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When we want to figure out the long-term evolution of a planet's atmosphere/orbit, when is perihelion more important than mean distance?

E.g. some processes (like Jeans Escape and escape of atmospheres) are disproportionately affected during perihelion (point of closest approach) rather than during aphelion.

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Well, you basically answered your own question- The more elliptical an orbit, the more pronounced the perihelion-only effects are. For planets, I don't think any have orbits so elliptical that it matters very much. Comets, on the other hand... I think outgassing is so pronounced for comets whose perihelion is in the inner Solar System that it actually affects their orbits, not just their atmospheres (er, tails).

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