It is scientifically feasible today. In fact, the reason we don’t send men to the moon anymore is mainly that technology is so much better now we don’t need to send people.
There’s very little benefit in sending men. They weigh a lot, need food and oxygen and all that life support which is just wasted weight. Now we have remote robots and far more sophisticated sensors, reducing the benefit of a person vs. the best electronics. So why spend extra money and risk a life?
As far as guidance systems go, the physics involved in planetary calculations are so elementary that they could probably be worked out on the back of a napkin – very little need for a computer-based guidance system. Of course, the more sophisticated the computer, the greater number of things that can be calculated, but for basic movement, timings and geolocation, anyone as highly trained as astronauts are can easily do all the necessary calculations by hand. Even so, there were, in fact, some rudimentary computers on board the spacecraft and in use at Mission Control.