In a recent question, the slow drift of a landing site on a rotating body relative to an orbiter came up.
This would sometimes require a plane change correction when one desires to recover the landing party.
What would the $\Delta v$ cost of such a maneuver be?
Some initial considerations:
- The landing site does not uniquely define a plane. While the latitude sets a minimum inclination, the inclination of the orbiter's initial orbit may very well be larger.
- Similarly, an entire family of planes are possible for the pickup orbit. Optimisation would require picking the closest one.
- Landing from an equatorial orbit would never require a plane change, and neither will a polar landing.
- When the initial inclination is low and/or the stay is short, the cost is low.
- For all configurations of inclination and latitude, there would be no need for a plane change exactly twice during the body's rotation.
- While the plane change can usually be done as a simple impulse, that's not always optimal. I would imagine calculation just the inclination change angle instead of the velocity change would be simpler
While not exactly a hairy problem, the 3-dimensional geometry is not quite trivial, so it would be nice to have an answer to this for future reference.