Any more efficient way to intercept this asteroid in Kerbin's SOI?

[cantab]

I'm trying to intercept an asteroid in Kerbin's SOI, but having trouble doing so without using a load of delta-V. The asteroid is coming in on about a 30 degree inclination and has a 20,000 km periapsis. This pass will then send it on to Duna (I already arranged that assist with a tug) and I want to send up a ship with more hardware for the Duna mission. The ship I'm sending is currently at my space station, in a 255 km equatorial orbit. I'd rather meet the asteroid during the Kerbin flyby so I can return the current crew and science while I'm at it.

My first idea was a prograde burn opposite the ascending node to give me an intersect at the ascending node, to make the plane change as cheap as possible. Unfortunately by the time I get to apoapsis the asteroid will be well past the intersect, making this not an option.

My next idea was this:

A plane change in my current orbit, then a prograde burn to get an intersect at the asteroid's periapsis. This will work, but gives me some huge burns - 1500 m/s for the plane change and 600 to raise apoapsis, and that's not even counting what I'll need to match speeds with the asteroid.

I have something like 5000 m/s of delta-V, so I could go this way, but I can't help feeling I should be able to do it more efficiently. Plus I'd like to keep my fuel for pushing the rock around when it gets to Duna. I've not been able to figure out a specific approach though to get said hoped-for more efficient intersect.

Any ideas?

Edited June 1, 2014 by cantab
Answered

[Kasuha]

First of all you should launch into orbit with corresponding inclination. That will solve you a lot of problems and save a lot of dv for free.

If nothing can be done about it at the moment, a good option might be to raise your apoapsis in the direction of your inclination point with the asteroid and change your inclination from there. That'll cost you probably less dv than doing so in LKO. And you can use that extended orbit to plan the rendezvous.

Edit: okay I see you already ruled out that option. You can of course raise your orbit just a bit, not all the way to the asteroid trajectory. That can be done faster. Otherwise I'd probably just keep playing with the maneuver node until I'd get an intercept at minimum dv.

Edited May 31, 2014 by Kasuha

[cantab]

Thanks for the suggestion.

In the end I plumped for a prograde burn to put apoapsis at 20,000 km at the ascending node, then a combined plane-change and circularisation burn at apoapsis. By waiting many orbits before making that first burn I can get an intersect of a few hundred km around the asteroid's periapsis, which I'll fine tune on approach.

For the common target orbit of 20,000 km circular with matched inclinations, this takes around 1100 m/s of delta-V, compared to 2300 m/s for the method I showed previously, and 2800 m/s if I tried to do a single burn from LKO to put apoapsis at the asteroid periapsis.

That's more like it by cantab314, on Flickr

In fact it looks like in this case I've got away without too much cost from not launching directly to inclination. Considering that 18 tons of the 150 ton ship was already at the station, and I can top-off the tanks at the 255 km orbit (rather than in a lower parking orbit), I may even have saved fuel.