Quick tools for the read-through.

• r = R + h
• v = √(GM / r)
• T = 2π √(r³ / GM)
• v_esc = √(2 GM / r)
• ground-track speed = v · R / r

Two-body, circular orbit about a spherical Moon of mean radius R. Real low lunar orbits are perturbed by mass concentrations and drift within days; this is the textbook number, not a mission design.

Units: GM in km³/s², r in km, so v is in km/s and T in seconds.

Uses: Mean radius 1737.4 km; Gravitational parameter GM 4902.8 km³/s². Sources in the table below.

• E_load = P · t_night
• E_nameplate = E_load / (DoD · η)
• m = E_nameplate / specific energy
• P_recharge = E_load / (η · t_day), with t_day = t_night

Constant load, one storage bank, no thermal or heater budget, no degradation margin, no losses in distribution. All of those add to the real number.

Depth of discharge and round-trip efficiency are yours to set; the defaults are placeholders, not recommendations.

Uses: Synodic period 29.53 days. Sources in the table below.

• waves = error_nm / λ_nm
• N = λ / error
• error at another wavelength: waves₂ = error_nm / λ₂

RMS in, RMS out. A peak-to-valley figure has no fixed ratio to RMS; it depends on the shape of the error, so do not convert one to the other with a constant.

The error is in nanometers of optical path, not surface height; for a reflecting surface at normal incidence the wavefront error is twice the surface error.

Uses: Helium-neon reference wavelength 632.8 nm; Neodymium-YAG wavelength 1064 nm. Sources in the table below.

• transition = |T_hot − T_cold| / ramp
• cycle = 2 · transition + dwell_hot + dwell_cold
• total = pump-down + ramp from 20 °C + n · cycle − one transition + ramp to 20 °C + return

Starts and ends at 20 °C. The first cycle begins at the hot plateau and the last ends at the cold plateau, which is why one transition is subtracted.

Ramp rate is the same in both directions and the chamber, not the article, sets it. Article-limited rates and stabilization criteria at each plateau lengthen the real test.

This is a schedule estimate. It quotes no acceptance limits and follows no particular standard's cycle counts.

• d = √(2 R h + h²), with R and h in meters
• separation = d_A + d_B

A smooth sphere of mean radius R. Crater rims, boulders, and slopes shorten every one of these numbers; the Moon has no atmosphere, so there is no refraction to lengthen them.

Useful as an upper bound for surface radio links and for the geometry of surface power beaming; not a link budget.

Uses: Mean radius 1737.4 km. Sources in the table below.

• θ = d / R (radians)
• ρ = √(R² + r² − 2 R r cos θ), r = R + h
• elevation = atan2(r cos θ − R, r sin θ)
• horizon ground distance = R · arccos(R / r)

Spherical Moon, no terrain masking. A negative elevation means the spacecraft is below the horizon for that ground distance.

Angles are computed in radians and shown in degrees.

Uses: Mean radius 1737.4 km. Sources in the table below.

• θ = M² λ / (π w₀)
• z_R = π w₀² / (M² λ)
• w(z) = w₀ √(1 + (z / z_R)²)
• η = 1 − exp(−2 a² / w(z)²)

A single-mode Gaussian beam, centered on a circular receiver, with no pointing error, no jitter, no scattering, and no atmosphere. The Moon has no atmosphere; everything else on this list costs capture in practice.

This is geometry only. Transmitter efficiency, receiver conversion efficiency, and thermal limits are separate terms, and the WIRES measurement definition exists to state each of them with its uncertainty.

Wavelength is entered in nanometers and converted to meters before use.

Uses: Neodymium-YAG wavelength 1064 nm. Sources in the table below.

• absorbed = α · S · cos θ / d²
• T = [ (absorbed + q) / (ε σ r) ]^¼
• r = radiating area ÷ sun-facing projected area

Isothermal body, steady state, radiating to deep space at 0 K, no conduction, no view to a warm surface such as the Moon or Earth, no albedo or planetary infrared load. Each of those raises the real temperature.

A planning estimate for a test article or a small exposed part, not a thermal model. The thermal-vacuum tool above is where the estimate becomes a test plateau.

Uses: Solar irradiance at 1 au 1361 W/m²; Stefan-Boltzmann constant 5.670 374 419 × 10⁻⁸ W/(m²·K⁴). Sources in the table below.

• W_moon = m · g_moon
• W_earth = m · g₀

Mass does not change. Surface gravity varies by a fraction of a percent across the Moon; the equatorial value is used.

Uses: Surface gravity 1.62 m/s²; Standard gravity (Earth) 9.806 65 m/s². Sources in the table below.