Most Efficient Escape Orbit

[MDZhB]

I am constructing an interplanetary spacecraft (specifically to Duna) at a small space station around the Mun. Once it is done, I will break out of the Mun's gravity and head towards Duna.

My question is this: Is it more efficient to do the escape burn at a really high orbit, like you get after leaving the Mun's gravity, or should I first lower my PE to around LKO?

I think burning to get a low PE would defeat the purpose of any extra efficiency, but I'm not sure.

Help is appreciated!

[Superfluous J]

I know it's more efficient from Minmus to burn back to Kerbin. From Mun, I'd not be surprised to find the Oberth savings are not worth the burn down to Kerbin from Mun. Especially when you consider Mun's big enough to get an effect from Oberth as well.

You can test this without going. Make a maneuver node to go to Duna directly from Mun, the most efficient way possible. Jot that number down. Then time warp about a half a month and plot 2 maneuver nodes, one to get your Kerbin Pe low and another to eject to Duna from that Pe. Add those up. Whichever number is lower, that's your most efficient route.

Note: This is for Duna, and maybe Eve. You may want to re-run the numbers for other planets as going farther sees different savings at different places.

[MDZhB]

Wow, I didn't know you could make maneuver nodes on orbits you weren't even on yet! I looked, and it seems I can save about 9 m/s Dv going directly from the Mun. Thank you!

[Snark]

@OhioBob did a really nice analysis of this a while back, had the numbers nicely racked up in some convenient tables.  I'm mobile at the moment so don't have the wherewithal to dig it up, but I seem to recall that the break-even point (i.e. the point above which it's worth diving down to get an Oberth ejection) is around 8000 km for Kerbin.

Since the Mun is higher than that, then it's worth your while to do it... but only slightly, it's pretty close to a wash.  For Minmus, you'd definitely want to do an Oberth dive, as 5thHorseman points out.

The above assertion is based on my fuzzy memory of the numbers in Bob's table, so take it with a grain of salt until someone digs up a link to that excellent analysis.

[Zhetaan]

OhioBob's Oberth Tables

He really ought to name it the Near-Kerbin Astronomical Gazetteer or something similarly important.

[OhioBob]

8 hours ago, MDZhB said:

I am constructing an interplanetary spacecraft (specifically to Duna) at a small space station around the Mun. Once it is done, I will break out of the Mun's gravity and head towards Duna.

My question is this: Is it more efficient to do the escape burn at a really high orbit, like you get after leaving the Mun's gravity, or should I first lower my PE to around LKO?

If the ejection burn Δv is greater than your current orbital velocity, then it is most efficient to drop your periapsis and perform the ejection burn close to Kerbin.  If the ejection burn Δv is less than your current orbital velocity, then it is most efficient to burn from your current orbit without dropping the periapsis.

For instance, out at the orbit of Mun the orbital velocity is 529.4 m/s.  If from that orbit your ejection Δv is 500 m/s, then don't drop your periapsis - just burn from where you are.  However, if from that orbit your ejection Δv is 600 m/s, then you can reduce that amount by lowering your periapsis and performing the ejection burn as you pass through periapsis.  The lower you drop the periapsis, the greater the Δv savings.

Of course the downside of lowering the periapsis is in the timing and phasing of the maneuver.  You have to make sure that when you arrive at periapsis you do so at the right location and at the right time.

Since you're just going to Duna, I don't think the savings that you get from lowering the periapsis is worth the trouble.  I wouldn't do it.  However, if you were going to Jool, then the ejection Δv is great enough that lowering the periapsis would provide significant savings.

 

Edited June 24, 2016 by OhioBob

[Yasmy]

Here's an old table of the cost of going from any of the moon to any interplanetary destination, either directly, or by dropping down to the parent planet and burning from there.

As others have said, from low Mun orbit, it is best to burn directly to Duna or Eve.  For other interplanetary destinations, burn down to LKO then complete your transfer burn.

For Mun -> Duna, you save about 80 m/s.

For Mun -> Eve, you can save up to about 110 m/s.

These are pretty small.  For further destinations though, the penalty for going directly from Mun is very bad. (300-500 m/s.) 

Edited June 24, 2016 by Yasmy

[bewing]

... except that low Munar orbit is full of free fuel (if you have drills) and fuel in LKO is always much more expensive. So you can always easily gas up with an extra 500 m/s of fuel at the Mun, and go -- and Oberth be damned.

[MDZhB]

Thanks for all the great answers guys. I think I will be launching from LKO from here on, because it's becoming just a little tedious launching huge payloads all the way to the Mun. I'll make sure to keep all of this in mind next time I launch something a little smaller from Mun orbit though.

[Waxing_Kibbous]

Here's a video demonstrating one of the methods- however the reason he went to the Mun was to refuel:

 

Edited June 24, 2016 by Waxing_Kibbous