05 · Expensive
Plane
Δv = 2 v sin(θ/2). At 7.8 km/s a 60° change costs a launch. Do it high and slow, or launch onto the inclination you actually wanted.
In English
Tilting the whole racetrack is brutal because you are already going 7–8 km/s. The formula is 2 v sin(θ/2). Do the tilt where you are slow, or launch onto the tilt you wanted.
- Try this
- Set 28.5° at LEO speed (Cape → GEO). Then drop speed as if you were at GEO. The bill should shrink.
- Keep this
- Plane changes cost 2 v sin(θ/2). Launch onto the plane you want.
Lab · turning the whole orbit
Δv = 2 v sin(θ/2). At 7.8 km/s, a 60° plane change costs about as much as launching. Do it high and slow (apoapsis, GEO) if you must. Better: launch onto the inclination you wanted.
Plane change 28.5°
Speed at the burn 7.80 km/s
Δv 3.84 km/s · worse than a new launch
Combined burns (plane + circularize) at GEO insertion are cheaper than a pure LEO plane change plus a Hohmann. The formula 2 v sin(θ/2) is the isolated cost.
A 90° change at LEO speed is 2 v / √2 ≈ 11 km/s — more than launch. Polar from a low-latitude pad is a job for a different pad, not a bigger second stage.