Bi-Elliptic Transfer Delta-V Calculator
Space mission astrodynamics: Compute 3-impulse bi-elliptic transfer $\Delta v$, intermediate apoapsis ($r_b$), transfer time, and evaluate Delta-V savings vs Hohmann transfer.
Primary Orbit Radii
e.g., LEO ~7,000 km
High orbit (e.g. 15× r₁)
Must be > r₂ (e.g. 2× r₂)
Gravitational parameter μ
When is Bi-Elliptic More Efficient?
If radius ratio $R = r_2 / r_1 < 11.94$, Hohmann transfer is always more fuel-efficient.
If $R > 11.94$, a 3-impulse bi-elliptic transfer with large enough $r_b$ saves $Delta v$, trading longer transfer duration for reduced propellant expenditure.
Delta-V Comparison
Bi-Elliptic Total Δv
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Hohmann Total Δv
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Individual Impulses (Bi-Elliptic)
Burn 1 (at r₁)
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Burn 2 (at r_b)
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Burn 3 (at r₂)
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Transfer Duration & Savings
Radius Ratio (r₂ / r₁):
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Delta-V Advantage:
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Bi-Elliptic Flight Time:
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Hohmann Flight Time:
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