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Head east at launch as if you were going to reach a low orbit, but keep thrusting prograde until your apoapsis reaches about 2863 km rather than stopping at 100 km or so. Wait until you reach apoapsis, then roughly circularize the orbit there. The orbit doesn't need to be perfectly circular, but you want the period as close to being exactly one day as possible. Once you're close, cut your engine to 0.5% of normal to fine tune your orbit until the period is within one second of being one day.
That first relay will remain within line of sight of KSC for several years of game time. That's long enough to use it to build out the rest of your CommNet around Kerbin. That relay is high enough that a connection to it from elsewhere in Kerbin's sphere of influence will only infrequently be blocked by Kerbin.
Once you've got that first relay up, launch several more to fill out a CommNet around Kerbin. This is a vehicle I've used for this in the past, and the page explains how to get 100% CommNet coverage of Kerbin guaranteed to remain stable for thousands of game years.
https://steamcommunity.com/sharedfiles/filedetails/?id=2434375943
I also put two RA-100s in high polar orbits, roughly in the same orbital plane, and with exactly the same periods. I spaced them about a quarter of a circle apart, so that on should always be in view of interplanetary probes.
I also put three HG-5s in orbit over Minmus. This is so probes on the far side of Minmus would be in contact. It was fun to get all three satellites into orbit over Minmus with a single rocket.
Also note that a geostationary orbit requires your orbital period to be one sidereal day, not one solar day: while the solar day is what most people will recognise as "one day", it isn't the time required for the planet to complete one revolution on its axis as the planet is moving around the sun at the same time, so needs to turn slightly further than 360 degrees so the sun is back where it started (relatively speaking). On Kerbin this works out to 5 hours, 59 minutes and 9.42 seconds. (360 degrees of solar orbit per year divided by 426 solar days per year = 0.845 degrees per solar day. Kerbin must therefore rotate 360.845 degrees per solar day of six hours, so one sidereal day is (360/360.845) * 6 = 5.98595 hours, or 5 hours 59 minutes and 9.42 seconds). If your relays are positioned high enough, that minor difference won't make too much of a difference long-term, but only as long as all your relays are closely synchronised in their orbital periods- a few seconds out and they'll soon end up out of position and you'll have communications blackouts for part of their orbits.
After you have a connection to Kerbin everywhere in low to moderate orbit over the planet, adding more relays is easy. The hard part is starting with only the KSC and not the extra groundstations, as relays that you try to put into a good orbit will tend to lose their connection to the KSC at some point before you have them in the intended orbit.
Geosynchronous orbit is obtipusly the best option. I admittedly don’t put the effort I to that though. Sometimes I’ll put a satellite into orbit, orbit the other way, and polar orbit (which also can scan Kerbin too), usually that works pretty well, though still it isn’t as effective as a geosynchronous orbit.
Alternatively, I just take a bunch of satellites and shotgun them into orbit. Never have a problem after that.
Con though: wouldn’t recommend going overboard. Game starts to lag even in the KSP once you hit about 300+ relays.*
*Don’t ask.
Edit: I should clarify, it isn’t hard to do the “I am asking for Kessler syndrom to be a problem” method for me, if you do what I do — Instead of putting a useless payload, personally I like to build a relay of a certain weight, a generic relay usually is what I do when designing new rockets. Since you need to blast something into space anyways, a cheap relay or a small probe or something usually isn’t a bad idea, imo.
and that's, minimum, 300,000m with 3 relay sats. if you add just 1 more, you can have your relay network anywhere (around kerbin)
what's most important is that their period is as close to the same as you can kerbally make it.
another important thing is remembering that antennas connecting to other antennas are both ranges multiplied together, and take the square root of that
otherwise known as make sure your kerbin satellites are the absolute strongest you can get
as far as actually setting up a relay early game, if you do a resonant orbit you should be able to maintain connection long enough to get all satellites in place in one mission. otherwise, just launch a few trash satellites to try and spread out your connection
https://meyerweb.com/eric/ksp/resonant-orbits/ is a fantastic tool for setting up relay networks by the way
The number of craft you can handle greatly depends on your computer.
Personally I have noticed issues with the game, small lag and longer loading times, with just 50 relays going. And while my machine isn't great it isn't that bad either, I 5 @ 3.5Ghz and 16 gig ram using a 1070.
I wanted to put 3 relay sats around each celestial body for setting up a solid comms net for colonization. That alone was 50 -60 sats. In the end I just buffed comms ranges to avoid having to use many at all so i could put out more colony ships.
So just wanted to advise that there are limits depending on hardware on what is practical for your purposes.
<end of wet blanket>
Depending on your occlusion settings, it's possible that none of your extra ground stations will be able to see each other or the KSC, making them basically useless.
You only need a geosynchronous orbit for the very first relay you put into space. Maybe you could make a case for putting three of them in geosynchronous orbits, but that's only a temporary stopgap until you can set up a proper CommNet with high orbits. Relays in higher orbits with longer periods will tend to remain stable for longer.
They worked fine on standard occlusion settings.
That depends very heavily on the difficulty level. On hard, it won't work at all. On easy, it always works. On normal or moderate, whether it works depends on exactly where you place the ground relays and the order in which you place them there.
I would consider standard to be normal.
Yes though, such a strategy would require tweaking at higher levels of occlusion. However, actual sats can help, I grew both networks at the same time, and they assist each other in talking to each other which could feasibly make it workable even on 100% occlusion.
However as I said originally, the real point isn't to be a particularly efficient solution to the problem, but it does provide a good reason to use planes early game; and some interesting design challenges/self made missions which I enjoyed. After all, just throwing up a sat network would have been the easy way to do it, which I find boring by this point.
playing career mode usually gets you enough step by step missions that eventually teach you all the mechanics that are related to relays and other such stuff.
started from zero and career tasks built up my experience and knowledge
they did good job with that