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API Reference
Dan Lee-Odinson edited this page Jun 15, 2026
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1 revision
Public functions of the orbital_thermal package (v1.0.0). Import name is orbital_thermal.
Signatures are abbreviated where noted; see each function's docstring for full keyword lists.
Optical/environment keywords. Functions marked (+env) also accept, after the shown arguments:
emissivity=0.91,solar_absorptivity=0.20,earth_ir=237.0,albedo=0.30,solar_constant=1361.0,t_space=2.7255. The orbit-coupled functions additionally require the keywordassume_sun_shielded(no default).
| Name | Value | Meaning |
|---|---|---|
SIGMA_SB |
5.670374419184429e-8 |
Stefan–Boltzmann constant (full binary64 SI-derived), W·m⁻²·K⁻⁴ |
ZERO_CELSIUS |
273.15 |
0 °C in kelvin |
| Function | Purpose |
|---|---|
net_flux(T, emissivity, T_sink=0.0) |
Net radiated flux of a gray surface, W/m² |
required_area(Q, T, emissivity, T_sink=0.0) |
Emitting area (m²) to reject Q W at T
|
area_ratio(T1, T2, T_sink=0.0) |
Exact area ratio A(T1)/A(T2) at equal duty (Cor. 1.1) |
effective_sink_temperature(view_factor, T_sink) |
Lumped F-weighted sink: T_s^eff = F^¼·T_s |
| Function | Purpose |
|---|---|
equilibrium_temperature(Q, area, emissivity, T_sink=0.0) |
Steady temperature to reject Q W through area
|
radiative_capacity(T, area, emissivity, T_sink=0.0) |
Heat-rejection capacity (W) at fixed T
|
| Function | Purpose |
|---|---|
fixed_work_area_per_watt(T_h, T_c, T_sink, emissivity=1.0) |
Reversible radiator area per watt of work, m²/W (Thm 1) |
optimal_cold_fraction(a=1.0, tol=1e-12, max_iter=1000) |
Area-optimal T_c/T_h (the 3/4 rule; Thm 2) |
nonzero_sink_optimum(T_h, T_sink, tol=1e-10, max_iter=1000) |
Optimal cold-side T_c* for T_sink>0 (Thm 3 quintic) |
quintic_residual(T_c, T_h, T_sink) |
Dimensionless residual of the Thm 3 quintic |
conversion_area_penalty(T_h, T_c, eta, T_sink=0.0) |
Area penalty A_engine/A_direct ≥ (T_h/T_c)³ (Cor. 2.1) |
carnot_cop_cooling(T_c, T_h) |
Carnot cooling-COP ceiling T_c/(T_h−T_c) (Thm 4) |
heating_cop(cop_cooling) |
First-law identity COP_h = COP_c + 1 |
heat_pump_overhead(cop_cooling) |
Electrical overhead per watt lifted, 1/COP_c |
heat_pump_area_ratio(cop_cooling, T1, T2, T_sink=0.0) |
Area ratio for rejecting at T2 vs T1 |
recirculation_amplification(eta) |
Self-powering bound 1/(1−η) (Thm 5) |
| Function | Purpose |
|---|---|
orbital_period(altitude_km) |
Circular orbital period, s |
orbital_radius(altitude_km) / orbital_velocity(altitude_km)
|
Radius (km) / speed (km/s) |
earth_angular_radius(altitude_km) |
Angular radius of Earth from orbit, rad |
nadir_view_factor(altitude_km) |
View factor of a nadir-facing plate (the maximum) |
sphere_view_factor(altitude_km, tilt_deg) |
Exact tilted-plate-to-sphere Earth view factor |
beta_critical(altitude_km) |
Beta angle above which the orbit never enters eclipse, deg |
eclipse_fraction(altitude_km, beta_deg) / eclipse_duration(...)
|
Shadow fraction (0–1) / seconds per orbit |
| Function | Purpose |
|---|---|
orbital_effective_sink_temperature(altitude_km, beta_deg, u_deg, tilt_deg=0.0, *, assume_sun_shielded) (+env)
|
Effective sink T, K, at one orbit phase |
sink_profile(altitude_km, beta_deg, tilt_deg=0.0, n=361, *, assume_sun_shielded) (+env)
|
(u_deg, T_s_eff) arrays over one orbit |
orbit_averaged_sink(altitude_km, beta_deg, tilt_deg=0.0, n=720, *, assume_sun_shielded) (+env)
|
Radiatively-weighted orbit-average sink (discrete) |
analytic_orbit_averaged_sink(altitude_km, beta_deg, tilt_deg=0.0, *, assume_sun_shielded) (+env)
|
Grid-free closed-form orbit-average sink |
sink_temperature_series(view_factor, beta_deg, u_deg, *, assume_sun_shielded) (+env)
|
Centralized sink equation (scalar or vectorized) |
sink_fourth_power_mean(view_factor, beta_deg, *, assume_sun_shielded) (+env)
|
Exact continuous mean of T_s_eff⁴, K⁴ |
analytic_albedo_orbit_mean(beta_deg) |
Exact ⟨max(0,cosβ·cos u)⟩ = cosβ/π |
subpoint_albedo_factor(beta_deg, u_deg) |
Subpoint albedo approximation max(0,cosβ·cos u) |
in_eclipse(altitude_km, beta_deg, u_deg) |
True if in Earth's cylindrical shadow |
disk_integrated_albedo_factor(...) |
Faithful disk-integrated albedo — NotImplementedError (roadmap) |
| Function | Purpose |
|---|---|
simulate(altitude_km, beta_deg, q_load, areal_heat_capacity, tilt_deg=0.0, *, assume_sun_shielded, ...) (+env)
|
March RK4 to periodic steady state; returns (t, T, T_sink) or (..., diagnostics)
|
averaging_bias(altitude_km, beta_deg, q_load, areal_heat_capacity, tilt_deg=0.0, *, assume_sun_shielded, require_convergence=True, **kw) |
Transient mean vs steady averaged-sink; dict of metrics (raises unless certified) |
steady_state_temperature(q_load, t_sink, emissivity=0.91) |
Closed-form steady temperature for a constant sink |
thermal_time_constant(areal_heat_capacity, temperature, emissivity=0.91) |
Linearized radiative time constant τ, s |
areal_heat_capacity(layers) |
C_A = Σ ρ·c_p·t from (material, thickness) layers |
build_areal_heat_capacity(build_name) |
C_A of a named build in REPRESENTATIVE_BUILDS
|
coolant_rho_cp(fluid='Ammonia', T=300.0) |
(density, specific heat) from CoolProp (needs [fluids]) |
simulate keywords (beyond +env): n_orbits=30, steps_per_orbit=2000, t0_guess=None,
convergence_tol_K=1e-3, energy_tol_K=1e-2, check_time_resolution=False, time_tol_K=1e-2,
time_safety_factor=2.0, max_orbits=None, return_diagnostics=False, raise_on_nonconvergence=False.
Data: MATERIALS (aluminum_6061, cover_glass, silicon, cfrp_substrate, ammonia_liquid, copper,
fr4_pcb) and REPRESENTATIVE_BUILDS (bare_aluminum_sheet_2mm, pv_on_substrate, radiator_with_coolant,
integrated_compute_radiator).
| Function | Purpose |
|---|---|
run_case(overrides=None) |
Full nested result for one parameter case (matches the oracle) |
calculate_thermal(s) / calculate_orbital(s) / calculate_breakeven(s)
|
The three coded sub-models |
nadir_view_factor(alt_km) / sun_tracking_view_factors(alt_km, beta_deg)
|
His heuristic view factors |
| Function | Purpose |
|---|---|
exact_per_face_view_factors(altitude_km, beta_deg, n=72) |
Orbit-averaged exact per-face Earth VF (side A, side B) |
equilibrium_temperature_with_view_factors(overrides, vf_side_a, vf_side_b) |
McCalip's heat balance with arbitrary per-face VFs |
eqtemp_exact_vf(overrides=None, n=72) |
His equilibrium temperature recomputed with exact VFs |
correction_table_vs_beta(betas=(0, 15, 30, 45, 60, 75, 90), overrides=None, n=72) |
Correction (K) vs orbit beta angle |
| Function | Purpose |
|---|---|
critical_temperature(fluid='Ammonia') / critical_pressure(...)
|
Critical point (K / Pa) |
critical_margin(T, fluid='Ammonia') |
Headroom to the critical point, T_crit − T (K) |
saturation_pressure(T, fluid='Ammonia') |
Saturation (vapor) pressure, Pa |
saturated_densities(T, fluid='Ammonia') |
(liquid, vapor) densities on the saturation curve |
phase_state(T, P, fluid='Ammonia') |
CoolProp phase label at (T, P) |
provenance(fluid='Ammonia') |
Pinned CoolProp version + EOS citation for the record |