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I'm trying to understand the Oberth effect and came across this paragraph that seems crazy to me:
when the rocket moves, its thrust acts through the distance it moves. Force multiplied by distance is the definition of mechanical energy or work. So the farther the rocket and payload move during the burn (i.e. the faster they move), the greater the kinetic energy imparted.
It makes sense to me that a force acting against an immovable object doesn't impart any change in kinetic energy- the fixed force of gravity can push the stones of Stonehenge into the ground for thousands of years, but if they don't move there's no energy changing hands.
What makes no sense at all to me is that the change in kinetic energy is directly proportional to the distance the object moves. What if the object just coincidentally happens to be moving anyway? Say you have two objects; one is at rest, and the other is coasting through space at 1000km per second. You impart a tiny little 1 newton force on both objects for a second or so. The first object moves a meter so you've increased its kinetic energy by one joule. But just because the second object happens to be traveling at hypervelocity already, you've imparted the kinetic energy of a stick of dynamite? How do those definitions of work and kinetic energy make sense?
Come to think of it, the Earth is moving around the Sun at 30 km/s so if I stand on one of the stones of Stonehenge around sunrise, is the weight of my body dumping 17 megawatts of energy into it? It seems that the definition of work contains some kind of caveat that the distance the object moves has to be related to the force somehow but that's completely unclear to me.
Also, how does the object moving through space at a constant velocity even "know" that it's moving? There is no universal inertial frame of reference that everything moves relative to; who's to say that the fast-moving object isn't at rest and we are the ones moving at 1000 kilometers per second?