Reaching the moon from Kourou RSS/RO

[MajorTomtom]

Hey !

I have recently installed RSS/RO/RP0 mods and I'm still struggling to get efficiently to the moon. I am launching from Kourou. I tried to set the moon as target and wait till relative inclination hits 0°, but it stays always above 23°. I understand the theory that I should wait for my launch site to be at the ascending/descending node of the moon, and that it should therefore be at 0° relative inclination, but it just never goes below 23°. Is it normal and have I missed something from the theory, or is it a problem ? How should I proceed for a moon launch then ?

Thanks in advance

 

PS : I checked at cape canaveral and it works there, I manage to get rel inclination to approx 0° just like in tutorials

Edited August 2, 2017 by MajorTomtom

[Streetwind]

You misunderstood how inclination works  

Orbits are two-dimensional things; they exist in a "plane" on which the elliptical path is drawn. When you have two different orbits, there is two possible configurations: their orbital planes can be identical (the orbits are coplanar, like the orbit of the Mun around Kerbin and the orbit of Kerbin around the Sun in stock KSP), or they can intersect each other.

Take a look at this picture. You have two orbital planes intersecting (the equatorial plane simply being an orbit that is coplanar with the planet's equator, which means it has zero inclination). Any intersection between two planes causes a virtual line to form. This "line of nodes" is where all possible intersection points are located - points where the actual orbital paths cross. These intersection points, of which there will always be exactly two - unless your orbit is coplanar, in which case they don't exist at all - are the ascending and descending nodes. In KSP, you may sometimes notice that when you match a target inclination very precisely, the info display on the AN/DN markers turns from 0° into NaN ("not a number"), which means the node ceased to exist within the scope of KSP's mathematical precision, and you are now considered coplanar.

Now for the part that you misunderstood:

The relative inclination between you and any given target is the angle between the two intersecting orbital planes. It is not the angle between your current position and the object's current position. (Current positions are meaningless in space anyway, since nothing ever stays where it currently is). Even though the Moon may coincidentally sit directly over Kourou at some point in time, you will never achieve a relative inclination of 0°. While your launch vehicle sits on the ground, it has an orbital plane with the inclination of the launch site, since you are basically riding the rotation of the Earth. This orbital plane will intersect with the orbital plane of the Moon, and if your launch site's inclination is not precisely the same as that of the Moon, you will never become coplanar with it without launching and performing a plane change.

People wait for certain moments to launch not because they think they can achieve 0° relative inclination, but because they seek to minimize the dV spent on plane changes in other ways. Of which there are two.

First, you can wait to match the longitude of ascending node of the target. This number describes how your orbit is oriented relative to the fixed backdrop of space. If yours and your target's LAN are identical, that means that your orbital planes are as closely aligned as they can ever get - the relative inclination is minimized. That happens when you see the 23° minimum inclination difference you report, or when a launch site with an inclination closer to that of the Moon, like Cape Canaveral, approaches 0°. With the differences between your orbits minimized, the cost to perform the plane change once in space is minimized. Also, because of how the geometry works out, you are pretty much on top of the ascending or descending node after you finish circularizing in low orbit, and thus you can proceed to orbit matching right away.

Second, you can wait until the target orbit crosses over your launch site. At this point, the difference between your orbital plane and that of the target is maximized, which appears to be a bad idea... until you realize that in this configuration, either the ascending or the descending node is automatically on top of you. Which means that you can plane change right then and there - you can integrate it into your launch. And combining burns is the most efficient way to perform a plane change that there is.

Ostensibly, you would use method one when the inclination difference is very small (a few degrees at most), because it is easy to fly. And you'd use method two when it is larger than that, because you have to manually steer into the right direction away from the optimal eastward trajectory the rocket naturally wants to fall into, which requires more piloting skill, and you'll likely end up a bit off anyway. However, you can pull off method two in KSP without any additional tools - you can just eyeball it effortlessly. Method one is much harder to eyeball. So people pretty much always use method two in KSP, and that is also the method I would recommend to you. Especially with an inclination difference as large as 23°  

Edited August 3, 2017 by Streetwind

[MajorTomtom]

Okay I totally misunderstood that Cape Canaveral geographic location was what made it so close to the moon orbit, I thought that this "relative inclination" indicator people waited for to reach 0 in tutorials was indeed a measure of when the orbit passed overhead (which seemed indeed strange as in stock it is the angle between orbit planes, and is also in RO/RSS...).

Thanks a lot for your complete answer