Calculator
Example data table
| Scenario | Mode | Speed(s) | Δi (deg) | Computed Δv (m/s) |
|---|---|---|---|---|
| LEO plane tweak | Pure | v = 7800 m/s | 5 | 680.246 |
| Combined transfer burn | Combined | v1 = 7800, v2 = 7500 m/s | 10 | 1378.097 |
| Circular from μ,r | Circular | μ=398600.4418 km³/s², r=6771 km | 15 | 2028.012 |
Formula used
- Pure plane change: Δv = 2v · sin(Δi/2), where v is the orbital speed at the burn point.
- Combined burn: Δv = √(v₁² + v₂² − 2v₁v₂cos(Δi)), treating the maneuver as one velocity vector change.
- Circular speed: v = √(μ/r), then apply the pure plane change formula.
How to use this calculator
- Select a calculation mode that matches your maneuver assumption.
- Enter the inclination change angle Δi in degrees.
- Choose velocity units, then enter speeds (or μ and radius).
- Press Submit to show results above the form.
- Use the download buttons to export CSV or PDF reports.
FAQs
1) What is a plane change maneuver?
A plane change rotates an orbit from one inclination to another. It changes the direction of the velocity vector, which can be costly when your speed is high.
2) Why does the pure plane change use sin(Δi/2)?
The maneuver is the vector difference between two equal‑magnitude velocity vectors separated by angle Δi. Geometry gives Δv = 2v·sin(Δi/2) for an instantaneous change.
3) When should I use combined burn mode?
Use combined mode when your burn changes speed and plane direction at once, such as during a transfer insertion. It models one vector change using v1, v2, and Δi.
4) Why are plane changes cheaper near apoapsis?
Orbital speed is lower near apoapsis. Because Δv scales with speed, performing the same angle change at a slower point typically reduces the required delta‑v.
5) What radius should I enter for circular mode?
Enter distance from the central body’s center to your orbit. For Earth, radius is Earth‑centered distance, not altitude. Add planetary radius to altitude if needed.
6) How do I avoid unit mistakes?
Select units first, then enter values consistently. For circular mode, keep μ and radius in matching systems. The tool converts km‑based inputs into SI internally.
7) Are these results valid for long burns?
The formulas assume an impulsive burn. Long burns, low thrust, or significant attitude constraints can change outcomes. Treat the output as a first‑order estimate.
8) What if I need a multi‑step maneuver plan?
Use this calculator to compare candidate burn locations and angles, then iterate. For complex missions, combine it with transfer analysis, constraints, and margin policy.