Orbital Manoeuvre Cost Calculator Formula

Understand the math behind the orbital manoeuvre cost calculator. Each variable explained with a worked example.

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Formulas Used

First Burn Delta-V

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

Second Burn Delta-V

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

Total Delta-V

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

Variables

VariableDescriptionDefault
r1Initial Orbit Radius(m)6571000
r2Target Orbit Radius(m)42164000
central_massCentral Body Mass(kg)5.972e+24

How It Works

Hohmann Transfer Delta-V

The Hohmann transfer is the most fuel-efficient two-burn manoeuvre between coplanar circular orbits.

Formulas

dv1 = sqrt(GM/r1) * [sqrt(2r2/(r1+r2)) - 1]

dv2 = sqrt(GM/r2) * [1 - sqrt(2r1/(r1+r2))]

Total delta-v is the sum of both burns.

Worked Example

LEO (200 km, r1 = 6571 km) to GEO (r2 = 42164 km) around Earth.

r1 = 6571000r2 = 42164000central_mass = 5.972e+24
  1. 01v1 = sqrt(GM/r1) = sqrt(3.986e14 / 6.571e6) = 7788 m/s
  2. 02dv1 = 7788 * (sqrt(2*42164/(6571+42164)) - 1) = 2457 m/s
  3. 03v2 = sqrt(GM/r2) = sqrt(3.986e14 / 4.216e7) = 3075 m/s
  4. 04dv2 = 3075 * (1 - sqrt(2*6571/(6571+42164))) = 1478 m/s
  5. 05Total dv = 2457 + 1478 = 3935 m/s

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