The cheapest two-impulse transfer
A Hohmann transfer moves a spacecraft between two coplanar circular orbits using exactly two impulses. It is nearly always the lowest-Δv option for moderate altitude changes.
Starting at radius r₁ and ending at radius r₂ (both measured from the central body's centre):
Δv₁ = sqrt(μ/r₁) · ( sqrt(2r₂ / (r₁+r₂)) − 1 )
Δv₂ = sqrt(μ/r₂) · ( 1 − sqrt(2r₁ / (r₁+r₂)) )
Δv_total = Δv₁ + Δv₂
Use the calculator below to try it. Earth's μ is 398,600.4418 km³/s². Earth's radius is ~6378 km, so for a 400 km altitude circular orbit use r = 6778 km.
Worked example
LEO (400 km) → GEO (35,786 km):
r₁= 6,778 km,r₂= 42,164 km- Δv₁ ≈ 2,440 m/s, Δv₂ ≈ 1,470 m/s
- Total Δv ≈ 3,910 m/s
Compare with our budgets table in the previous lesson — this is exactly why getting to GEO is expensive.