# Panoptes model notes — 5 September 2026

This is an exploratory mission study, not a detailed spacecraft design, certified observing capability or launch trajectory. All interactive models run locally in the browser and make no network requests. No real object detections or real planetary images are claimed. JavaScript source: physics.mjs (equations), app.mjs (visualizations). Values use SI internally except labelled interface units.

## Solar lens

Solar Schwarzschild radius rg = 2 GM/c². The limb minimum for an infinitely distant source is zmin = RSun²/(2 rg), about 547.76 AU with the constants used here. Finite source distance d gives effective distance zeff = zd/(z+d), Einstein impact parameter b = sqrt(2 rg zeff), angular ring radius b/z and solar radius RSun/z. Exterior strong-focusing geometry requires b > RSun. Projected source diameter is D z/d. The rendered ring is a geometric display, not a coronal-background simulation. The Sun's multipoles, plasma, dust, dynamic foreground and aperture response are absent.

The normalized monochromatic point response uses J0²[2π/λ sqrt(2rg/z) ρ], using a piecewise rational/asymptotic approximation to J0. Displayed at 550 nm and 650 AU. No aperture integration or spectral averaging. The separate 16×16 reconstruction uses a positive 1/sqrt(r²+0.09) envelope surrogate normalized per measurement. This is NOT the full lens response. Synthetic albedo, deterministic sinusoidal noise, nonnegative clipped gradient descent, step .8; image-quality numbers are in-simulation residuals, not predicted exoplanet resolution. The fixed-source example omits rotation and motion.

Primary basis: https://arxiv.org/abs/1908.01948 ; https://arxiv.org/abs/2112.03019 ; https://doi.org/10.1103/PhysRevD.103.124038 ; https://doi.org/10.1093/mnras/stad2655

## Flight

Parabolic incoming orbit is the default. vp = sqrt(vinbound∞² + 2GM/q). Ideal prograde impulse Δv yields outgoing v∞ = sqrt(vinbound∞² + 2 vp Δv + Δv²). The outbound hyperbola uses a = GM/v∞² (positive magnitude), e = 1 + q/a, H = acosh[(r/a+1)/e], t = sqrt(a³/GM)(e sinh H − H). Exact for the stated two-body coast. Inward travel and assembly are a user-provided time allowance, not propagated from a launch ephemeris. The chart samples the analytic coast and the finite burn; the scrubber numerically inverts coast time to distance.

Braking uses fixed electrical power P, efficiency η=.7 and effective exhaust speed ve: thrust F=2ηP/ve, mass flow μ=2ηP/ve², initial/final mass ratio exp[(vi−vf)/ve], burn time (mi−mf)/μ. Distance = [vi(mi−mf) − ve(mi−mf−mf ln(mi/mf))]/μ. v_i is approximated as asymptotic cruise speed; the braking segment neglects gravity and begins no closer than 50 AU, otherwise marked invalid. At the low end of allowed velocities even 50 AU may not make that approximation sufficiently accurate; full trajectory propagation is required for engineering use. Burn duration includes propellant depletion. Fixed final mass includes retained reserves and excludes burned braking propellant.

Ideal departure mass multiplier exp(Δv/g0 Isp) acts on the brake-fuelled observatory. Discarded departure-stage dry mass, shield, reserves, tank growth, inward-flight propellant and earlier stages are omitted: shown mass is a LOWER BOUND. Optimizer searches only the stated perihelion/impulse grid under the lower-bound mass ceiling and outer-braking-domain condition. It does not optimize launch windows, gravity assists, thrust steering, finite Oberth duration, stage count, cruise acceleration or power-system design. Higher electrical power at fixed dry mass is a sensitivity experiment; real mass and radiator growth must follow. No absolute maximum speed claimed.

Nuclear thermal preset uses correct generic rocket-equation mass scaling but the electrical-power duration is not an NTP reactor model. The 1,000-km/s branch is an effective jet-speed comparison, not a demonstrated engine. Nuclear electric exhaust is working propellant, not inherently spent reactor fuel. Direct fission-product exhaust is discussed as unresolved, with no reactor recipe.

Primary context: https://arxiv.org/abs/2602.04198 ; https://ntrs.nasa.gov/citations/20230000047

## Power and data

Reactor thermal power Pth=Pe/efficiency; conversion waste=Pth−Pe. Ideal two-sided planform A=Q/(2 ε σ T⁴), ε=.9. No view-factor losses, gradients, piping or auxiliary loads. 4,800m² reference is eight 20×30m wings; separate cold radiators and additional system heat remain to be closed. 600t architecture is a bottom-up allocation, not a weighed hardware build. Installed power20MWe, nominal jet electrical budget18MWe, one-module-out budget13MWe. Allocation changes do not automatically re-close flight hardware.

Raw data bits/s = pixels × bits × cameras / cadence. Camera count4, depth16bit. Retained fraction is user-selected, not validated lossless compression. Assumed sustained downlink ignores aperture, transmitter power, pointing, receiving network, coding and outages. Example does not establish optical-link capability. Frames are intensity, not complex optical fields. No radiation-qualified performance or FLOP count is asserted for the 0.6MW compute allocation.

## Direct interferometer

Bprojected = |B sin θ|; formal angular scale λ/Bprojected, linear scale λ d/Bprojected. θ is between baseline and source. Geometric delay B cosθ/c, approximate coherence length λ²/Δλ, bandwidth-smearing field λ²/(Δλ Bprojected). Gaussian RMS path jitter gives ideal visibility multiplier exp[-(2πσpath/λ)²/2]. These are separate necessary scales, not a complete correlation SNR.

AB zero-point 3631Jy, flat flux density over a narrow band, Δν≈cΔλ/λ². Photon rate Fν Δν area throughput/(hc/λ). Each aperture4m, throughput.3, photon example1,000s. Real correlated flux may be far lower. The finite-band approximation degrades for broad fractions; this calculator permits 100nm at550nm as a rough broadband scenario. Formal baseline resolution does not change photon collecting area. Two-source fringe graph is normalized and illustrates ambiguous 1D fringes; no real recovered image. Motion time is one formal resolution element divided by transverse speed, not a strict exposure bound if accurate track compensation is available. SGL mutual coherence is not implemented and must not be inferred from the direct-telescope calculation.

Primary context: https://www.eso.org/sci/facilities/paranal/telescopes/vlti/documents/VLT-MAN-ESO-15000-4552_v99.pdf ; https://arxiv.org/abs/1911.06029

## Moving-object study

Mass = πρD³/6 atρ3000kg/m³; kinetic energy (γ−1)mc² evaluated stably at smallβ. Mt TNT is an energy unit (4.184e15J), not an impact or extinction forecast. Travel time = rectilinear remaining distance/speed. No Earth impact probability, full gravitational trajectory or survey-discovery probability is calculated. Gas speed, Earth-relative impact speed and closing speed are conflated only in this first-order sensitivity control and explicitly distinguished in prose.

Gas kinetic power per frontal area = n mH v c²(γ−1); upper capture assumption; full redistribution across a sphere gives T⁴=flux/(4 εσ)+TCMB⁴. Density specified in a simple ambient rest frame; no relativistic gas-density transform at the upper speed range. This heuristic is not a relativistic shock or radiation-transport calculation. Solar heating, realistic energy deposition, dust, ablation and local flashes omitted. Wien peak≈2897.77/T micrometres. Reflected magnitude: H=5log10[1329/(Dkm sqrt(p))], mV=H+5log10(rSun Δobserver) at full phase and p=.05. Geometry is not a physical orbit configuration. Cloud size changes apparent extent only, not integrated brightness.

Synthetic survey: AB photon count at550nm/100nm band, 1m aperture, throughput.3, sky23ABmag/arcsec², pixel1arcsec, read noise3e−. Aperture area approximates π(max(1arcsec,cloudDiameter)/2)² + trailLength max(1arcsec,cloudDiameter). Signal is assumed integrated within that footprint, an optimistic simplification. S/N=S/sqrt(S+nPixels(background+readNoise²)). Not a matched-filter, confusion, trials-factor or completeness model. All-sky sweep =41252.96deg²/(4 FOV) × exposure / .5 duty. No required repeat visits, overlap, exclusions or slews; an optimistic arithmetic bound. Field per camera is a free design input, not proven for the reference apertures.

Primary context: https://arxiv.org/abs/1608.05284 ; https://science.nasa.gov/mission/neo-surveyor/ ; https://www.eso.org/sci/publications/announcements/sciann17403.html

## Work still needed to turn the reference into an engineered mission

- Full thermal and finite-thrust departure trajectory; launcher/assembly chain and launch dates.
- Power, radiator, shielding transport, structure, vibration and tankage closure at each mass/power choice.
- Instrument optical prescriptions, throughput, coronagraph residuals, focal planes, detector noise and calibration budgets.
- Coupled SGL two-station field propagation and practical optical correlation/link demonstrations.
- Survey injection/recovery across realistic populations, moving backgrounds and false-alarm trials.
- Spacecraft reliability tree, autonomous maintenance qualification, radiation/dust exposure and lifetime propellant reserve.
- The current mission authority is the author’s explicit brief. Archive recovery is not required for this study.

## Configuration authority
The 180m axial arrangement is one packaging study, not a required silhouette. Common powered sections, robotic docking and a large optical/instrument body are the current architecture direction. Assembly thrust is distinct from the departure burn. Individual sections may require multiple launches. The mass and power reference remains usable while topology is compared.

## Inline study revision — 5 September 2026

All substantive chapters and ten experiments now live in `index.html`. The five
former chapter URLs redirect to corresponding inline sections. `instruments.mjs`
contains authored geometry, functional hardware and data-flow diagrams and the
additional experiments below. Static diagrams are schematics, not CAD or an
ephemeris. The full numerical allocation tables remain inline.

- Direct exhaust: the separate experiment applies `brake` with efficiency 1
  because its input is **directed jet kinetic power**, not reactor thermal or
  electric input. Expelled mass is ideal useful exhaust only; fuel utilization,
  engine mass, electrical services and radiator closure are not supplied by it.
  The comparison graph uses logarithmic ratios relative to the selected point,
  clipped to 0.01–100 times that point. It spans 100–10,000 km/s effective exhaust.
- Aperture sampling: the normalized real dirty beam is the average of
  `cos(2*pi*(u*x+v*y))` for the selected unit-radius spatial frequencies. Each
  represents a conjugate baseline pair. Orientations sample `[0, span)` evenly.
  The displayed angular square spans ±3 lambda/B. This is a static, noiseless
  sampling response, not an image reconstruction or sensitivity model.
- Survey display: three independent, deterministic Gaussian noise realizations
  contain a Gaussian/trail template normalized in L2 to the analytic single-frame
  aperture-sum S/N. Thus its matched-template significance scale is tied to the
  photon budget, rather than arbitrarily brightened. It is an explanatory
  significance-space rendering, not an electron-level detector simulation; low
  photon counts would need Poisson simulation in an instrument study. Display
  samples can aggregate native pixels. The gold marker identifies the known
  injection, not a successful blind discovery. The ideal sqrt(3) combination
  assumes an already known track and independent equal-noise frames; there is
  no trajectory-trials correction or completeness claim.
- Hazard frames: encounter speed, closing speed and gas-relative speed now have
  independent inputs. Heating remains the approximate complete-capture model;
  ambient-density frame transformations and high-beta plasma physics are not
  modeled. The maximum speed is below 0.3c. The straight-line time is an elapsed
  travel scale, without acquisition or reporting latency.
- The published June 2026 SGL benchmark is a cited external comparison, not the
  output of this page's 16×16 envelope inverse. Its 128×128 raster at 1,800 s per
  sample implies 341.33 days of integration before overhead.

Verification: physical invariants and input-bound runtime tests are in
`tests/panoptes_physics.test.mjs` and `tests/panoptes_runtime.test.mjs`. Browser
checks supplement the small DOM adapter, including actual canvas initialization,
unique IDs, populated results, inputs, and responsive layout.

## Isotope precursor integrated into the programme

The former `technosignature-isotope-survey` idea is now the inline
`#isotope-stage` section. It supplies early research, candidate targets and
instrument requirements to Panoptes. The production/persistence/export/resolution
chain, candidate comparison (Nd-148, Ru-99, Xe-129, Ba-135/137, Pb and Hg), natural
baselines, industrial-Earth observability test, blind archive search, independent
follow-up and informative null results are preserved in the rewritten stage.
Both source illustrations retain their provenance as concept art. They are not
laboratory measurements or actual spectra. Programme diagrams describe dependency
and evidence flow, without imposing a schedule or making isotope discovery a
prerequisite for all other Panoptes science.

The previous source is retained under `web/ideas/_archive/`, outside catalogue
discovery. The standalone release path is retired and the hosting configuration
redirects its page URL to `/ideas/panoptes/#isotope-stage`.