Orbital Insertion Delta-V Calculator

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:

1. Burn 1 (perigee kick): At the lower orbit, fire prograde to enter an elliptical transfer orbit
2. 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):

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