Adventures in Thought Space

(The following assumes familiarity with high school calculus and physics.)  For over two hundred years before the advent of propulsion systems and heavier-than-air flight, “escape velocity” only pertained to projectiles trying to flee Earth’s gravity. While the physics hasn’t changed, the implied meaning of “escape” unfortunately has. Although spaceships do exceed escape velocity for reasons I’ll explain, this has cultivated the misimpression that a hypothetical vessel must.  Newton’s quantification of gravity wasn’t just an achievement in itself; it also showed that gravity is merely a force, one not altogether different than the force that projected the cannonballs in his thought experiments. Since gravity is just a force, any propulsion system with a sufficient stored energy to mass ratio could escape going an inch a second. Relative to what’s hypothetically possible, however, modern propulsion ships are primitive and easily weighed down--requiring high accelerations where ...

  (The following assumes familiarity with high school calculus and physics.)    Newtonian mechanics is the study of motion, force, and energy—which, in turn, forms the basis of the rest of physics. Acceleration, speed, velocity, force, power, and energy have great practical utility and meaning. Comprehending them is arguably more important than knowing how to calculate them—solving calculational problems is largely a means to that end. If understanding physics means understanding these phenomena and how they have fit in with each other, it’s imperative that students intelligently (and actively) distinguish between them and their variants: energy vs. power; contact force vs. net force; net work vs. “internal work”( e.g., the energy expenditure of the muscles of a weightlifter)—etc. In proving the path independence of kinetic and potential energy, the following thought experiments will expound these relationships in ways other treatments don’t.     ...