Sir Isaac Netwon did not quite understand what gravity was, but the math he developed describes normal gravity extremely well. When you hear how artillerymen before Newton thought their projectiles behaved it is tempting to wonder how intelligent they were. Of course, they were no dummies, but humanity did not have the mathematical knowledge to describe how projectiles behave in our gravitational situation. Einstein’s understanding of gravity is much more intimate, it gets much closer to truly understanding WHAT gravity really is, but I’m talking about skiing down our mountains at speeds substantially less than the speed of light (be careful there or you will get fined & jailed)!
Newton’s mathematics did not come all from him, but he built on the works of Galileo, Nikolas Copernicus, Tycho Brahe, and Johannes Kepler. It was those gentlemen who laid the foundations leading to the understanding of planetary motion that gave Newton the laboratory to test his mathematics on.
Galileo and Copernicus broke the shackles of earth centered universe model (Galileo performed some other experiments and made some other observations that also apply to gravity), Brahe and Kepler developed the observations and general characteristics (Brahe observed and recorded, Kepler provided the analysis) of planetary motion. Newton developed the math to describe and predict how bodies influenced by gravity move.
So, how does this apply to skiing and snowboarding? Well, gravitational energy is the main energy driving us down the hill. When you are at the top of a ski run think of yourself as a spring under tension. That energy you have is potential energy and that is the potential ability to do work. In this case the work is to move yourself down and over the ski run. The energy stored is not at all dependent upon the length of the run, but solely determined by the difference between your current altitude and the altitude of the lowest spot you will be skiing through. The pitch of the run has nothing to do with how much energy you have stored up at the top of the run. However, the pitch will dictate how quickly you convert that energy into motion (acceleration and speed).
More to come on this!