Suppose we detect an object on an orbit that will pass close to Earth, entering our SOI, but escaping after just a few days. If we wanted to mount a mission to intercept that object, how would we go about determining the most delta-v efficient trajectory to accomplish it? Full disclosure, this is a question inspired by a situation in a game, but it seemed like it might be an interesting situation in real life as well.
As an aside, have we ever actually done a real mission like this?
My current thought is that, intuitively, you'd want to time it so that your interceptor's apoapsis intersects the periapsis of the inbound object, then match velocity at closest approach, but I have no idea if this is actually the most efficient way to do it.
Per request for more information (estimating how the game's situation would map to more real world units):
- Periapsis of inbound object to Earth is about 0.17 lunar distances.
- Inbound orbital inclination (relative to sun) is 0.168 degrees.
- Eccentricity of orbit is 0.388.
I'm willing to do some math to figure things out, but I'm not sure where to get started.
Per request, here are images from the game situation.
Solar orbit of the inbound object (teal arc is inbound, violet is the estimated post-encounter orbit):
Orbit near Kerbin: