Intercepting for Mun orbit from Kerbin Orbit - come in wide or screaming narrow at Mun?

[jpinard]

I have 3 choices for my maneuver node.  I want to go from a Kerbin orbit to a Mun orbit.  You can see all 3 options in the screenshot.  

#1 - Grab the moon coming around the opposite side.

#2 - Coming in very, very tight.

#3 - Coming in wider and easier.

Which will use the least amount of fuel?  And then later which might let me land on the Mun easier and/or with less fuel used?  Thanks!

 

Edited July 3, 2019 by jpinard

[bewing]

2 is better for fuel, both for arriving and leaving and landing.

1 is called a "free return trajectory". It takes more fuel when you are leaving from Kerbin -- but it allows the astronauts to come back "automatically" if there is a rocket failure. Which is why the Apollo missions used that trajectory.

3 costs more fuel when you arrive at the Mun, because you are not taking advantage of the 550 m/s of Oberth Effect that you can get in LMO.

 

[Zhetaan]

12 hours ago, jpinard said:

Which will use the least amount of fuel?  And then later which might let me land on the Mun easier and/or with less fuel used?  Thanks!

2 for both questions.  I won't repeat @bewing's answer, but I will add that 2 also appears to show you leaving from low Kerbin orbit; that will save you a bit of fuel, as well.  If you could miraculously start at a higher circular orbit--for example, 250 km instead of 80 km--then it would cost less fuel to go to the Mun from that higher orbit because you're already partway there.  However, since all rockets ultimately start from the launchpad, the total cost is higher to start from a 250 km orbit because it costs fuel to circularise that 250 km orbit, which is an extra, unnecessary step.

There are situations where it would be to your benefit to start from a higher orbit, drop down to 75 km, and make the bulk of your burn there, but they still have the problem of getting to that higher orbit in the first place.

I will add that in addition to the extra fuel efficiency involved in capturing to low Mun orbit (it's called the Oberth effect, as already mentioned, and is worth about two semesters' worth of study in itself), it sets up a much more fuel efficient landing to begin in low Mun orbit.  That may seem counter-intuitive, because while you're lower in altitude, you are also moving much faster, but it's true.  Your orbital motion is a combination of components, and for a snapshot of a tiny piece of your orbit (the piece which you will use for landing), we can approximate those components as vertical and horizontal.  Perhaps you've heard the analogy of an orbit as moving sideways quickly enough as you fall that you miss the ground (because it curves away under you), but the point is that horizontal velocity doesn't cause you to hit the ground unless you set your periapsis too low and find a mountain.  You can dissipate it largely at your leisure; so long as you keep a balance between it and the vertical component, you will have easy landings.

Vertical velocity, on the other hand, is a problem, because it does cause you to hit the ground, and, what's more, it keeps increasing because of that whole gravity thing.  Some people get the wrong idea about Mun landings and take their landers to high orbit where the orbital velocity is low, cancel that velocity with a tiny burn, and simply fall whilst trusting their engines to keep them from crashing.  The problem with that is that it's extraordinarily difficult to get that correct, and while the initial de-orbit burn is cheap, you end up burning to fight gravity nearly the entire trip down.

If you come in to a low orbit and burn to cancel your horizontal velocity, then it will stop you dead with as little as 100 metres left to drop to land.  That is a lot more controllable and you don't need to fight gravity nearly so much.

Edited July 3, 2019 by Zhetaan

[Vanamonde]

Among other reasons, #2 will save you fuel braking into orbit thanks to Herr Oberth. 

[Pecan]

On 7/3/2019 at 3:59 AM, bewing said:

2 is better for fuel, both for arriving and leaving and landing.

1 is called a "free return trajectory". It takes more fuel when you are leaving from Kerbin -- but it allows the astronauts to come back "automatically" if there is a rocket failure. Which is why the Apollo missions used that trajectory.

3 costs more fuel when you arrive at the Mun, because you are not taking advantage of the 550 m/s of Oberth Effect that you can get in LMO.

 

Just to add;

Which side of the moon you arrive at requires exactly the same burn.  If you time your #2 burn slightly later in your Kerbin orbit you arrive slightly ahead of Mun, and end-up orbiting clockwise instead of behind it and anti-clockwise.  Even changing that within Mun SOI, once you get the encounter, takes a very minor burn.  The main advantage of one orbital direction over the other is that, if you are landing, you want to be orbiting in the same direction as the body is rotating, for a slightly reduced braking dv.

[Kerbart]

The Oberth effect has to do with the rocket engine doing more Work (Force x velocity) and while there definitely is a positive effect, most of the gains of a low altitude intercept come from the simple fact that with a higher orbital velocity, you need to slow down less to inject into orbit.

The gains are very real and it’s a legit reason to inject at low altitudes but unless someone shows me the math I’m not convinced it’s mainly Oberth.

[Aegolius13]

3 hours ago, Pecan said:

The main advantage of one orbital direction over the other is that, if you are landing, you want to be orbiting in the same direction as the body is rotating, for a slightly reduced braking dv.

I'd add that the Mun rotates quite slowly, so that the difference in landing delta-v between a retrograde munar orbit (#1) and a prograde / regular orbit (#2) is going to be pretty negligible.  That said, there's no particular reason not to aim for the prograde orbit -- unless you want the free return trajectory in case of a problem that keeps you from injecting into Munar orbit.  I always aim for the prograde orbit, but mostly out of habit.

[jpinard]

Wow, fantastic explanations.  Makes a lot of sense.  Thanks so much!