Take the mean distance of the moon and the sun from the earth to be 0.4×10⁶ km and 150×10⁶ km respectively. Their masses are 8×10²² kg and 2×10³⁰ kg respectively. The radius of the earth is 6400 km. Let ΔF₁ be the difference in the forces exerted by the moon at the nearest and farthest points on the earth and ΔF₂ be the difference in the force exerted by the sun at the nearest and farthest points on the earth. Then, the number closest to ΔF₁/ΔF₂ is:

ΔF₁ = F₁ − F₂
ΔF₂ = F′₁ − F′₂
ΔF₁ = GmMₑ/(0.4×10⁶ − Rₑ) − GmMₑ/(0.4×10⁶ + Rₑ)
ΔF₂ = GmMs/(150×10⁶ − Rₑ) − GmMs/(150×10⁶ + Rₑ)
ΔF₁/ΔF₂ = GMmMe/(0.4×10⁶ − Rₑ) − GMmMe/(0.4×10⁶ + Rₑ) / GMₑMs/(150×10⁶ − Rₑ) − GMₑMs/(150×10⁶ + Rₑ)
= Mm/Ms × (0.4×10⁶ + Rₑ)(0.4×10⁶ − Rₑ)/(150×10⁶ − Rₑ)(150×10⁶ + Rₑ)
= Mm/Ms × (0.4×10⁶)² − Rₑ²/(150×10⁶)² − Rₑ²
= Mm/Ms × (0.4×10⁶ − Rₑ)(0.4×10⁶ + Rₑ)/(150×10⁶ − Rₑ)(150×10⁶ + Rₑ)
= Mm/Ms × (150×10⁶ − Rₑ)(150×10⁶ + Rₑ)/(0.4×10⁶ − Rₑ)(0.4×10⁶ + Rₑ)
= (150 − 0.0064)(150 + 0.0064)/(0.4 − 0.0064)(0.4 + 0.0064)
= Mm/Ms × 149.99 × 150.0064/0.3936 × 0.4064
= 8 × 10²²/2 × 10³⁰ × 149.99 × 150.0064/0.3936 × 0.4064
≈ 10⁻⁶