Kinetic Energy Required to Reach the Nearest Stars Within Stated Cruise Times

This paper addresses a single quantitative question about interstellar objects and interstellar traversal: What kinetic energy per kilogram do the nearest stars demand if the crossing must finish in twenty, fifty or a hundred years? Working from published survey values for the known interstellar objects and for the local interstellar medium, the paper computes required speeds and specific kinetic energies for five nearby systems at three cruise durations. The headline values obtained are E_prox_50 = 3.26e+08; beta_prox_50 = 0.085; E_prox_20 = 2.1e+09. Each number is produced by the deposited computation script from inputs that are stated in full, so the result can be reproduced, checked and updated as survey measurements improve. The study is a computation from stated assumptions and published data; it presents no new observations. Its contribution is a transparent budget: a set of numbers, the relations that produce them, and an explicit account of how sensitively each number depends on the assumptions behind it.