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Least delta-V to get out of Kerbin's SOI?


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Yes, it's the only practical thing in Kerbin orbit to give a delta-v boost.  You might be able to shave a few m/s off by using a double assist, but it's not really worth the bother and it's already difficult enough to know where you'll head.

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Problem with mun gravity assist is that you don't take you anywhere, yes you escape SOI but you need to do more burns to reach stuff like Duna. 

Put an orbital refueling station in Mun orbit, refuel here, have an satellite in LKO plan an burn to location say Moho, Set satellite as target, burn back towards low earth so you Ep intercent the node on satellite. some hours to soon or late don't matter. Make node, note that the 830 m/s going to Mun is paid back with interests. 

Minmus works even better but is harder to pull off. 

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A Mun gravity assist is of limited use. The thing is it takes 860 m/s to get from LKO to a Mun encounter, and in fact the bare minimum won't give you a useful gravity assist, so you need more like 900. It only takes 950 m/s to escape Kerbin's SOI directly and another 90-130 to reach Eve or Duna.

So let's say you're going to Duna, it's 1100 m/s (from LKO) without a Mun assist or 1000 m/s with one. For most missions it's not worth the trouble.

Other gravity assists can give much more significant delta-V savings. For example reaching Jool directly takes around 2000 m/s, but reaching it via an Eve assist can take about 1100. Using Tylo or Laythe to capture into orbit round Jool can save several hundred there too.

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21 hours ago, rikieboy1 said:

So since i am bored i wanted to ask what's the strategy is tu use the least delta-V to leave Kerbin's SOI

Fly by from outside Kerbin's sphere of influence for an interplanetary encounter; in that case, it takes zero m/s to leave.

Escape velocity for any given starting altitude is the velocity of a circular orbit at that altitude multiplied by the square root of 2.  Note that the surface rotational velocity is not the same as orbital velocity; also note that surface velocity is greatest at the equator, zero at the poles, and affects your orbital velocity depending on the direction that you launch.  For a real answer on how to reduce your necessary delta-V, the best I can give you is to launch east from the highest equatorial mountain you can find using the most aerodynamic rocket that you can build, and make use of a Mun assist.

If you have a specific destination in mind, then I defer to the others who have already responded.  I will add that a Mun assist can be worthwhile if you accept that it won't do the entire job, but the value of its help is limited, oddly enough, by its total lack of inclination.  Every interplanetary destination is inclined with respect to Kerbin and that makes a Mun assist potentially more a harm than a help, except for trips to Duna whose relative inclination is tiny.

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17 hours ago, cantab said:

the bare minimum won't give you a useful gravity assist

Sure?
I'm away from KSP so I can't simply check myself, but IIRC any close encounter with the Mun will fling you into a solar orbit (which is all the OP seems to care about, so... useful enough I'd say).

@rikieboy1Beyond that, you may be able to shave off a few more m/s by doing a direct ascent, that is, not stopping for circularisation in LKO. Getting that right requires a lot of practice, though, and the savings are slim. So I guess it boils down to "just how bored are you"?

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If all you want to do is to reach Kerbol orbit, then using the Mun saves you a bit -- around 100 m/s or so. If you look at Delta-V maps, you need 950 or so to get to Kerbol orbit, while getting an encounter with the Mun will easily get you there too, at the cost of just 850 or so.

However, if you're trying to travel to other places, then getting that assist is likely to actually cost more, because you'll need to burn in Kerbol orbit (and the loss in Oberth Effect is way more significant than the 100 m/s you gained from the assist).

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