Which scientific ideas have to do with spaceflight? What are the benefits and limitations of science related to spaceflight?Newton's Laws and Kepler's Laws
Newton's Law basically states that whatever goes up must come down. It's the law of gravity. The earth's centrifugal force holds everything down and it requires great force, or energy, to counteract gravity. In order for something to break the gravitational pull, there must be an equal and opposite force to gravity. So, man has devised the rocket, which exerts phenomenal force to force objects into space where gravity has little or no force at all. But, then there's the other part of the equation: the coming down part.
Air, while being invisible, is matter and as such is a barrier to an object pushing against it. When a spacecraft re-enters the earth's atmosphere, it pushes against the air and creates friction, which heats up the spacecraft to extraordinary temperatures! To counteract these extreme temperatures, man has devised heat shields on the bottoms of the space vehicles and adjusted the angle with which spacecraft hits the atmosphere to create the least resistance. These two safeguards create the most protection to the craft and enable it to safely reach the earth's surface.
Another of Newton's Laws was that anything once set into motion remained in motion until something acted upon it to stop. The rockets forcefully fling the spacecraft out of the earth's atmosphere and centrifugal force and inertia keep it in orbit around herself until rockets move it back within earth's gravitational pull again to bring it back home.
Science and mathematics have everything to do with safe and accurate spaceflight. As far as their benefits, we must adhere to the laws of nature and we are limited only in our imaginations and technology at this point. I believe we have only touched the tip of the iceberg when it come to spaceflight and there's much more to come in the future.