The Energy Cost of Capturing an Interstellar Object into a Bound Orbit

This paper addresses a single quantitative question about interstellar objects and interstellar traversal: How much velocity change, applied at perihelion, would bind a passing interstellar object to the Sun? Working from published survey values for the known interstellar objects and for the local interstellar medium, the paper computes capture velocity increments and specific energies for four approach speeds at two perihelia. The headline values obtained are dv26_1au = 7.54; dv26_5au = 13.51; dv10_1au = 1.17. 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.