First-principles tile model / 0.7.0

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

β=78° snapshot geometry

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.

Physics 0.7.0 · Terrestrial silicon cells · shared preset

The operating snapshot beside the bound.

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

Cell technology

OPERATING SNAPSHOT / ηCELL 18.0%

Dawn–dusk geometry

β = 78°

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

GEOMETRIC BOUND / ηCELL 18.0%

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
Electrical bus design point	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%

100 kWe minimum-β sizing800 tiles
152 kWh

Fixed-field audit: the installed 604-tile / 7.02 kWh snapshot field cannot sustain 100 kWe through the modeled seasonal eclipse. The field's array-energy ceiling caps compute at 75.57 kWe and requires 114.87 kWh; with the installed buffer, continuous eclipse ride-through is 4.62 kWe. Low-order audit only; 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.

Low-order case solved / β=78° / ηcell=18.0%

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

Payload / platform electrical: 100.0 / 20.0 kW
Continuous bus: 120 kWe
Verified optical / RF export: 0.0 / 0.0 kW
Local rejected heat: 120.0 kW
Energy-ledger residual: 0.000000 kW
Bus power per tile: 198.7 W
Local heat per tile: 198.7 W
Junction-to-radiator resistance budget: 0.142 K/W
Compute load for 100,000 TOPS: 100.00 kW @ selected efficiency
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
Modelled / target tile mass: 12.89 / 9.0 kg
Mass margin per tile: -3.89 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. Internal carrier power receives no heat credit; only verified power crossing the spacecraft boundary is subtracted. Radiation, launch margin, mechanisms, redundancy and service life remain outside this result.

04 / Equation ledger

Every output has a denominator.

Registered constants are source-backed. Adopted audit inputs and coefficients remain explicit 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-01conductive path bound

Junction-to-radiator resistance

R_θ,j→rad ≤ (T_j,max − T_rad) / P_heat,tile
P_heat,tile = P_heat / N

P_heat,tile: 198.7 W
R_θ,max: 0.142 K/W

THM-02gray radiator

Emitting area vs panel area

P_heat = P_bus − P_{optical,export} − P_RF,export
q″ = εσT⁴F_alloc
A_emit = P_heat/q″ ; A_2-side = A_emit/2

P_heat: 120.0 kW
residual: 0.000000 kW
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

model: 12.89 kg/tile
target: 9.0 kg/tile

CMP-01company North Star

Useful compute per kilogram

Q_useful = 1000P_compute,kW ξ_TOPS/W
P_compute,kW = Q_useful / (1000ξ_TOPS/W)
ξ_m = Q_useful / m_modelled

throughput: 100,000 TOPS
load at 100,000 TOPS: 100.00 kW
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 / Solar Swarm vehicle boundary

One panel can fly itself.

The panel-level rocket is an orbital manoeuvre system after shared carrier deployment. A dedicated single-stage Earth launcher per tile is shown beside it as an ideal lower bound that rejects the architecture, not as proof that staged launch is mathematically impossible.

PRP-01orbital vehicle / assumption

Panel-level propellant

MR = exp[Δv / (g₀I_sp)]
m_prop = m_dry(MR − 1)

Δv / Isp: 100 m/s / 1500 s
mass ratio: 1.0068
propellant only: 88 g

PRP-02single-stage lower bound / rejected

Dedicated single-stage launcher per tile

MR = exp[9300 / (g₀·320)]

ideal mass ratio: 19.37
propellant fraction: 94.8%
before: tanks / engines / guidance

PHO-01photonic system boundary

Useful photons do not erase heat

E_op,wall = P_system / OPS_useful
Q_reject = P_bus − P_export − dE_stored/dt

verified radiant export: 0.0 kW
wall efficiency: measurement open
RF / exhaust / storage: closure open

The 88 g result is propellant only. Thruster, PPU, tank, plume clearance, GNC, collision avoidance, disposal reserve and qualified wet mass remain open. Model 0.1.0.

06 / 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

PWRFrameless silicon laminate

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

18% effective commodity-cell assumption × packing × conversion × pointing; 2.5 kg/m² laminate coefficient

Cell supplier, AM0 response, 0.10–0.15 mm coverglass trade, thermal cycling, radiation fluence, encapsulation and lifetime

ISOPV / electronics MLI break

Architecture shown; no thermal-leakage number claimed

Vacuum conduction + radiation only; crinkled aluminized-Kapton MLI suppresses radiative exchange

PV temperature, effective emittance, seams, edge leakage, attachment conductance, atomic oxygen and blanket mass

STRCheckpoint + eclipse storage

7.0 kWh snapshot / 114.9 kWh at the 604-tile seasonal array ceiling / 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

THMDirect interface + passive heat transport

198.7 W heat/tile; Rθ,junction→radiator ≤ 0.142 K/W; 313.4 m² emitting area

120 kW bus − 0 kW verified radiant export = 120 kW local heat; die-down interface / wedge lock reference; passive aluminium–ammonia heat pipe; 350 K radiator face

Measured carrier export, conversion losses, TIM/contact resistance, heat-pipe limits, freeze–thaw, startup, leakage, view factors, fin efficiency and qualified mass

MECIntegrated tile mass

7,783 kg / 604 tiles = 12.89 kg/tile; 3.89 kg over target

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

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

CMPHardened consumer compute

100,000 sustained TOPS / 12.85 TOPS/kg

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

BOM screening, coating/staking process, pure-tin mitigation, named workload, radiation errors, memory, networking and service life

PHOPhotonic compute + optical terminal

Energy and photon-counting boundaries defined; zero verified optical export remains in the reference ledger

Wall-plug useful-work efficiency and Qreject = Pbus − Pexport − dEstored/dt; export includes optical, RF and propulsive exhaust

Measured wall power, workload throughput, package mass, laser pumps, ADC/DAC, memory, pointing, apertures, wavelength and link availability

PRPSolar Swarm orbital vehicle

1.0068 ideal mass ratio / 88 g propellant-only result at 100 m/s and 1500 s Isp

One autonomous propulsive vehicle per tile after deployment by a shared carrier

Thruster, PPU, tank, plume geometry, duty cycle, GNC, collision avoidance, disposal reserve, qualification and complete wet mass

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

07 / Benchmark readout

Triple-junction benchmark679.6 → 409.6 m²

β=0° bound area → β=78° operating area at 26.5% EOL; continuous area, not integer tile count

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.

08 / Source register

Trace every input.

Registered sources are shown below. Unsourced audit inputs and design coefficients remain 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

S13ESA — Lower-cost Solar Cells

Low-cost cell strings bonded to panels and 0.10–0.15 mm coverglass practice

S14Qcells — Framed Module Datasheet

≈11 kg/m² packaged terrestrial module benchmark; not the modelled flight laminate

S15NASA-STD-8739.1

Workmanship basis for staking, bonding and conformal coating

S16NASA-STD-6016

Materials, outgassing, venting and electronic-material controls

S17NASA NEPP — Pure Tin Prohibition

Pure-tin finish and tin-whisker control basis

S18NASA GSFC — Passive Heat Pipes

Passive aluminium–ammonia heat-pipe reference architecture

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.
The current coefficients produce 12.89 kg/tile and miss the 9.0 kg/tile target.
Mission-specific orbit, power, thermal, structural, radiation and link closure is required.