IndisputableMonolith.Astrophysics.ExoplanetHabitability
The module defines RS-native quantities for exoplanet habitability in dimensionless units. It supplies the year as base time, orbital periods, eccentricity penalties, moon mass ratios, and a composite habitability score with certification. Astrophysicists using Recognition Science would reference these when adapting standard exoplanet models to the phi-based framework. All content consists of definitions and simple non-negativity lemmas.
claimDefine the dimensionless year as $1$. Let $T_{RS}$ be the orbital period in RS units. The eccentricity penalty is a non-negative function of eccentricity. The habitability score combines period, penalty, and moon mass ratio in the appropriate band.
background
Recognition Science works in native units with the time quantum $ au_0 = 1$ tick from the Constants module. The Cost module supplies the J-cost functional for defect calculations. This module applies those to astrophysics by setting the year as the working time unit and defining derived quantities such as orbital period from Keplerian relations and habitability score as a function of period, eccentricity, and moon mass ratio.
The module introduces the phi-ladder scaling for planetary parameters and the Berry creation threshold in the context of habitable zones. It treats eccentricity as a defect measure whose penalty vanishes at zero and remains non-negative elsewhere.
proof idea
This is a definition module, no proofs.
why it matters in Recognition Science
It establishes the basic objects for exoplanet habitability within the Recognition Science framework. The definitions support certification via the habitability certificate declarations. It connects the core constants and cost structures to planetary observables, enabling application of the eight-tick octave and phi-ladder to habitability questions.
scope and limits
- Does not compute numerical habitability for specific exoplanets.
- Does not derive the underlying RS constants or the J functional.
- Does not include general relativity or multi-body orbital effects.
- Does not address atmospheric composition or stellar spectral type.
depends on (2)
declarations in this module (11)
-
def
year_dimensionless -
def
T_RS_period -
def
eccentricity_penalty -
theorem
eccentricity_penalty_zero -
def
moonMassRatioInBand -
theorem
T_RS_period_pos -
def
habitability_score -
theorem
habitability_score_at_zero_ecc -
theorem
eccentricity_penalty_nonneg -
structure
ExoplanetHabitabilityCert -
def
exoplanetHabitabilityCert