EMBARK: An Atlas of the Earth-Departure Interstellar Reachable Set, Surveyed on a Real Catalog as a Function of Departure Epoch and Technology Level

Abstract

Abstract (English) When humanity launches interstellar probes with propulsion technologies that actually exist, how does the set of reachable stellar systems grow as a function of departure epoch t and technology level P? Using a clean eligible catalog of 37,498 stars built on Gaia DR3, we compute single-segment (direct) and multi-hop (transfer) reachable sets as statistical objects defined across an error ensemble of 2,000 realizations; to our knowledge this is the first survey of this question on a real catalog. Technology is treated strictly as 3-parameter bands (delta-v budget, cruise speed, operational lifetime), swept over 4 bands from the historically demonstrated band (Voyager class, 17.0 km/s) to the published concept-study envelope (0.2c). Our main findings are: (1) at the published demonstrated lifetimes, the flyby-reachable set of every band contains only 0-2 stars (the rendezvous set is empty for every band); the extent of the reachable set is limited first by operational lifetime, not by cruise speed. (2) Fast bands at or above 0.045c have identically empty rendezvous sets; only slow bands can seed transfers. (3) 60.3% of transfer edges occur beyond an endpoint's astrometric horizon, and (4) the stable gain of the reachable set from transfers is at most 1 star under our conservative model: the effective bottleneck of the transfer network is astrometric precision, not propulsion, and improved astrometry (Gaia DR4 and beyond) is the most direct route to enlarging the reachable set. This atlas is a survey, not a proof. Every statement is conditional, with the catalog, band, and cost model made explicit. 要旨(日本語) 人類が実在する推進技術で恒星間探査機を送り出すとき、出発時刻 t と技術水準 P の関数として、到達可能な恒星系の集合はどう広がるか。本研究は、Gaia DR3 に基づくクリーン適格 37,498 星のカタログ上で、単段(直行)および多段(乗り継ぎ)の到達可能圏を、誤差アンサンブル 2,000 実現を横断する統計的対象として計算した(我々の知る限り、実測カタログ上でこの問いを扱う初の測量である)。技術は(Δv 予算・巡航速度・稼働寿命)の3パラメータ帯として扱い、歴史実績帯(Voyager 級 17.0 km/s)から公刊概念研究の上限包絡(0.2c)までの 4 帯を掃引した。主要な発見は次のとおりである。(1) 公刊実証点の稼働寿命では全帯の会合到達可能圏は 0–2 星(同行圏は全帯で空)であり、圏の広がりは巡航速度ではなくまず稼働寿命に律速される。(2) 0.045c 以上の高速帯は同行到達が恒等的に空であり、乗換の起点になり得るのは低速帯のみである。(3) 乗換エッジの 60.3% は天測ホライズン外で生起し、(4) 乗り継ぎによる安定な到達増分は保守モデル下で ≤1 星にとどまる — 乗換網の実効ボトルネックは推進技術ではなく天測精度であり、Gaia DR4 以降の精度向上が到達可能圏を拡大する最も直接的な経路である。本アトラスは測量であって証明ではない。全ての言明は、カタログ・技術帯・コストモデルを明示した条件付きの形で与えられる。 Files. Papers in English and Japanese (PDF; the markdown sources ship alongside), the three released data products (embark_atlas_v1.json, departure_opportunities_v1.json, MANIFEST.json with sha256), the public error ledger (r3), and the verification-log bundle. Full repository: https://github.com/yukie-lab/embark (tag v1.0). Browser simulator: https://github.com/yukie-lab/embark-atlas (GitHub Pages). Code files are additionally licensed under MIT; the record as a whole is CC BY 4.0. Sister project. WAKE (arrival statistics of the solar neighborhood): doi:10.5281/zenodo.21966305.