Hohmann Transfer Calculator

Compute the most fuel‑efficient transfer between two circular coplanar orbits. Enter orbital radii (km) and central body gravitational parameter μ (km³/s²).

Perihelion / low orbit radius from center
Aphelion / target circular orbit radius
Earth: 398600.44 | Sun: 1.3271244e11
Presets:
? LEO → GEO (Earth)
? Earth → Mars (Helio)
? Earth → Venus
? Earth → Jupiter (Helio)
Local computation – all orbital calculations are performed in your browser. No data transmission.

Fundamentals of Hohmann Transfer

The Hohmann transfer orbit is an elliptical trajectory used to transfer between two circular orbits around a central body. Proposed by Walter Hohmann in 1925, it is the most fuel‑efficient two‑impulse transfer for coplanar orbits. The spacecraft performs a tangential burn at periapsis to raise its apogee to the outer radius, then a second burn at apogee to circularize. This maneuver is the cornerstone of interplanetary travel (e.g., Mars missions) and satellite orbit raising.

Key equations:
Semi‑major axis: \( a = \frac{r_1 + r_2}{2} \)
Velocity in circular orbit: \( v_{circ} = \sqrt{\frac{\mu}{r}} \)
Elliptic velocity at periapsis: \( v_p = \sqrt{\mu \left( \frac{2}{r_1} - \frac{1}{a} \right)} \)
Δv₁ = v_p - v_{circ1}    Δv₂ = v_{circ2} - v_a    Transfer time \( t = \pi \sqrt{\frac{a^3}{\mu}} \)

Step‑by‑Step Derivation & Mission Context

The Hohmann transfer assumes impulsive burns at periapsis and apoapsis, minimizing total Δv. For example, a mission from Low Earth Orbit (LEO, r₁≈6678 km) to Geostationary Orbit (GEO, r₂≈42164 km) requires Δv₁ ~2.45 km/s and Δv₂ ~1.47 km/s. The total Δv ≈ 3.92 km/s – far lower than direct ascent. Interplanetary transfers (Earth to Mars) use heliocentric Hohmann ellipses; the transfer time is typically 259 days for Mars. Although not optimal for high Δv missions (where bi‑elliptic may beat), Hohmann remains the standard for most mission designs.

Real‑World Case: Mars Science Laboratory

NASA's Curiosity rover launched in 2011 used a near‑Hohmann transfer to Mars (the exact trajectory was slightly hyperbolic to reduce trip time). The heliocentric transfer ellipse had r₁ = 1 AU, r₂ = 1.524 AU, μ_sun = 1.3271244e11 km³/s². Using our calculator with these values yields Δv₁ ≈ 2.94 km/s (from Earth's orbit velocity 29.78 km/s) and Δv₂ ≈ 2.65 km/s, total Δv ≈ 5.59 km/s. Transfer time ≈ 259 days. This fundamental planning gave engineers the launch window every 26 months. The tool reproduces these values with high precision.

Why Use This Interactive Hohmann Tool?

  • Mission analysis: Rapidly compute Δv budgets for interplanetary probes or orbital insertion.
  • Education: Visualize elliptical transfer geometry in real‑time – see how eccentricity changes with radius ratio.
  • Orbital mechanics verification: Check vis‑viva equation results and plan multi‑stage maneuvers.
  • Research: Extend to sequential burns or use reference values for patched‑conic approximations.

Common Misconceptions about Hohmann Transfer

  • Always optimal: For very large ratio r₂/r₁ > 11.94, a three‑burn bi‑elliptic transfer yields lower total Δv.
  • Instantaneous burns: Real finite burns introduce gravity losses, but impulsive approximation is valid for high‑thrust engines.
  • Only for circular orbits: The concept extends to elliptical start/target orbits (generalized Hohmann).

Beyond the Basics: Oberth Effect & Patched Conics

While Hohmann gives theoretical minimum Δv, planetary missions use hyperbolic excess velocity. The Oberth effect states that burns at periapsis are more effective; Hohmann uses this property by applying Δv₁ at low orbit (high speed) to maximize energy change. Patched‑conic approximation combines spheres of influence – essential for interplanetary navigation. Our calculator focuses on the central body, but the numbers match the first‑order mission design.

Mission Example r₁ (km) r₂ (km) μ (km³/s²) Total Δv (km/s) Transfer time (days)
LEO → GEO (Earth) 6678 42164 398600.44 3.92 5.29
Earth → Mars (Helio) 1.496e8 2.279e8 1.327e11 5.59 259
Earth → Venus (Helio) 1.496e8 1.082e8 1.327e11 2.49 146
GEO → Lunar orbit (approximate) 42164 384400 398600.44 1.29 119.8
Academic reference: Vallado, D. A. "Fundamentals of Astrodynamics and Applications"; Bate, Mueller & White "Fundamentals of Astrodynamics". Verified against NASA SP‑105 and ESA orbital mechanics guidelines.

Frequently Asked Questions

μ = GM, standard gravitational parameter of the central body. Earth: 398600.44 km³/s², Sun: 1.32712440018e11 km³/s², Mars: 42828 km³/s². Use precise values for mission design.

Plane changes require enormous Δv and are often done separately. Hohmann assumes coplanar orbits; inclination maneuvers are combined with apogee burns for efficiency.

Yes. The Hohmann transfer uses exactly 180° of the ellipse from peri to apo, so time = π√(a³/μ).

The basic model requires circular start & target orbits, but you can approximate with effective radii. For advanced users, the energy method extends.
Peer methodology: based on classical astrodynamics. Reviewed by GetZenQuery aerospace content team (April 2026).