Rescuing Kerbals from a polar sun orbit

[dakota558]

I had a mission to get a space station in an orbit around the sun, which was quite easy to achieve. Now, after researching all the data in the science lab, I want to get them back. I had som fuel left in the station, so I tried to get an encounter with Kerbin. Instead I ended up with an encounter with Jool, and I figured I go past it to get some more science. This however left me in a more or less polar orbit around the sun (Ap 43,500,000,000m and Pe 25,900,000,000m roughly), and no fuel left.

So now I´m planning a rescue mission. I have a craft built that may be sufficient for the task, but my question is, what is the best way to rendevouz (if thats even possible)? I´m thinking maybe going to Jool first, and use that as a starting place?

I´m using the 1.2 pre release, so I don´t have MechJeb unfortunately. 

[John Cochran]

I do believe that you're going to have lots and lots of fun with that rescue, even if you had MechJeb. I would agree that Jool would be a good place to start. The most efficient method would be to have a Jool interception when Jool is at the AN/DN for its orbit and the station's orbit. Getting the timing correct for that interception is gonna be tricky, but if you do, then before entering Jool SOI, make an adjustment burn so you go over the appropriate pole of Jool to get deflected into an orbit with approximately the same orbital plane as the research station. Then make the same adjustments as you would normally do (match planes, hohmann maneuver, etc). But to be entirely truthful, it just may be easier to brute force the plane change (after all, getting deflected into a polar orbit by Jool isn't all that useful if the resulting orbit is 90 degree out of plane of the research station. Hence the tricky timing consideration). I trust you're using a nuke or other high ISP engine for this rescue? After all once you're actually in orbit, absolute thrust doesn't matter too much, and ISP is the major player.

[Aegolius13]

Ions might make sense for an upper stage, even if you use fuel cells for power. Their effective ISP is still tops. One you change planes, TWR ain't gonna matter much since you won't be hitting any celestial bodies.  Nukes below that, probably.

Agree a Jool assist will probably be of use.

 

[Snark]

Jool could be useful... but that's going to be really tricky, for this reason:

18 hours ago, John Cochran said:

The most efficient method would be to have a Jool interception when Jool is at the AN/DN for its orbit and the station's orbit. Getting the timing correct for that interception is gonna be tricky

(emphasis added by Snark)

^ just want to make sure that you didn't lose sight of this really critical point in JC's great explanation.  It's gonna be the kicker.  You'll likely have to wait for quite a few orbits to make this line up, since you have to get three things lining up instead of just two (Kerbin, Jool, and the AN/DN).  This is, theoretically, probably the lowest-dV way to make the rescue, but you'd have to wait a long time to get it just so.

If I were doing this myself, I wouldn't bother with Jool (it feels to complex to me, and I hate using up that much calendar time).  The following approach would probably hit the "sweet spot" for me, in terms of a compromise between dV efficiency and reasonably short navigation / wait times.

Option 1:  Wait until Kerbin's located at the AN/DN of its orbit with respect to the station's orbit.  Launch from Kerbin straight into the plane of the station's orbit, such that the Ap touches the station's orbit.  Coast to Ap, then do just enough of a prograde burn to get an intercept within a couple of orbits.  Match velocities at intercept.

Option 2:  Wait until Kerbin's located at the AN/DN of its orbit with respect to the station's orbit.  Launch equatorially from Kerbin, same as if you were going to the Mun or something (i.e. no plane change, such that you launch into a solar orbit with Ap that crosses the station's orbit right at the AN/DN.  Coast up to the Ap, then do a burn that matches planes with the station and adjusts Pe by enough to get an intercept within a couple of orbits.  Match velocities at intercept.

I'd run the numbers for those two options, then pick whichever one is less dV.  My guess is that option 2 would probably be cheaper, since, 1. it lets you take advantage of Kerbin's rotation for a few hundred m/s of speed, and (more critically) 2. the big solar plane change (which is the hugely most expensive thing about the whole process) will take place at a much higher solar altitude and therefore will be less expensive.

 

[dakota558]

I will try to get my rescue vessel to a Jool orbit, and then see if I'm able to match the orbit and get an intercept.

Meanwhile I'm trying to complete a rescue contract with a guy orbiting the sun. Didn't look to hard until I saw that the orbit was clockwise... Guess I need a lot of dv to complete that one

[John Cochran]

Just to make the point on how long you would have to wait for the proper Jool intercept. Assuming that you always want the same phase angle for a transfer from Kerbin to Jool, then you'll have a window for Jool approximately every 1.096 Kerbin years. Now assuming that you are willing to accept a 5 degree error on the intercept, that means you need a possible intercept every 10 degrees (that will get you with 5 degrees worse case since you can accept the intercept either in front of or behind the desired point. Worse case is if both possible intercepts have exactly 5 degree errors). So running the calculations, you have a wait of anywhere between 0 and 69 years to get the desired intercept. The largest angular distance between adjacent possible intercepts is 8.9 degrees for a worse case of 4.45 degrees. The average error from the best case of the 63 potential intercepts is 1.73 degrees. So if you go the Jool intercept to use gravity to swing into a polar orbit for the rescue, you'll have a good window sometime within the next 69 Kerbin years. When I don't know, but I will tell you that between adjacent intercepts Jool will advance on average 34.71 degrees each time (won't be exactly that amount since Jool's orbit is a bit eccentric. I'd probably suggest going with one of Snark's options unless you're really patient. 

Edited October 3, 2016 by John Cochran
Got the quoting wrong.