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Relay Satellites are used to communicate with the Kerbal Space Center without the need for a direct connection to it. Without a connection to the Kerbal Space Center, an unmanned probe will either not be able to function, or will be in limited probe control, depending on your settings for the game. (A spacecraft consisting of a pilot would not be affected.) With the fact that each antenna has a limited range, this makes relay satellites a necessity for almost every interplanetary mission. Relay Satellites give the function for other Probes to stay connected to the Kerbal Space Center without having the requirement to be in the line of Kerbin, or the range.
A relay satellite must have at least one relay-capable antenna and sufficient electricity to operate it. It must be placed where it has a connection to the rest of the CommNet network, either it being a ground station on Kerbin or another Relay satellite. However, no matter how much the distance between the satellites, the transmission will ultimately end up at Kerbin, or else the transmission will not be established at all.
Relay satellites are exceptionally useful if put into a suitable type of Orbit according to the circumstance.
- In early career saves, there may be a certain area where you cannot get any signal because of the lack of ground stations. This does not happen all the time, but when it does, you can put a simple relay satellite right above it with a semi-major axis of the thereabouts of 2868.3 to 2868.8, with the Orbital Period of exactly 6 hours. - In later career saves where Mun and Minmus are being extensively visited, a decent Relay Network with medium-high Polar Orbits around Kerbin may be most useful. - In extremely progressed saves, or perhaps, sandbox mode saves, a powerful relay network in high orbit of Dres and Kerbol orbit at the same orbit of Dres but different locations may potentially be useful for Jool expeditions.