Principia Challenge: Munar Retrograde Rendezvous (1.2.2)

[maccollo]

Seeing as Principia is getting to the point where it is quite useable, it seems to be a good time to do this.

The challenge is fairly straight forward. A space station has been placed in a magical square orbit around Mun. 
The objective is to pilot the cargo vessel, which is in low Kerbin orbit, and rendezvous with the station, using as little delta V as possible.

 

You will need a 1.2.2 installation of KSP with a stock planetary setup, and Principia Catalan, then load this save file.

https://www.dropbox.com/s/d9vbdw0wba0jkxv/rendezvous.zip

Rules:

1. No use of cheats or performance altering mods. Telemetry and visual enhancement mods are allowed.
2. Since this is not a docking challenge, you only have to park within a 100 meter distance from the station, with a relative velocity less than 0.3 m/s. Submissions are scored based on how much delta V remains after rendezvous is complete.
3. The Kerbals must not exit the station. Also crashing into the station to slow down is not allowed
4. The time limit is 5 Kerbin years. This is just a technicality since I can't be certain the orbit of the station will be stable 1000 years from now.

This is not a super serious challenge so extensive documentation is not really required. Just post an screenshot showing your overall approach, and one after you've completed the challenge showing how much delta V you have left.
However, feel free to show your approach in greater detail if you complete the challenge with a small amount of delta V.

Edited May 31, 2017 by maccollo

[Streetwind]

Screenshots like this make me realize just how much I don't understand real n-body orbital dynamics. I'm just like "what? how? whyyyyyyyyy?"  Unless this was taken from outside the reference frame, I probably wouldn't understand how this orbit can exist even if you tried explaining it to me...

I'm pretty sure I can get a rendezvous with it anyway, so I just might try it. Could end up being the weekend until I have time, though.

[ZooNamedGames]

Is it using L points? If so, that will likely take extra DV to rendezvous with.

[maccollo]

On 6/1/2017 at 3:46 PM, ZooNamedGames said:

Is it using L points? If so, that will likely take extra DV to rendezvous with.

No. It's just a retrograde orbit. Altough it's just outside the hill sphere of Mun it's still stable. This is a neat characteristic of retrograde orbits. Anyway, I've made sure there is enough deltaV on the cargo vessel to perform the rendezvous.

On 6/1/2017 at 11:49 AM, Streetwind said:

Screenshots like this make me realize just how much I don't understand real n-body orbital dynamics. I'm just like "what? how? whyyyyyyyyy?"

The native patched conics trajectory will be highly inaccurate, though that's sort of the point. The real trajectory makes a lot more sense when you actually see it in motion.

[eggrobin]

My attempt at this: 959 m/s Δv. The flight plan was 917 m/s to an approach of (4 km, 8 m/s), so it should be possible to do much better if the burns are executed with more care. Things would probably have been easier with RCS, because trajectory corrections were a bit tricky here (needed to shut down engines and point the vessel in various directions).

See the following imgur album for details. This was with a version of Principia more recent than Catalan, as you can see from the trajectory of the target trajectory being shown in target-mobile frames (added in 1436), the nodes being displayed in frames with a physically significant reference plane (added in 1433), and the relative velocity being displayed on target approaches (added in 1406). These features will be present in Cauchy.

 

[septemberWaves]

How does the square orbit work in terms of physics? It looks extremely odd and very interesting.

[UmbralRaptor]

1 hour ago, eloquentJane said:

How does the square orbit work in terms of physics? It looks extremely odd and very interesting.

We're still trying to figure it out. I *think* eggrobin's the maccollo polygon is the result of a craft orbital period half that of the Mun, and something about resonances keeping the apoapses at the leading/trailing edges of the Mun, while the periapses are along the Mun-Kerbin line. (Apparently reversing where the apses are makes the orbit unstable)

Also not sure what happens if the orbital period is, say, 1/3 or 1/4 that of the Mun.

Edited June 10, 2017 by UmbralRaptor

[septemberWaves]

13 minutes ago, UmbralRaptor said:

Also not sure what happens if the orbital period is, say, 1/3 or 1/4 that of the Mun.

Well, if an orbital period of 1/2 that of the Mun causes a square, my first assumption would be that 1/3 and 1/4 would cause a hexagon and an octagon respectively. Although I really don't know anything about n-body physics other than the fact that Lagrange points exist, so I imagine it could quite possibly just be something unique to the 1/2 period.

[eggrobin]

An attempt at getting a lower bound for the Δv needed for this challenge from energy considerations in the PCR3BP: from the starting orbit, ~827 m/s is the theoretical minimum needed to pass L1 (and thus reach the Mun), about the same (1 m/s more or thereabouts) to escape through L2.

Excluding trajectories that go far outside of the Mun's orbit, at least 843 m/s should be necessary to rendez-vous with the target (that's the required Δv to reach its energy by a burn from the initial orbit, which is as low in the potential—and therefore as fast—as we can get).

If we do go beyond L2 (any such trajectory requires at least 828 m/s Δv to start with), we can enlist the help of the Sun, perhaps reducing the Δv required. This would be an outer transfer, along the lines of this Earth-Moon transfer by @maccollo. It becomes much harder to give a minimum Δv, since we are no longer dealing with the PCR3BP.

Bear in mind that those are just lower bounds, assuming that the Δv is applied instantly at the fastest point, and looking only at the energy and not the actual trajectory. My attempt required 858 m/s to pass L1, because the burn was done in an inertially fixed direction, and the thrust is low, so the tangent drifts from the burn direction quickly. Planning with instant burns, one finds trajectories that pass L1 from an 834 m/s burn, so it may be possible to do something along those lines with a burn that tracks the tangent direction (unfortunately Principia doesn't provide tooling to plan that at this time), or with several smaller burns at successive Kerbin periapsides.

Edited June 11, 2017 by eggrobin
unmatched parenthesis