A First Order Filter for the Detection of Potentially Habitable Exoplanets

The search for potentially habitable exoplanets is a primary objective in modern astrophysics, yet the vast number of candidates discovered by missions like Kepler and TESS presents a significant challenge for detailed follow-up characterization. An efficient and reliable method for prioritizing the most promising targets is therefore essential. In this paper, we propose a novel first-order filter for identifying potentially habitable worlds based on a simple geometric ratio: the orbital semi-major axis to the stellar diameter ($d/D_s$). Using data from the NASA Exoplanet Archive, we demonstrate that the ideal value for this ratio is not constant, but is dependent on the host star's spectral class. We establish a tiered framework of ideal ratios, beginning with $\approx 108$ for G-type stars (anchored by the Earth-Sun system), and decreasing by a factor of two for K-type ($\approx 54$) and M-type ($\approx 27$) stars, respectively. Our analysis reveals a strong correlation, showing that exoplanets whose $d/D_s$ ratios are close to these empirically derived values consistently exhibit high Earth Similarity Index (ESI) scores. We propose that these tiered ratios represent "Habitability Main Sequences," analogous to the Hertzsprung-Russell diagram for stars, providing a valuable and straightforward tool for the astronomical community to rapidly screen large datasets and efficiently shortlist high-priority candidates for further investigation with next-generation observatories.