Could a Mars rover go to Phobos or Deimos instead of going to Mars? The choice is made after launch, and no further modifications can be made to the rover. Could it land safely? Up to what point could it change its trajectory to encounter them? Is there any difference in safety and fuel between going to one of Mars's moons versus Mars itself?
No, for a lot of reasons.
- The Mars rovers slow down based on aerodynamics, heat shields, and parachutes. None of that is available on one of the Moons, meaning that the fuel requirements are much higher. Just to give you an idea, the spacecraft enters the atmosphere of Mars going at 12500 miles/hour (5.6 km/s). That speed in a spacecraft landing on Mars is slowed down by the atmosphere. Almost all of that speed would have to be slowed by a rocket somehow, which there isn't enough rockets. Some portion of this with a lot of work could theoretically be done via an aerocapture, but that hasn't actually been done, and would require really accurate models of the atmosphere. It would require at least 1 km/s delta-v to finish an orbit after an aerocapture, which is more than most rovers have when landing on Mars.
- Even if they somehow could be diverted and land, the landing sequence would need to be drastically altered, which would be hard to do even in 6 months that it takes to switch targets. This one could theoretically happen, but it'd be a tough thing to do from scratch.
- They likely couldn't move very well on the moon, as there isn't enough gravity.
- The power situation would likely be okay. The days are 8 and 30 hours for Phobos and Deimos, so that's likely to be fine.
Bottom line, it couldn't happen with any past or planned mission to Mars.
The skycranes don't throttle enough, a landing is impossible.
I note objections based on the EDL systems not having the delta-v to do it. This is a high hurdle but not actually a complete showstopper. If you could guide the vehicle through the atmosphere on just the right path (note that the path will vary based on atmospheric conditions, you would need something else to tell you where to aim) you could do an aerocapture, jettison the chute unused and use the skycrane rockets to circularize.
The showstopper problem is the skycrane is horrendously overpowered for the landing. I would also be surprised if the rovers could move once it's landed, it's not built to be so light.