How do I calculate the required antenna size for a satellite ground station at a given frequency band?

The ground station antenna size is determined by the required gain (G) to close the link budget. For a parabolic dish: G = η × (π × D / λ)², where η = aperture efficiency (0.55-0.65 typical) and D = dish diameter. Solving for D: D = (λ/π) × √(G/η). For G = 40 dBi (10,000 linear) at 12 GHz (λ = 0.025 m): D = (0.025/π) × √(10000/0.6) = 1.03 m. The beamwidth: θ ≈ 70 × λ/D degrees. For D = 1 m at 12 GHz: θ ≈ 1.75°. For LEO tracking: the beamwidth must be compared to the angular rate of the satellite (up to 1°/s) to determine if mechanical tracking is fast enough or if an electronically steered antenna is needed.