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On manned-missions which take its participants further and further into space it will be quite difficult to have a control center on Earth as it takes longer an longer to communicate.

It takes the light around 8 minutes to travel from the surface of the sun to Earth. Without any delay this would be 16 minutes for two-way communication and there's surely a point/zone on/in which it will be impractical to communicate.

Is there research on this topic?

For example:

"For missions with 'M' crew members that will take its crew 'X' AU (astronomical unit[s]) away from Earth it is reasonable to have mission control solely on Earth. The crew members are not allowed to make mission-critical decisions on their own"

"For missions with 'M' crew members that will take its crew 'Y' AU away from Earth it is reasonable to have a hybrid-solution. After 'X' AU (...). Crew members should decide democratically."

"For missions with 'M' crew members that will take its crew 'Z' AU away form Earth it is reasonable to have mission control solely in the hands of the crew. It's recommended to base this on a hybrid solution. After 'Y' AU (...). When 'M' exceeds 'N' high ranked members voices count twice."

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    $\begingroup$ The ship's captain (or master) have all final decisions. Even within communication range. $\endgroup$ – user39 Jul 20 '13 at 20:56
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There is this work at USC, "Research to explore communication delays in space", going on right now under a NASA grant. The investigation is being supervised by Professor Lawrence Palinkas:

The three-year study will involve simulating communication lag between astronauts on the International Space Station and ground control staff to determine how crew members cope with stressful situations and new forms of isolation.

[...]

Crew members will be asked to perform a set of specific tasks during the course of four weeks, split between the beginning and end of their six-month stay on the space station. During two of those weeks, they’ll experience a 50-second delay in interaction with mission control.

In addition, the jobs will vary in terms of how novel and critical they are in nature — that is, whether the astronauts received any training for each task and whether each situation is life-threatening or menial. “Cleaning out the toilet is not novel or critical,” Palinkas said, “but responding to a medical emergency could be.”

[...]

Palinkas is hopeful that findings from the project will prove useful in terms of improving training programs for astronauts to handle anxiety and stress, as well as developing technology that helps mitigate the negative effects of communication delays.

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