Hohmann Transfer Calculator Formula

Understand the math behind the hohmann transfer calculator. Each variable explained with a worked example.

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Formulas Used

First Burn Δv

dv1 = abs(sqrt(6.674e-11 * central_mass / r1) * (sqrt(2 * r2 / (r1 + r2)) - 1))

Second Burn Δv

dv2 = abs(sqrt(6.674e-11 * central_mass / r2) * (1 - sqrt(2 * r1 / (r1 + r2))))

Total Δv

dv_total = abs(sqrt(6.674e-11 * central_mass / r1) * (sqrt(2 * r2 / (r1 + r2)) - 1)) + abs(sqrt(6.674e-11 * central_mass / r2) * (1 - sqrt(2 * r1 / (r1 + r2))))

Transfer Time

transfer_time = pi * sqrt(pow((r1 + r2) / 2, 3) / (6.674e-11 * central_mass))

Variables

VariableDescriptionDefault
r1Initial Orbit Radius(m)6571000
r2Final Orbit Radius(m)42164000
central_massCentral Body Mass(kg)5.972e+24

How It Works

Hohmann Transfer Orbit

A Hohmann transfer is the most fuel-efficient two-impulse manoeuvre between two coplanar circular orbits.

Key Equations

1. dv1 = v1 (√(2 r2/(r1+r2)) - 1) 2. dv2 = v2 (1 - √(2 r1/(r1+r2))) 3. Transfer time = π √(a_t³ / (G M)) where a_t = (r1 + r2)/2

Worked Example

Transfer from LEO (200 km alt, r1 = 6 571 km) to GEO (r2 = 42 164 km).

r1 = 6571000r2 = 42164000central_mass = 5.972e+24
  1. 01v1 = √(GM/r1) ≈ 7 789 m/s
  2. 02dv1 = 7789 × (√(2×42164/(6571+42164)) - 1) ≈ 2 457 m/s
  3. 03v2 = √(GM/r2) ≈ 3 075 m/s
  4. 04dv2 = 3075 × (1 - √(2×6571/(6571+42164))) ≈ 1 478 m/s
  5. 05Total dv ≈ 3 935 m/s

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