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Any higher isn't really needed since you can put relays around the Mun and Minmus.
You don't even need relays around Kerbin unless you have extra ground stations turned off.
I followed the video Matt Lowne did on youtube. It definitely sounds more intimidating than it is.
Interplanetary? Consider a highly elliptical polar orbit - you'll almost never hit signal eclipses, and your time spent transiting kerbin will be <10 min.
Kerbin soi? I'd say no more than 5Mm circular with at least a single RA-2. You start trading a hundred dV for each % of signal strength for vehicles in Minmus SOI
No extra ground stations? Keosyncronous orbit is 2.868Mm (or a 1 day period)
You'll rarely have dropouts, just keep the peri low and the apo high.
2 'molniya-esque' sats (your choice whether it's northern or southern coverage) for "I'm making an effort' level laziness. Keep that apo high.
1 polar sat + 1 geostationary for optimized laziness
2 'molniya-esque' sats + 1 geostationary for "I'm really making an effort now!" level laziness
4 'molnyia-esque' sats opposing each other + 1 geostationary for "THIS WORLD IS MINE AND I SEE EVERY ANGLE" level. Caution: This level does not qualify as lazy. Points are detracted for attempting this foolish endevour.
3 relays will always give you full coverage if they're all in the same orbit and evenly spaced out but where's the fun in that.
The level of the signal is affected by the adjustment of the complexity of the game, the number and power of the repeaters on the satellite.
In the simplest case, 3 repeaters (in the form of an equilateral triangle) are sufficient in a circular equatorial orbit higher than the radius of the planet.
One repeaters can be placed in the polar orbit, the poles are not very often visited.
The higher the orbit the more near the polar regions will be covered, but the weaker the signal. (so far in the career are not open powerful repeaters)
But if in the career mode in the middle stages you need 100% signal strength for the transfer of scientific data, everything becomes more complicated.
https://steamcommunity.com/sharedfiles/filedetails/?id=819703903
To put things in perspective, the Mun is 12 Mm away, Minmus 47 Mm, Duna between 7.1 to 34.3 Gm, and Eeloo up to 126.6 Gm away.
The earliest relay antenna has a 5M rating, or class 2. That's more than enough to connect any two relays in the Mun or Minmus' SOI (less than 2.5 Mm radius), and to make a direct KSC connection with any tracking station.
P.S. If you want these relays to talk to vessels with a class 1 antenna, drop that down to (1580 - moon's radius) altitude in km (1,380 km Mun, 1,520 km Minmus). And if you need to talk to ships without antennas at all... Let's just say you really don't want to skip having antennas.
If you turn off extra ground stations, you can expect more complications and limitations. If you're using that HG-5 relay over Kerbin, and want your relay to be able to talk to any other weak Kerbin relay, you may not want to go above 1,900 km altitude (5 Mm range / 2 [opposite sides of planet] - Kerbin's 600 km radius). And if those relays are talking to craft with class 1's in orbit, 980 km might not be a bad upper limit (1,580 range - 600 kerbin's radius again).
Unfortunately the game doesn't say how adding additional antennas affects power, other than "diminishing returns."
I have done a few experiments though with signal strength using a simple RA-100 relay satellite, cheat codes, and KER in a sandbox game. At 9.19 Gm, 100% signal; at 9.6 Gm, 99%; at 51.8 Gm, 75%; at 81.12 Gm, 49%; at 100.9 Gm, 30%; at 120.8 Gm, 15%; at 140.7 Gm, 4%; at 155.6 Gm, 1%; at 160.5 Gm, no signal. Make of this as you will.
https://steamcommunity.com/sharedfiles/filedetails/?id=1335788398
https://steamcommunity.com/sharedfiles/filedetails/?id=1335788328
Going through the math, I can see each relay had a signal strength of 14.142 M, or 14,142 k. The max range it had with a Communotron 16 is sqrt( 14,142k * 500k ), or 2,659 km. Subtract Kerbin's 600 km radius, and you get 2 Mm. My probes were flying one megameter too high at their Ap. This explains why I'd have trouble controlling my salvage probes in LKO, when the relay was directly overhead and had a clear line of sight.
Because the laws of diminishing returns kick in early, but don't punish until you hit 32 relays on one satellite. Which means even the basic ♥♥♥♥♥ one turns into a planet connecting lazer beam.
It's only really important to have one geostationary satellite, ground tracking KSC so you avoid the issue of the mountains blocking KSC's wide angle view, which then allows a lot more freedom with launching unmanned ships. Add a polar sat and you're set up for going behind kerbin too, also to the Mun and Minmus if both satellites are peppered with enough relays for the job.
In this light, you can very quickly set up your relays and they don't need replacing until you decide you want to go to Jool or Moho. Which is pretty hilarious if you ask me.
https://steamcommunity.com/sharedfiles/filedetails/?id=1341511071
https://steamcommunity.com/sharedfiles/filedetails/?id=1354368992
To get to exact orbits I use "Kerbal Engineer Redux" and "Anatid Robotics - MechJeb". The first gives the necessary and useful information, and the latter can perform the specified maneuver up to a thousandths.
The process of creating an equilateral triangle seems incomprehensible only at the beginning.
Full communication allows you to save weight on the "pilot", which is more than half a ton, it is essential for flying to the moons.
Saving half a ton on a pilot is far from "essential" to reach Kerbins moons.
This is important for a career mode.
This is 7k. Put this in Munar orbit on a basic launcher and it will do all that. Not that funds are even an issue in stock Career mode. We won't even get into all the Crew reports you are missing out on. (Or the fact that your "money saving scheme" seems to ignore the cost of the satellite network you sent up to facilitate it.)
https://steamcommunity.com/sharedfiles/filedetails/?id=1193873660
I mean it's fine if you prefer unmanned, telling people it's "essential" (as in required) is quite the stretch though.