With robots that can run for years on nuclear batteries, and in some cases even perform basic repairs to themselves, they seem like pretty capable instruments for space exploration. Aside from the obvious study of how the human body copes in extra-terrestrial situations, are there any advantages to sending manned space missions, as opposed to solely robotic ones?
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To add on to what Rory Alsop said about machines lacking problem solving capability:
At least the rovers we have sent to Mars so far are not fully autonomous - they are not controlled at all time either, but are queued up with a set of plans. But if something unexpected does happen, it is not easy for a person to take the wheel, so to speak.
Depending on the relative positions of Earth and Mars, the time delay to issue a command could be about 12 minutes, and the time it takes to find out what happened the same. By the time your signal gets there it could already be too late to react.
Earlier this year Curiosity sat around for a month because the sun came in between the Earth and Mars. They could have queued up exploration instructions for a month, but of course they wouldn't have trusted the rover to handle things on its own.
But AI that could manage on its own is probably not far off, especially for a rather inactive planet such as Mars.
As well as the political and outreach benefits, we also have:
- Machines still do not have our problem solving capability, so if something outwith their programming happens, they may well fail to respond appropriately
- We can learn skills and techniques to help us prepare for migrating off this planet (yep, long term, but is likely to be needed at some point)
If we could find a way to exploit spooky action at a distance we could eliminate manned space flight altogether.
As the other answers suggest, the inability to make decisions in a timely manner limits what a robot can do in space exploration (such as the rovers). The speed of light and great distance limits how fast decisions can be sent to a rover or deep space probe. If we can find a way to communicate with a probe on Europa at the same speed as a machine right next to you then we would have no need to "experience" space from our own eyes any more.
Ultimately, robotic missions are far better (from a scientific point of view) than manned missions, so long as we can communicate with the robots in real time.