An Opposition-Class Mission to Duna with Eve Flyby

[PLAD]

My first trip to Duna was a conjunction-class mission, that is, I went there and back on near-minimum energy trajectories. These are about 1050 m/s from low-Kerbal orbit (LKO) to Duna and then about 650 m/s from low Duna orbit to return to Kerbal. The problem is that I had to wait at Duna for 146 days for the return window to open and I only had a few days worth of stuff to do with this first tiny mission. The whole mission was about 280 days. So I started looking at higher energy missions, often called opposition-class missions. Here is a little NASA paper that looks at the two mission types for more background.

http://nssdc.gsfc.nasa.gov/planetary/mars/marsprof.html

NASA has found that opposition missions can be much faster for not too much more delta-V if you can flyby Venus on the way to or back from Mars. So I searched for such opportunities using Eve in KSP. And hooboy did I find them. The synodic period between Eve and Duna is 97 days and it turns out that there is a path from Duna, flying by Eve, and arriving at Kerbin with no thrusting required after you leave Duna (except for correcting small errors) every single synodic period! The delta-V required at Duna, assuming you start in a 60km circular orbit, varies between 1100 and 1300 m/s.

Most take too long to get from Duna to Kerbin (up to 200 days) and others leave too late to beat the next conjunction window back to Kerbin (so why bother?). But 2 are quite fast, and here is the best one. Only 1 day on Duna though!

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I am working on a program to find flybys and right now, and I am confirming that the results are real by flight-testing them as well as determining what information is needed to make it easy to find the right path. Here is how I describe the flight shown above:

KeY2D154:1145m/s Z+48,-DuY2D205:land: DuY2D206:1123m/s Z+248,-EvY2D264.5 -KeY2D310

That's 'leave Kerbin on Year 2 Day154 (Assume 0 hours if not mentioned) with a speed of 1145m/s (above the circular orbit speed you already have) that has a normal component of +48m/s, arrive at Duna on Year2 Day205, land ( or do whatever while there), Depart Duna on Y2 Day206 with a speed of 1123 m/s with a normal component of +248m/s, flyby Eve at Year 2 Day 264.5 (so day 264 and 12 hours) and arrive at Kerbin on Year 2 Day 310".

I find that with just the start speed and the time of flight I can find the right path with the node editor, though I have to search a bit. Oh, and you have to know that I always start in a 75x75km orbit at Kerbin, 60x60km at Duna, and I always use 24-hour days and 365-day years.

So this flight was 155 days total with about 2300 m/s in the two orbit departures. A conjunction-class mission is about 285 days and 1700 m/s for comparison. Here is the fastest mission before Y4:

KeY1D58:1288m/s Z-3,-DuY1D94:land: DuY1D95:1298m/s Z-427,-EvY1D146 -KeY1D166

108 days for about 2600m/s. But at these energies there is a direct return to Kerbin that is 100m/s less and just 3 days longer, so this one is not too useful either. If anyone asks, I can give all 10 of the first Duna-Eve-Kerbin flybys and leave it to you to decide the best way to get to Duna in the first place.

[KeithStone]

In my near year in kerbal I've learned I'm more of a brute force or mechjeb kinda flyer, since I prefer to design craft. However, I am endlessly fascinated by the real math behind it all (i just dont care to spend the time in game, especially if there's over-engineering to be done!). This is a beautiful discovery, and a sweet mission!

[PLAD]

Thanks! I love the math.

Now the other way. I had not looked at going Kerbin-Eve-Duna and then flying directly back from Duna to Kerbin because the NASA study points out that it would be bad for humans to arrive at Mars after a longer flight. A Venus flyby on the way to Mars is therefore is generally not preferred for humans. But careful studies have shown that Kerbals are not affected by long periods of zero-G, so why not?

It turns out there are not as many of these flights though because the synodic period between Kerbin and Eve is 170 days unlike the Eve/Duna of 97 days. It also take more energy to go from Eve to Duna so you have to arrive at Eve with more energy and the start boosts are bigger at around 1200-1500 m/s. On the good side returning from Duna to Kerbin is much cheaper, as low as 650m/s, so overall you save delta-V by going Kerbin-Eve-Duna, land, Duna-Kerbin instead of Kerbin-Duna, land, Duna-Eve-Kerbin. But it takes longer. Here's a quick look at the best one in the first 3 years:

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KeY1D166, 1237m/s Z+850 -EvY1D214 -DuY1D244. You have a huge amount of leeway on the return from Duna to Kerbin. If you leave right away it's DuY1D245, 858m/s Z+38 -Ke332, but you can leave anytime in the next 29 days and the delta-V required just keeps dropping until a minimum at DuY1D274, 640m/s Z-32 -KeY1D341.

So 166 to 175 days duration, total boosting around 2100m/s to 1900m/s. There is that 5000m/s arrival speed at Duna to deal with though, I bet you'd have to aerobrake down to about 8500 meters to be captured.

I had a weird problem when trying this, the encounter graphic would disappear when Kerbal would normally switch from the little white arrows to the colored ball that indicates you will pass in to the SOI of the target planet. So I had to guess and I missed the launch time and had a 111m/s error to correct. Doh! So I gave up for now. If anyone does this whole flight I'd love to see it.