 kg/m² array, 10,000 kg other mass and sizing factors are editable scenario assumptions, not a qualified design or supplier specifications.
• NASA/Boeing ISS ATCS Overview, attached PDF page 3, gives a PVR mass of 740.7 kg and deployed dimensions 3.12 × 13.6 m. That is approximately 17.5 kg/m² of footprint, substantially above the optimistic default radiator assembly density. Its different temperatures, geometry and environment prevent using its rated heat load as a direct 350 K radiator benchmark.
• Launch price is an illustrative input in USD/kg dated 27 October 2026. No provider tariff, vehicle capacity, discount or future price forecast is assumed.

Use for preliminary comparisons of circular Earth orbits from 200 to 2,000 km. The cylindrical shadow ignores penumbra, finite Sun size, atmospheric refraction, Earth oblateness, eccentricity and seasonal orbit evolution. The thermal calculation is steady-state peak sizing with no thermal storage credit. The background model is an equivalent radiative environment, not a local air temperature.

Processor junction temperature must exceed the radiator temperature by the entire cold-plate, coolant and panel temperature drop. Raising the surface temperature to reduce area does not establish that the computing hardware can tolerate it. Battery mass is energy-limited only; verify power capability, charge rate, cycle life, thermal control, end-of-life capacity, eclipse contingency and operational reserves separately.

Launch mass is only as complete as the entered assembly masses and other spacecraft allowance. There is no calculation of shielding, redundancy, propellant, structural modes, deployment, micrometeoroid damage, repair, data throughput, station keeping or disposal. Launch cost excludes manufacture, integration, development, orbital assembly and operations.

GAO-26-109012 (28 April 2026) describes unproven large-scale cooling and power systems. The FCC notice of 4 February 2026 accepted SpaceX's application for filing and comment; that notice is not an operating authorization or engineering validation. No regulatory-compliance determination is made.