How much time does it take for light to travel from here to Mars?

Mars moves in orbit around the sun, as do we. This makes it hard to say, as the distance is never the same. At any given time you are looking at 50 million to 400 million kilo meters, so about 3 to 20 minutes for light from there to reach us. (give or take)

It is robotic, so can navigate itself. The drivers will send commands to the rover saying, “Go here,” or “do that”. Then the computer will do it.

I just looked this up the night Curiosity landed. It varies from about 4 minutes to 20 minutes, as Earth & Mars may be on the same side or opposite side of the sun. The sun is 8 minutes from Earth.

Well, if it’s on the opposite side of the Sun, we won’t be able to communicate at all as radio signals don’t pass through the sun. I don’t know if there are relay satellites at L4 or L5, but if there are, it will take even longer. I’ll check with one of Curiosity drivers and get back to you.

And…just that quick I get an answer. They fly solo for 2 weeks
http://www.space.com/10684-mars-rover-opportunity-solar-conjunction.html

@Rarebear Nice link. They say this is the 4th time Mars is in conjunction with the Sun since Opportunity landed in 2004. Not bad – the spacecraft is out of touch about two weeks every two years, i.e., 2% of the time. Able to communicate the other 98% of the time.

At the time on landing, signals from Curiosity took 14 min to get to Earth. Note that re-entry took 7 min, so everything was automated. In fact, Curiosity’s command receivers were turned off during that time to prevent stray signals from being interpreted as new commands. The pre-programmed commands, with pre-programmed backup plans, were enough.