Hohmann Transfer Calculator
The most efficient two-burn maneuver for moving between circular orbits: compute Δv1, Δv2, total Δv, travel time, and transfer ellipse shape — from LEO to GEO, Earth to Mars (258.9 days), to Earth to Jupiter (997.8 days).
at = (r1 + r2) / 2 · Δv1 = √(μ/r1)·(√(2r2/(r1+r2)) − 1)
Δv2 = √(μ/r2)·(1 − √(2r1/(r1+r2))) · t = π·√(at³/μ)
Δv2 = √(μ/r2)·(1 − √(2r1/(r1+r2))) · t = π·√(at³/μ)
Quick presets
Input
Results
Total Δv
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Δv1 (at r1) —
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Δv2 (at r2) —
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Travel time
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Transfer ellipse semi-major axis at
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Kecepatan orbit
| Point | Kecepatan |
|---|---|
| Initial circular orbit (r1) | – |
| Transfer ellipse at r1 side | – |
| Transfer ellipse at r2 side | – |
| Orbit lingkaran tujuan (r2) | – |
Scope limits. This calculator computes transfers between two circular orbits around satu the same central body (idealized two-body model, coplanar, no inclination). For the velocity needed to escape gravity entirely (parabolic/hyperbolic trajectories, not orbit-to-orbit transfers), use Escape Velocity Calculator.
Methodology & notes
- All calculations use the vis-viva equation with standard gravitational parameters μ (m³/s²): Sun 1.32712440018×1020, Earth 3.986004418×1014.
- Signed Δv: positive = prograde burn (speed up, outward transfer); negative = retrograde (slow down, inward transfer). Total Δv = |Δv1| + |Δv2|.
- For interplanetary missions, the Δv here is heliosentris — not yet including the injection Δv from the parking orbit (computed via patched-conic / C3).
- Planet orbital radii use average values; real planet orbits are slightly elliptical and not perfectly coplanar.
- Verified example: LEO 400 km → GEO needs Δv1 = 2.3975 km/s, Δv2 = 1.4565 km/s (total 3.8540 km/s) in 5.29 hours.
Pertanyaan umum
What is a Hohmann transfer?
The Hohmann transfer is the most fuel-efficient two-burn maneuver for moving between two coplanar circular orbits. The spacecraft enters a transfer ellipse tangent to the initial orbit on one side and the target orbit on the other. The transfer ellipse semi-major axis a_t = (r1 + r2) / 2, computed from the vis-viva equation. The first burn (Δv1) raises/lowers the spacecraft onto the transfer ellipse, and the second burn (Δv2) circularizes the orbit at the destination.
How much Δv is needed from a 400 km LEO to GEO?
With this calculator: Δv1 = 2.3975 km/s (prograde burn at LEO), Δv2 = 1.4565 km/s (circularization at GEO), total Δv = 3.8540 km/s. Travel time 5.29 hours with a transfer ellipse semi-major axis of 24,471 km. Initial circular orbit velocity 7.669 km/s and GEO orbit 3.075 km/s.
How long is an Earth-to-Mars Hohmann transfer?
The Earth–Mars Hohmann transfer travel time (average orbital radii) is 258.9 days, with a transfer ellipse semi-major axis of 188,770,847 km. Heliocentric Δv requirement: Δv1 = 2.945 km/s and Δv2 = 2.649 km/s, total 5.594 km/s. This is why launch windows to Mars open every ~26 months — the target planet must arrive at the rendezvous point when the spacecraft gets there.
What are the Δv and travel time from Earth to Venus?
The Earth–Venus Hohmann transfer (inward, toward the Sun) needs a total heliocentric Δv of 5.202 km/s with a travel time of 146.1 days. Because the target orbit is smaller, both burns are retrograde (deceleration): the calculator shows Δv1 and Δv2 with negative signs, and the total is computed from the sum of their absolute values.
What is the difference between a Hohmann and a bi-elliptic transfer?
The Hohmann transfer uses 2 burns via a single transfer ellipse. The bi-elliptic transfer uses 3 burns: first climb to a very distant apoapsis, maneuver there (cheap because velocity is low), then descend to the target orbit. Bi-elliptic only wins when the radius ratio r2/r1 exceeds 11.94 theoretically (about 15.58 in practice, because its travel time is far longer). For LEO to GEO (ratio ~6.2) Hohmann remains the most efficient.
Why can the Δv result be negative?
A negative sign means a retrograde burn — the spacecraft must slow down, not speed up. This happens on inward transfers (r2 < r1), e.g. from GEO down to LEO or from Earth to Venus. The calculator shows Δv1 and Δv2 with their signs so the burn direction is clear, while total Δv is always summed from the absolute values.
Can r1 equal r2?
No. If r1 = r2, no transfer occurs — the spacecraft is already in the target orbit — so the calculator shows an error message. The same applies if either radius is zero/negative, or if an orbit lies inside the central body’s surface (e.g. negative altitude).
Why is the travel time only half the ellipse period?
The spacecraft travels only half the transfer ellipse: from the tangent point at the initial orbit to the tangent point at the target orbit on the opposite side (180° apart). Hence travel time t = π × √(a_t³ / μ), exactly half the full orbital period of that ellipse.
Does the Δv here include launch costs from the planet’s surface?
Not yet. This calculator computes Δv between orbits around the same central body. For interplanetary missions, the heliocentric Δv1 figure (e.g. 2.945 km/s for Earth–Mars) is not the injection Δv from LEO — real launches are computed with the patched-conic method using the characteristic energy C3 from the parking orbit. Use altitude mode with the LEO preset for the Earth-bound segment.
What are this calculator’s limitations?
The calculator uses an idealized two-body model: both orbits are treated as perfect circles, coplanar (zero inclination), with a single central gravity body. Ignored effects: inclination and plane-change maneuvers, other bodies’ gravity, planets’ actually slightly elliptical orbits (average orbital radii are used here), mid-course corrections, and gravity during sphere-of-influence crossings. For first estimates and learning orbital mechanics, accuracy is excellent; for real mission planning, use full astrodynamics software.
Free tool by NRTechStudio