First-principles tile model / rev 0.4

Two geometries.
One mass register.
TOPS per kilogram.

The β=78° sunlit snapshot sits beside the β=0° eclipse bound. Cell technology, storage practice and every kg/m² coefficient stay visible.

Compare both cases ↓Inspect equations

SILICON / β=78° SNAPSHOT1 M² TILE

1.361kW solar / m²

1 AU design reference

0.18 η_Si,effective0.90 η_pack0.95 η_PCU0.95 η_point

q_tile

0.199kWe / m²

Continuous at snapshot

604 installed tiles / 7,783 modelled kg

ξ_m

12.85TOPS / kg

Conditional North Star

Every mass and compute coefficient below is editable. This is not a flight mass claim.

Rev 0.4 · same machine, two geometries

The operating snapshot beside the bound.

One electrical load, one thermal model and one mass register. Only solar beta changes between columns.

Cell technology

OPERATING SNAPSHOT

Dawn–dusk geometry

β = 78°

PV face: 603 m²
Checkpoint battery: 7.0 kWh
Compute / mass: 12.85 TOPS/kg

GEOMETRIC BOUND

Worst eclipse plane

β = 0°

PV face: 1,001 m²
Eclipse battery: 249.9 kWh
Compute / mass: 7.27 TOPS/kg

Common-coefficient comparison of the two solar-beta cases
Solved quantity	β = 78° snapshot	β = 0° bound
Continuous electrical bus	120kWe	120kWe
Required PV face	603m²	1,001m²
Eclipse per orbit	0.00min	35.61min
Battery nameplateEclipse load or checkpoint buffer, whichever is longer.	7.0kWh	249.9kWh
Radiating surface	313m² emitting area	313m² emitting area
Two-sided radiator wingBoth faces must retain a clean view to the cold sink.	157m² planform	157m² planform
One-square-metre tiles	604tiles	1,001tiles
Installed radiator backs	604m²	1,001m²
Modelled installed massConditional on every editable mass coefficient above.	7,783kg	13,762kg
Sustained compute	100,000TOPS	100,000TOPS
North StarCompute delivered per modelled installed kilogram.	12.85TOPS/kg	7.27TOPS/kg

02 / Seasonal qualification

β=78° is a snapshot.

The annual envelope is solved independently so the orbit thesis cannot hide seasonal storage behind a nominal beta angle.

SSO inclination97.593°

Annual beta59.0–90°

Eclipse season97.7 days

Maximum eclipse21.66 min

Annual sunlight95.13%

Seasonal-worst battery152.0 kWh

Low-order result for an exact 06:00/18:00 mean-LTAN plane at 550 km. A propagated ephemeris remains required before mission use.

03 / Full sizing surface

Change every coefficient.

The detailed model sizes the integer tile field, checkpoint or eclipse storage, radiator geometry, installed mass, useful compute and elevation-dependent RF range.

Solved instantaneous case

12.85 TOPS/kg

100,000 sustained TOPS / 7,783 modelled kg

Integrated tiles6041 m² each / power governs

PV face required603m² continuous-bus area

Battery nameplate7.0kWh / 1.0 min support

Continuous bus: 120 kWe
Orbit period: 95.65 min
Eclipse / orbit: 0.00 min
Continuous array density: 0.199 kWe/m²
Radiating face required: 313.4 m²
Two-sided wing planform: 156.7 m²
Installed radiator backs: 604 m²
Array / radiator utilisation: 99.8% / 51.9%
Array + radiator mass: 4,228 kg
Battery / compute / balance mass: 35 / 500 / 3,020 kg
Ground slant range: 993 km @ 30°
Free-space path loss: 180.69 dB
Critical eclipse beta: 67.02°

TOPS/kg is conditional on the selected workload and all five mass coefficients. Radiation, launch margin, mechanisms, redundancy and service life remain outside this result.

04 / Equation ledger

Every output has a denominator.

Constants are source-backed. Coefficients are editable engineering assumptions. SOLVED means only that the stated low-order equation closes.

ORB-01two-body / circular

Orbit period

T = 2π √[(R_E + h)³ / μ]

h: 550 km
T: 95.65 min

ORB-02cylindrical shadow

Instantaneous eclipse

β_c = asin(R_E/r)
f_e = acos[cos β_c / cos β] / π

β_c: 67.02°
t_e(β=0): 35.61 min

ORB-0306:00 mean-LTAN audit

Annual dawn–dusk beta

sin β = sin i cos δ + cos i sin δ
δ = asin(sin ε sin λ_☉)

β annual: 59.0–90°
sunlit: 95.13%

PWR-01conversion chain

Sunlit tile density

q_sun = S η_cell η_pack η_PCU η_point

S: 1.361 kW/m²
q_sun: 0.199 kWe/m²

PWR-02per-orbit conservation

Continuous bus density

q_cont = q_sun · [f_sη_rt / (f_e + f_sη_rt)]

β=78°: 0.199 kWe/m²
β=0°: 0.120 kWe/m²

STR-01support energy

Battery nameplate

t_support = max(t_eclipse, t_checkpoint)
E_bat = P_bust_support / (DoD·η_dis)

β=78°: 7.0 kWh
β=0°: 249.9 kWh

THM-01gray radiator

Emitting area vs panel area

q″ = εσT⁴F_alloc
A_emit = P_heat/q″ ; A_2-side = A_emit/2

A_emit: 313.4 m²
A_2-side: 156.7 m²

MEC-01integrated 1 m² sandwich

Integer tile count

N = ceil[max(A_PV, A_rad,1-side) / 1 m²]

constraint: power
N: 604 tiles

MEC-02editable coefficient register

Modelled installed mass

m = N(ρ_PV + ρ_rad + m_balance) + P_computeρ_compute + 1000E_bat/e_pack

m: 7,783 kg
status: ASSUMPTION

CMP-01company North Star

Useful compute per kilogram

ξ_m = [1000P_compute,kW ξ_TOPS/W] / m_modelled

throughput: 100,000 TOPS
ξ_m: 12.85 TOPS/kg

RF-01elevation to vacuum loss

Slant range and FSPL

d = √[r²−R_E²cos²e] − R_Esin e
L_FS = 20 log₁₀(4πdf/c)

30°: 993 km / 180.69 dB
5°: 2,206 km / +6.93 dB

05 / Constraint closure

Solved does not mean qualified.

Each row separates the low-order mathematical output from the component data, environmental analysis and verification still required for hardware.

SystemModel resultBasisNot yet closed

ORBDawn–dusk orbit

59.0–90° β envelope; 95.1% annual sunlight

550 km exact 06:00/18:00 mean-LTAN, J2 Sun-sync inclination, mean-Sun geometry, cylindrical shadow

Numerical ephemeris, penumbra, launch date, LTAN drift, manoeuvres and operational attitude

PWRSilicon PV face

0.199 kWe/m² at β=78°; 603 m² required

18% effective silicon assumption × packing × conversion × pointing × orbit/storage balance

AM0 response, thermal cycling, radiation fluence, coverglass, encapsulation, lifetime and supplier data

STRCheckpoint + eclipse storage

7.0 kWh snapshot / 249.9 kWh β=0 bound

1 min minimum reserve; 30% DoD and 95% discharge efficiency

Cell chemistry, C-rate, cycle life, calendar life, containment, redundancy and seasonal operating policy

THMHeat rejection

313.4 m² emitting area / 156.7 m² two-sided wing

350 K face, ε=0.90, 50% allocated ideal flux, 120 kWth conservative load

Chip-to-face ΔT, view factors, Earth IR, albedo, solar leakage, fluid loop, pumps and two-face visibility

MECIntegrated tile mass

7,783 kg modelled / 604 installed tiles

Editable PV, radiator, battery, compute and balance-of-tile coefficients

Shielding margin, deployment mechanisms, launch adapter, propellant, redundancy and verified component masses

CMPUseful compute

100,000 sustained TOPS / 12.85 TOPS/kg

1 sustained TOPS/W assumption at 100 kWe payload divided by modelled installed mass

Named workload, precision, utilisation, radiation errors, memory, networking, fault recovery and service life

RFData downlink geometry

993 km @ 30° / 2,206 km @ 5° / +6.93 dB

550 km spherical slant range and 26 GHz vacuum free-space loss

EIRP, G/T, atmosphere, rain, pointing, coding, availability, gateway network and spectrum

06 / Benchmark readout

Triple-junction benchmark680 → 410 m²

β=0° bound to β=78° snapshot at 26.5% EOL

1.47×silicon area / TJ area

12.85silicon TOPS/kg

18.33TJ TOPS/kg at same mass coefficients

Cheaper $/m² and higher TOPS/kg are different objectives. The site makes no cost ratio claim without supplier quotations.

07 / Source register

Constants are traceable.

Design coefficients remain visibly editable because they are assumptions, not laws of nature or component qualifications.

S01NASA GSFC — Total Solar Irradiance

1361 W/m² design reference at 1 AU

S02JPL — Astrodynamic Parameters

Earth GM used in the two-body orbit period

S03JPL — Planetary Physical Parameters

Earth equatorial radius used by the spherical model

S04NASA GPM — Geolocation Toolkit ATBD

Critical beta and cylindrical eclipse geometry

S05DLR — TerraSAR-X/TanDEM-X Eclipse Operations

Observed eclipse season in a 06:00 SSO near 550 km

S06NASA — Li-ion Battery Performance

LEO cycle-life testing at 30–40% depth of discharge

S07US DOE — Crystalline Silicon PV

20–22% terrestrial module performance context

S08ESA — Next-generation Solar Cells

26.5% mature triple-junction EOL benchmark

S09NIST CODATA 2022

Stefan–Boltzmann constant

S10NASA — Small Spacecraft Thermal Control

Radiator view, surface and environmental caveats

S11NASA — Two-sided Radiator Study

Two-sided emitting-panel geometry and areal-density context

S12ITU-R P.619-6

Spherical-Earth slant geometry and free-space attenuation

Model boundary / read before use

Reference calculation.
Not a flight design.

Concept stage; no flight hardware has been built.
No operational service, capacity, availability or cost is claimed.
TOPS/kg is conditional on workload and the complete visible mass register.
Mission-specific orbit, power, thermal, structural, radiation and link closure is required.