Orbital Insertion Delta-V Calculator
Calculate Hohmann transfer delta-v budget between two circular orbits around Earth, Mars, Moon, or Jupiter.
Includes both burns and total delta-v in km/s.
Delta-v (Δv, “delta-vee”) is the total change in velocity a spacecraft must achieve to complete a maneuver. It is the fundamental currency of spaceflight — more important than thrust, because it directly determines how much propellant is needed for a given mission. Every orbit change, every rendezvous, every planetary capture is budgeted in Δv.
The Hohmann Transfer — Most Efficient 2-Burn Maneuver: Named after Walter Hohmann (1925), the Hohmann transfer is the most fuel-efficient way to move between two coplanar, circular orbits. It uses exactly two engine burns:
- Burn 1 (perigee kick): At the lower orbit, fire prograde to enter an elliptical transfer orbit
- Burn 2 (apogee kick): At the upper orbit apogee, fire prograde again to circularize
Formulas: Let μ = gravitational parameter (km³/s²), r1 = lower orbit radius, r2 = upper orbit radius.
- v₁ = √(μ/r₁) — circular velocity at r₁
- v₂ = √(μ/r₂) — circular velocity at r₂
- Transfer semi-major axis: aₜ = (r₁ + r₂) / 2
- Transfer periapsis velocity: v_t1 = √(μ × (2/r₁ − 1/aₜ))
- Transfer apoapsis velocity: v_t2 = √(μ × (2/r₂ − 1/aₜ))
- Δv₁ = |v_t1 − v₁|
- Δv₂ = |v₂ − v_t2|
- Total Δv = Δv₁ + Δv₂
Reference Delta-V Table (approximate):
| Maneuver | Δv |
|---|---|
| Surface to LEO (200 km) from Earth | ~9.4 km/s |
| LEO to GEO (35,786 km) | ~3.9 km/s |
| LEO to Trans-Lunar Injection | ~3.1 km/s |
| Moon landing from lunar orbit | ~1.9 km/s |
| Earth to Mars (Hohmann) | ~5.6 km/s |
| Mars orbit insertion | ~0.9–2.1 km/s |
Connection to the Rocket Equation: The Tsiolkovsky rocket equation links Δv to propellant mass: Δv = Isp × g₀ × ln(m_wet / m_dry)
Where Isp is the engine’s specific impulse (seconds), g₀ = 9.81 m/s², and m_wet/m_dry is the mass ratio. For a chemical rocket with Isp = 450 s, a Δv of 3.9 km/s requires a mass ratio of about 2.4 — meaning over half the spacecraft must be propellant.
Why Δv Savings Matter: Even 100 m/s of Δv savings translates to hundreds of kilograms of extra propellant mass on a large spacecraft, or equivalently, a much larger payload for the same launch vehicle. Mission designers optimize trajectories obsessively over tiny Δv gains.
Gravitational Parameters Used:
- Earth: μ = 398,600 km³/s², R = 6,371 km
- Mars: μ = 42,828 km³/s², R = 3,390 km
- Moon: μ = 4,905 km³/s², R = 1,737 km
- Jupiter: μ = 126,686,534 km³/s², R = 69,911 km