Orbital Plane Change Delta-V Calculator
Astrodynamics & orbital transfers: Calculate impulse velocity requirements for pure inclination adjustments and combined maneuvers (altitude + plane change).
Maneuver Parameters
e.g. Cape Canaveral to equatorial = 28.5°
Combined burn saves large Δv
GTO apogee speed ~1.608 km/s (or LEO ~7.7 km/s)
GEO circular speed ~3.075 km/s
Vector Triangle & Law of Cosines
For a combined plane change and velocity adjustment, the impulse is given by the law of cosines:
$$\Delta v = \sqrt{v_1^2 + v_2^2 - 2 v_1 v_2 \cos(\Delta i)}$$
For a pure plane change ($v_1 = v_2 = v$): $\Delta v = 2 v \sin(\Delta i / 2)$.
Delta-V Requirement
Maneuver Required Δv
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Optimal Thrust Pitch Angle (α)
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Comparison: Combined vs Separate Burns
Separate Speed + Plane Change
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|v₂ - v₁| + 2 v₂ sin(Δi/2)
Combined Burn Savings
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Propellant saved via vectoring
LEO vs GTO Apogee Plane Change
Equivalent Pure LEO (v=7.7 km/s) Δv:
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Efficiency Lesson:
Perform plane changes at slowest point!
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