🌑 Orbital Mechanics — Gravity Assist & Lagrange Points
Explore two key concepts in spacecraft navigation: the gravitational slingshot (gravity assist) where a spacecraft steals orbital energy from a planet, and the 5 Lagrange equilibrium points of a two-body system where gravitational forces balance.
Mode
Gravity Assist
State
ΔV ≈ 2·v_planet·sin(δ/2)
where δ = deflection angle
Planet loses tiny orbital
energy by conservation.
Lagrange Points:
L1, L2, L3: unstable on axis
L4, L5: stable if m₂/m₁ < 0.038
How Gravity Assists Work
A gravity assist (gravitational slingshot) uses a planet's gravity and orbital motion to accelerate or decelerate a spacecraft — essentially "stealing" kinetic energy from the planet's enormous mass. In the planet's reference frame, the spacecraft's speed is unchanged but its direction rotates. In the Sun's frame, the change in direction produces a net speed gain of up to 2·v_planet. NASA used this technique to send Voyager 1 & 2 on trajectories that would otherwise be impossible with available propellant. Lagrange points L1–L3 are unstable saddle points; L4 and L5 (equilateral triangle with the two masses) are stable if the mass ratio m₂/m₁ < 0.0385 (Routh criterion).