Mean lunar reflectivity at 10 GHz — Near side, Far side, and Global

Short answer: Using representative values ε′(mare)=4.0 and ε′(highlands)=2.7 with simple area fractions, the normal‑incidence mean reflectivities at 10 GHz are:

Assumptions

Representative permittivities: ε′(mare) = 4.0, ε′(highlands) = 2.7.
Area fractions used: Near side ≈ 30% mare / 70% highlands; Far side ≈ 2% mare / 98% highlands; Global ≈ 16% mare / 84% highlands (maria ≈16% of lunar surface, concentrated on near side).

Formula and method

Normal‑incidence Fresnel reflectivity from vacuum to a dielectric:

R = ((n1 - n2) / (n1 + n2))^2 with n1 = 1 (vacuum), n2 = sqrt(ε′)

Step‑by‑step example calculation

1) Compute refractive indices

n_mare = sqrt(ε′_mare) = sqrt(4.0) = 2.000 n_high = sqrt(ε′_high) = sqrt(2.7) ≈ 1.643

2) Compute normal‑incidence reflectivities

R_mare = ((1 - 2.000) / (1 + 2.000))^2 = (-1 / 3)^2 = 1/9 = 0.111111... ≈ 0.1111 (11.11%) R_high = ((1 - 1.643) / (1 + 1.643))^2 = (-0.643 / 2.643)^2 ≈ (-0.2433)^2 ≈ 0.0592 (5.92%)

3) Weighted averages using area fractions

Near side (30% mare / 70% highlands): R_near = 0.30 * R_mare + 0.70 * R_high = 0.30 * 0.111111 + 0.70 * 0.0592 = 0.033333 + 0.041440 = 0.074773 ≈ 0.0748 (7.48%) Far side (2% mare / 98% highlands): R_far = 0.02 * 0.111111 + 0.98 * 0.0592 = 0.002222 + 0.058016 = 0.060238 ≈ 0.0602 (6.02%) Global (16% mare / 84% highlands): R_global = 0.16 * 0.111111 + 0.84 * 0.0592 = 0.017778 + 0.049728 = 0.067506 ≈ 0.0675 (6.75%)

Summary table

Scope Area fractions (mare / highlands) Weighted ε′ Reflectivity R (normal incidence)
Near side 30% / 70% ε′ = 0.30·4.0 + 0.70·2.7 = 3.09 0.0748 (7.48%)
Far side 2% / 98% ε′ = 0.02·4.0 + 0.98·2.7 = 2.73 0.0602 (6.02%)
Global (whole Moon) 16% / 84% ε′ = 0.16·4.0 + 0.84·2.7 = 2.91 0.0675 (6.75%)

Caveats and interpretation

• These values are normal‑incidence Fresnel baselines. Real radar backscatter depends strongly on incidence angle, polarization, surface roughness, blockiness, subsurface layering and possible ice; any of these can increase or decrease measured backscatter relative to the Fresnel baseline.
• Representative ε′ values and area fractions are simplifying assumptions for a first‑order estimate. Local variability (porosity, ilmenite/glass content, regolith thickness) can change ε′ and measured R by roughly ±20–30%.
• For mission design or detailed radar modeling, compute angle‑dependent TE/TM Fresnel curves, include roughness and multiple scattering models, and use multi‑frequency/polarimetric data where available.