Aristotle would have never gone to the moon

Interplanetary travel is impossible.  At least it was at one point.  Not because the lack of technology or resources.  No, it was intrinsically impossible, at least as the world was understood.  No one grew up dreaming about walking on the moon or on Mars, because no force could get one there, and there was nothing there to stand on. 

First, the moon, sun, planets and stars were different. Not just different sizes, temperature or structure, but made of completely different stuff than that on earth.  Aristotle was a great, influential thinker who systematically analyzed the world around us, including why things move and what stuff is made of.  Both were based on the classical understanding that everything we encounter is composed of four elements: earth, water, air and fire.  Not only did this shape his understanding of the material world around us, but also how things move and fall. Things with more of the heavy elements than their surroundings would naturally move down and things with more light elements would naturally move up, with earth as the heaviest and fire the lightest. But the heavenly bodies were far above everything, even above fire, and never came down.  So Aristotle postulated there must be an element lighter than even fire, and which traveled in perfect circular motion around the earth unlike the others that moved up and down.  If the moon was made out of a perfect substance lighter than fire, it is unlikely one could ever stand on it.

Second, for something to move upward it either had to be lighter than the surrounding medium or have a force continuously applied from some agent.  For the former, that would mean someone would need to somehow gather enough of this special fifth element and attach themselves to it.  But how to get hold of this stuff that only existed in the heavens, and even if one could, how to hold onto it?  The other option would be to somehow apply a force all the way.

That, however, would be quite difficult to do within the theory of force and motion Aristotle had developed. At one level, Aristotle's ideas seem to fit with what one might think of as common sense, but there are important differences from the Newtonian theory of forces that makes interplanetary travel possible.

1. Aristotle asserted that the natural state of objects was at rest, that "everything that is in motion must be moved by something" whereas Newton's first law states that objects in motion will continue in (uniform) motion unless a force is exerted on them.  So according to Aristotle, a force would have to be exerted on the space ship all the way to the moon.  In the Apollo missions, they simply got it moving in that direction and then let it "coast" with rockets only used to adjust course.
2. Aristotle believed force and velocity were directly related.  "The rules of proportion will be observed...  [I]f a given force move a given weight a certain distance in a certain time and half the distance in half the time, half the motive power will move half the weight the same distance in the same time." (Physics VII.5)  Newton, however, understood that force is related to the change in the velocity of an object.  Forces were needed to speed something up, or overcome other forces, but not to simply keep a moving object moving.
3. Aristotle distinguished between two types of motion, "natural" and "violent".  Natural motion described the falling of heavy objects and rising of light objects, where as violent motion was the result of a force that caused it to move in a way different from the natural motion. Gravity wasn't a force in Aristotle's theory; forces were only exerted directly. In Newton's theory, all motions followed the same laws.  
4. Aristotle considered that only active agents--people, animals, etc.--were capable of exerting forces to cause violent motion.  Stationary rocks don't exert forces, they are just there (perhaps in the way).  Newton asserted that if one exerts a force on a rock, the rock exerts a force right back on the person.  Newton's action-reaction pairs are critical to the functioning of rockets; the force of the rocket expelling its exhaust causes the the exhaust to exert and equally great force back on the rocket, causing it to move forward.  Related, Aristotle considered self-forces possible; a dog can walk because it exerts a force on itself to move itself forward.  In the Newtonian understanding, the dog actually moves forward because in the process of pushing back against the ground with its feet, the ground pushes the dog forward.  Aristotle would have needed a ladder, a mountain, a giant or some other physical object to use to reach the moon.

Aristotle's ideas were not ridiculous; in the real world pretty much all objects will come to rest after a force is no longer applied (though modern science attributes this to friction and air resistance, not intrinsic physics) and it does take more force to get something going faster, especially if air or water resistance plays a role. The motion of a object falling when nothing is touching it seems different from something being pushed, and we think of people, not rocks as that which is "doing something."  This is a practical, common sense way to think about the world that works if all we are interested is a conceptual description. It is not uncommon to encounter students in physics classes that think about the world something like this; unfortunately, this way of thinking creates difficulties for physics students because it interferes with learning Newtonian ways of thinking.
Aristotle was no fool, and his ideas are not totally unreasonable,  But Newton and others helped us develop better ways to describe forces and motion, which among other things makes interplanetary travel possible (though still not easy).