Number of Kerbin-Duna Transfers

[palioxis1248]

Why make fuel silos out by Minmus when you can refuel in LKO? Burning up there, circularizing to rendezvous, and then leaving for Duna is gonna be less efficient than doing the same thing down in LKO due to the Oberth effect, plus it's a bigger pain to time everything.

The thing is you don't leave directly from the fuel silo. With the SOI-edge-scraping fuel silo, you rendezvous and refuel, then expend 200m/s to drop your periapse to about 80km thereabouts, then use the Oberth effect at periapse to sling yourself further. Of course you have to really get the dates of the rendezvous right, which is the whole point of me asking this question in the first place.

[palioxis1248]

Honestly, you really only one fuel station because of how the transfer windows work. But any dV you save is almost entirely negated by the fact that you have to rendezvous with your target. (Discussed at length here)

If you read further on you'd see that I posted about how one might exploit orbital silos to the logical ultimate in that same thread.

[alexmun]

Ok, if I understand what you're trying to do correctly, you should be able to do it with just one fuel depot.

Kerbin's orbital period is ~106.5 days. The synodic period between Kerbin and Duna (which is the time between Hohmann transfer windows) is ~227.4 days. That means Kerbin will complete 2.135 (227.4 / 106.5) orbits between transfer windows. Therefore Kerbin's prograde direction will move by 360 * 0.135 = 48.4 degrees from one transfer window to the next. All you need is an orbit for your fuel depot that completes x.135 orbits in 227.4 days where 'x' is an integer. That will make sure that your fuel depot is at the same angle to Kerbin's prograde at every Hohmann transfer window.

A circular orbit right at Kerbin's SOI boundary would have a period of ~29.9 days. That would have about 7.6 orbits per synodic period, so let's pick an orbit that would have 8.135 orbits per synodic period or ~27.9 days per orbit. That gives an orbit with a semi-major axis of ~80505.5 km or an altitude of ~79905.5 km (that's within 4000km of the SOI).

You will still need to position the station so that in the time it takes to go from its altitude to your periapsis where you're executing your ejection burn you end up at the correct ejection angle. But if you get it right for one transfer window with a station at that altitude it should continue to be right for all subsequent transfer windows.

Edited February 9, 2014 by alexmun
Math errors

[palioxis1248]

That was really helpful! Thanks a lot!