Gravity Assist & Hyperbolic Orbit Calculator
Interplanetary trajectory design: Compute hyperbolic encounter deflection angle ($\delta$), impact parameter ($b$), and heliocentric velocity gain from planetary gravity assists.
Flyby Planet & Approach Velocity
Assisting celestial body
Approach speed relative to planet
Closest approach height above planetary radius
Hyperbolic Encounter Physics
In the planet-centered frame, energy is conserved ($v_{in} = v_{out} = v_\infty$). However, the velocity vector is deflected by turning angle $\delta$:
$$\sin\left(\frac{\delta}{2}\right) = \frac{1}{e} = \frac{1}{1 + \frac{r_p v_\infty^2}{\mu}}$$
In the heliocentric Sun-centered frame, vector addition yields up to $\Delta V = 2 v_\infty \sin(\delta/2)$ in orbital velocity.
Encounter Kinematics
Deflection Angle (δ)
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Max Heliocentric ΔV
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Hyperbolic Geometry
Eccentricity (e)
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Hyperbolic: e > 1
Closest Approach Speed (v_p)
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Peak speed at periapsis
Impact Parameter & Targeting
B-Plane Impact Parameter (b):
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Periapsis Radius (r_p):
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Atmospheric Safety Margin:
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