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How do I get a communication satellite into a highly eccentric polar orbit around the sun, oriented orthogonal to the ecliptic in the most efficient manner?

The idea is that this orbit would create a relay that would be outside of the ecliptic and would have a direct line of sight to almost anywhere inside the ecliptic.

Thoughts so far:

  1. How can I use Jool to put a spacecraft into a solar polar orbit?
  2. I need a high altitude to efficiently perform the inclination change
  3. I can use gravity assists only while I'm more or less still in the ecliptic ... so I should do the inclination change starting with the last gravity assist
  4. If my eccentricity is not circle-ish after I do the inclination change I have to rotate the argument of the periapsis around the sun

Which leads me to the following order of maneuvers:

  1. use Duna to get into a highly eccentric solar orbit that encounters Jool
  2. use Jool to assist with the inclination change to solar polar orbit
  3. make orbit circle-ish
  4. fly over the sun and reduce the periapsis until the orbit is highly eccentric again - this time its orthogonal to the ecliptic though
  5. optional: fly to periapsis and reduce the apoapsis to around 30% of the maximum range of the used communication antennas.

My actual question: Is this the most efficient way and if not what could I do to reduce the ΔV cost even more?

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If you really want a solar polar orbit, I'd probably start like you suggest, with a flyby over Jool's poles to change the inclination. You won't be able to do a full 90° inclination change just with a passive fly-by, but a burn at Jool periapsis (to maximize the Oberth effect) ought to be able to finish the job, as I've just suggested in an answer to the earlier question you linked to.

That said, if your actual goal is to build a communications network that will cover the entire solar system, there are other ways to do it that don't involve going far out of the ecliptic. For example, you could start by parking two high-power commsats in the same orbit around the Sun as Kerbin, but 120° ahead of and behind it. If you don't mind waiting a while, you can do this with very little delta-v; basically just enough to escape Kerbin's SOI, plus a tiny bit more to recircularize orbits once the satellites have drifted far enough from Kerbin.

Such a network will give you near-perfect coverage of Moho and Eve, and will also mostly cover the day sides of the outer planets, even when Kerbin itself happens to be behind the Sun. The triangle formed by the two commsats and Kerbin should be wide enough in the sky that eclipses should mostly be a non-issue, since even Ike isn't big enough when seen from Duna's surface to eclipse all three corners of the network at once. I suppose you might get occasional comms blackouts on Laythe when it goes behind Jool, though.

If you want to also cover the night sides of the outer planets, you'll have a bit more work to do. One option would be to send a constellation of three or four commsats into an orbit way out beyond Eeloo (again putting them in orbits about equally space around the Sun, in the corners of a triangle or a square, and with orbital periods matched as closely as you can). This will take considerably more delta-v than just drifting around Kerbin's orbit (and you'll need more antennas on the satellites, since they'll be further away), but probably still less than going into a polar orbit around the Sun.

The other option, of course, is to just deploy separate clusters of commsats around each planet. Honestly, this might be the simplest way to do it, especially if you can piggyback the satellites on another mission to the same planet.

(Also, by spamming enough max-level relay antennas on a single craft, it's actually not hard at all to make a commsat with more antenna power than the maxed-out DSN has. Launching one into, say, high polar Kerbin orbit way out beyond Minmus will improve your CommNet strength and also somewhat reduce the risk of random eclipses cutting off your comms at just the wrong moment.)

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