Hohmann Transfer — Animated
Two-burn transfer between circular orbits. Δv₁ at departure, Δv₂ at arrival; to-scale ellipse animated.
Vis-Viva Velocity
v=√(µ(2/r−1/a)); circular & escape too.
Orbital Period & Escape
T=2π√(a³/µ); v_esc=√(2µ/r).
Plane Change Δv
Δv=2v·sin(Δi/2) — do it where v is slow.
J2 Nodal Regression
Ω̇=−1.5√µ·J₂R_E²/((1−e²)²a^3.5)·cos i.
Formula reference & constants
vis-viva v=√(µ(2/r−1/a)); Hohmann Δv₁=√(µ/r₁)(√(2r₂/(r₁+r₂))−1), Δv₂=√(µ/r₂)(1−√(2r₁/(r₁+r₂))), t=π√(a_t³/µ).
plane change 2v·sin(Δi/2); escape √(2µ/r); period 2π√(a³/µ); J2 nodal Ω̇=−1.5√µ J₂R_E²/((1−e²)²a^3.5)cos i.
Earth µ=3.986e5 km³/s², R_E=6378 km, J₂=1.0826e-3. Sun-sync at i≈98° gives Ω̇≈0.986°/day.