Skip to content
SpaceWonder

    Type to search · ↑↓ to move · Enter to open

    Orbital mechanics

    Hohmann Transfer Calculator

    Two-burn transfer between circular, coplanar orbits: both burns, total delta-v and transfer time.

    aₜ = (r₁ + r₂)/2 · Δv₁ = √(μ(2/r₁ − 1/aₜ)) − √(μ/r₁) · Δv₂ = √(μ/r₂) − √(μ(2/r₂ − 1/aₜ)) · t = π√(aₜ³/μ)

    Inputs

    Results

    Total Δv
    3.89261 km/s
    Departure burn Δv₁
    2.42577 km/s
    Arrival burn Δv₂
    1.46684 km/s
    Transfer time
    5.27501 hours
    5 h 16 min
    Transfer semi-major axis
    24,421 km
    Worked solution
    1. aₜ = (6,678,000 + 42,164,000) / 2 = 24,421,000 m
    2. v_circ,1 = 7,725.8 m/s, v_circ,2 = 3,074.7 m/s
    3. Transfer orbit: v_periapsis = 10,152 m/s, v_apoapsis = 1,607.8 m/s
    4. Δv_total = 2,425.8 m/s + 1,466.8 m/s = 3,892.6 m/s
    5. t = π √(aₜ³/μ) = 5 h 16 min

    How it works

    Walter Hohmann described this manoeuvre in 1925. One prograde burn stretches a circular orbit into an ellipse that just touches the target orbit; a second burn at the far point circularises it.

    Between circular coplanar orbits it is the most fuel-efficient two-impulse transfer for radius ratios below about 11.94. An Earth-to-Mars Hohmann transfer around the Sun takes about 259 days.

    Variables

    • r₁, r₂ — radii of the initial and target circular orbits
    • aₜ — semi-major axis of the transfer ellipse
    • Δv₁, Δv₂ — departure and arrival burns
    • t — transfer time (half the transfer orbit period)

    Assumptions and limits

    • Both orbits are circular and in the same plane
    • Burns are impulsive (instantaneous)
    • Two-body dynamics: for interplanetary transfers the planets' own gravity (escape and capture) is not included
    • No plane change

    For education only. These models are simplified and are not suitable for spacecraft navigation or safety-critical engineering. See our scientific accuracy policy.