What Δv means
Δv (delta-v) is the change in velocity a spacecraft has to produce with its engines to get from one place to another. It is the currency of spaceflight: every manoeuvre has a price in metres or kilometres per second, and the prices add up along a route. Reaching low Earth orbit costs about 9.4 km/s once air drag and gravity losses are included, even though the orbital speed at 400 km is only 7.7 km/s. From there, about 3.1 km/s more sends a ship towards the Moon, 0.8 km/s puts it into a low lunar orbit and 1.9 km/s brings it down to the surface.
The route map above shows those prices on each leg. They are typical values from published Δv maps, rounded to 0.1 km/s. Where a planet has an atmosphere, a heat shield lets the ship brake against the air instead of burning propellant: dropping from the Mars transfer into low Mars orbit falls from 2.1 km/s to about 0.3 km/s, and landing on Mars from 4.1 km/s to about 0.7 km/s.
How to read the rocket equation
The calculator turns Δv into propellant with the Tsiolkovsky rocket equation:
Δv = Isp · g₀ · ln(m₀ / m₁)
Isp is the engine’s specific impulse in seconds, a measure of how efficiently it uses propellant. Multiplied by standard gravity g₀ (9.81 m/s²) it gives the exhaust velocity. m₀ is the ship’s mass before the burn and m₁ its mass after. Because the masses sit inside a logarithm, each extra km/s costs more propellant than the last.
A worked example: a methane–oxygen engine with an Isp of 380 s has an exhaust velocity of 3.7 km/s. To fly the 5.8 km/s from low Earth orbit to the lunar south pole, m₀ / m₁ has to be e5.8 / 3.73 ≈ 4.7. In other words, about 79% of the ship’s mass at departure must be propellant, and only the remaining 21% can be structure, engines and cargo. A hydrogen–oxygen engine at 452 s needs a mass ratio of about 3.7 for the same trip, but liquid hydrogen is so thin (71 kg/m³) that its tanks are larger and heavier.
Why making propellant in space changes everything
If every tonne of propellant has to be launched from Earth, it first pays the 9.4 km/s toll to reach orbit. A depot that makes propellant where it is used breaks that chain. The calculator counts this as “made in space”: try the “refuel on the Moon” example and more than 800 t of the propellant burned comes from the lunar surface instead of from Earth.
What a depot can make depends on what is there. The Moon’s permanently shadowed polar craters hold water ice; at Cabeus crater, the LCROSS impact measured about 5.6% water by mass. Water splits into hydrogen and oxygen, so a lunar plant can supply hydrogen–oxygen ships and nuclear-thermal ships that run on pure hydrogen. It cannot supply methane, because there is very little carbon on the Moon.
Mars is different. Its atmosphere is 95.1% carbon dioxide. Combining that carbon dioxide with hydrogen from Martian water ice in the Sabatier reaction (CO₂ + 4 H₂ → CH₄ + 2 H₂O) produces methane, and splitting the water gives oxygen. NASA’s MOXIE experiment on the Perseverance rover has already made oxygen from Martian air, 122 g in total. That is why methane–oxygen ships make sense for Mars: they can refuel for the trip home on arrival.
Low thrust versus high thrust
Chemical engines are high-thrust. An RS-25 pushes with about 2,280 kN, enough to lift a heavy lander off the Moon in minutes. Their weakness is efficiency: Isp stays below about 460 s.
Electric thrusters are the opposite. A Hall thruster ionises xenon and accelerates it electrically to an Isp of 2,000–2,600 s, so the same Δv needs far less propellant. But thrust is tiny: NASA’s 100-kW-class X3 thruster produced 5.4 N. A cargo tug with a megawatt of power accelerates at a few hundred-thousandths of a g, so instead of a short burn it spirals outwards for months. That spiral also costs more Δv. The calculator uses the Edelbaum approximation, where the cost is roughly the difference between the two circular orbital speeds: about 7.7 km/s to escape Earth from low orbit, against 3.2 km/s for a chemical burn. Electric ships can never land or take off, so the calculator blocks those legs.
Nuclear-thermal engines sit in between. NASA’s NERVA engine was designed for about 825 s and 334 kN (75,000 lbf), and ground-tested reactors of the 1960s reached 825–850 s, but no nuclear rocket has flown.