Both architectures must deliver the same total mission Δv, split across two burns of roughly equal size: an outbound leg (Earth departure → lunar orbit insertion → descent) and a return leg. The rocket equation ties propellant mass to Δv exponentially:
Δv = Isp·g₀·ln(m₀/m_f)
m₀/m_f = e^(Δv / Isp·g₀)
Direct launch sizes one rocket for the entire Δv at once — its launch mass is dry mass times that full exponential mass ratio, so it grows explosively as Δv rises.
Depot-staged splits the trip at a cislunar waypoint. The crew vehicle only carries enough propellant for the outbound leg to the depot, then docks and refuels there for the rest of the journey. The depot itself is filled ahead of time by separate tanker launches, each carrying a fixed payload of propellant. More tankers means more total launches, but every individual launch — crew vehicle or tanker — stays far smaller than the single direct-launch giant.
- Mission Δv — raise it and watch the direct-launch mass ratio (and hence rocket size) climb exponentially, while the depot's per-launch size grows only linearly.
- Isp — higher exhaust velocity reduces propellant needs for both, but the exponential gap remains.
- Tanker capacity — a bigger tanker delivers more propellant per flight, cutting the number of resupply launches needed to fill the depot.
Real-world relevance: NASA's Artemis architecture and proposed Mars missions both lean on propellant depots and orbital refueling (e.g. SpaceX Starship) precisely to avoid needing a single rocket sized for the full round-trip Δv — no vehicle built to date can loft that much propellant in one launch.