Astrodynamics: Best Route for Grand Tour

[sevenperforce]

Was pondering this question and thought it might be interesting to pose to the forum. What's a more efficient planetary grand tour: going to the Mun first, or going to Minmus first?

The way I see it, there are two moderately-high-efficiency routes.

Minmus first

• Burn from LKO into a Mun flyby to get a gravity assist to Minmus
• Capture and land on Minmus
• Launch and orbit Minmus
• Burn from Minmusian orbit into a Hohmann transfer to the Mun
• Capture and land on the Mun
• Launch and orbit the Mun
• Burn from Munar orbit into a Kerbin aerocapture

Mun first

• Burn from LKO into a Hohmann transfer to the Mun
• Capture and land on the Mun
• Launch and orbit the Mun
• Burn from Munar orbit into a Hohmann transfer to Minmus
• Capture and land on Minmus
• Launch and orbit Minmus
• Burn from Minmusian orbit into a Mun flyby to get a gravity assist to a Kerbin aerocapture

For the sake of the question, we can assume the entire trip uses a single stage starting from a 100km circular Kerbin orbit, and that TWR is high enough to make gravity drag negligible on launch.

Is a Mun-first approach more efficient, less efficient, or equal to a Minmus-first approach? Would it be different if the Mun was the same mass as Minmus?

[Aegolius13]

Unless you're trying to optimize for the sake of optimization, the delta-v differences are going to be really minor  That, said, a few thoughts:

-When I have a ship visiting both moons, I prefer to go to Minmus first.  This is not because of delta-v, but because it's much easier to plot a a transfer from Minmus to the Mun than the other way around.  

-Getting a gravity assist from the Mun to Minmus is likely going to be more trouble than it's worth.  It's only an extra 50-70 delta-v required anyway to get your apoapsis from Mun-level to Minmus-level. I just don't think it's worth the trouble of waiting for a proper Mun-Minmus alignment, and you're likely to eat up a significant amount of the savings doing maneuvers to get the gravity assist just right.

-On the other hand, on the return trip to Kerbin, it is more feasible to use a reverse Mun gravity assist to get your orbit down closer to Kerbin.  Again this does not save a lot of delta-v, but less precision is required in this direction, so it requires less effort and less fuel spent on adjustments.  

-If you are using a staged rocket, one argument in favor of the Mun first is that, since gravity is a lot higher than Minmus, you may want to use more powerful rockets here.  Then you can stage those off and use a lower TWR setup for Minmus.  

-But if you're going single stage as you say, the opposite is probably true.  Your TWR is going to get higher as you burn off fuel, so you may want to hit Minmus first, then send your lighter, zippier rocket to the Mun.  

[sevenperforce]

Yes, all good considerations. Going to Minmus first is easier if you are using a single stage because you burn fuel at Minmus, which increases your thrust ratio for the Mun landing.

I was definitely wondering for the sake of optimization, though. There are certain things that will be equal with each approach, but it's still difficult. The Minmus capture coming from a Mun slingshot will cost less dV than coming from LKO, and a Munar capture coming from a Minmus transfer will cost less than coming from LKO. I'm just not sure how much. Unfortunately there's no dV map that shows transfers between the moons.

[Rhomphaia]

15 minutes ago, sevenperforce said:

Yes, all good considerations. Going to Minmus first is easier if you are using a single stage because you burn fuel at Minmus, which increases your thrust ratio for the Mun landing.

I was definitely wondering for the sake of optimization, though. There are certain things that will be equal with each approach, but it's still difficult. The Minmus capture coming from a Mun slingshot will cost less dV than coming from LKO, and a Munar capture coming from a Minmus transfer will cost less than coming from LKO. I'm just not sure how much. Unfortunately there's no dV map that shows transfers between the moons.

The maps may not but Alex Moons launch window planner does.

 

You could also check out KSP Trajectory Optimisation Tool if you really want to optimize the efficiency of your flybys.