An orbit is not floating. The International Space Station is falling toward Earth at every instant — it just moves sideways fast enough that the ground curves away beneath it at the same rate it drops. Get that one idea right and most of orbital mechanics follows. Get its economics right and you understand why the space industry prices everything in velocity, not kilometers.
Kepler describes, Newton explains
Johannes Kepler, working from Tycho Brahe's observations, extracted three laws: planets move in ellipses with the Sun at one focus; a planet sweeps out equal areas in equal times (it moves faster when closer); and the square of the orbital period is proportional to the cube of the orbit's semi-major axis. Description without mechanism — Kepler knew the what, not the why.
Newton supplied the why: every mass attracts every other with a force proportional to the product of the masses and inversely proportional to the square of the distance. All three of Kepler's laws fall out of that one equation. The same law governs the apple and the Moon — which was the point. Push an object fast enough sideways and it falls forever without landing; push harder still — past escape velocity, about 11.2 km/s from Earth's surface — and it leaves and never comes back.
Delta-v: the true cost metric
Konstantin Tsiolkovsky's rocket equation says the velocity change a rocket can achieve depends logarithmically on its mass ratio — fuel mass compounds brutally, because fuel must lift fuel. The consequence: space is not priced in distance. It is priced in delta-v, the total velocity change a mission requires.
This produces a counterintuitive map. Earth's surface to low Earth orbit costs about 9.4 km/s of delta-v — the single steepest toll in the inner solar system. Landing on the Moon costs several km/s more on top of that. But some near-Earth asteroids can be reached, rendezvoused with, and departed for less total delta-v than landing on and returning from the lunar surface. Energetically, parts of the asteroid belt's vanguard are closer than the Moon. Distance lies; the rocket equation doesn't.
Einstein's correction
Newton is an approximation — superb, but an approximation. Mercury's orbit precesses by a small amount Newtonian mechanics cannot account for; general relativity, treating gravity as curved spacetime rather than force, predicts the discrepancy exactly. A century later, LIGO detected gravitational waves from merging black holes — ripples in spacetime itself, confirming the theory in its most extreme regime. GPS satellites correct for both relativistic effects daily; ignore them and positions drift by kilometers per day.
Why it matters to a builder
Delta-v is the cleanest example of finding a system's true cost function. Naive metrics (distance) mislead; the real constraint (velocity change, compounding exponentially through the rocket equation) reorders the entire opportunity map — it is why asteroid mining is a serious business thesis and not science fiction. Every system has its delta-v: the actual variable costs compound against. Find it before you plan the mission.