Hohmann Transfer Orbit Delta-V
Calculates the total velocity change (Delta-V) required to transfer a spacecraft between two coplanar circular orbits using an elliptical two-impulse trajectory.
\[ \Delta v_{total} = \sqrt{\frac{\mu}{r_1}} \left( \sqrt{\frac{2 r_2}{r_1 + r_2}} - 1 \right) + \sqrt{\frac{\mu}{r_2}} \left( 1 - \sqrt{\frac{2 r_1}{r_1 + r_2}} \right) \]
Plain Text Formula:
Delta_v = sqrt(mu/r1) * (sqrt(2*r2/(r1+r2)) - 1) + sqrt(mu/r2) * (1 - sqrt(2*r1/(r1+r2)))
📐 Variable Definitions & Parameters
| Symbol | Variable Name | Standard Unit | Physical Definition |
|---|---|---|---|
| \[ \Delta v_{total} \] | Total Transfer Delta-V | m/s or km/s | Sum of periapsis injection burn and apoapsis circularization burn |
| \[ r_1 \] | Initial Orbit Radius | m | Radius of starting circular orbit |
| \[ r_2 \] | Target Orbit Radius | m | Radius of destination circular orbit |
| \[ \mu \] | Gravitational Parameter | m³/s² | Central body standard gravitational parameter |
💡 Worked Engineering Example
Problem Statement:
Why is the Hohmann transfer the most fuel-efficient two-burn orbital maneuver?
Step-by-Step Solution:
- The burns occur tangentially at orbital apsides where kinetic energy is maximized or minimized
- Maximizes the Oberth effect by applying thrust at maximum orbital speed
- Requires zero out-of-plane plane changes
🎯 Result: Delivers minimum fuel expenditure for coplanar orbital transfers.