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Planetary Systems & Earth

Orbit, radiation, atmosphere and climate connect cosmic matter to habitable and non-habitable worlds.

interactivemodel assumptions visibleestablished science separated from analogy

Story step: Cosmic matter assembles into bound worlds. Planetary science connects orbital mechanics, radiation, atmospheres, interiors and climate feedbacks.

1 · Kepler orbit explorer

For a small body orbiting a one-solar-mass star, the orbital period in years obeys P² = a³ when a is in AU.

P = √(a³) r(θ)=a(1−e²)/(1+e cosθ)

semi-major axis a (AU)

eccentricity e

—orbital period

—periapsis

—apoapsis

2 · Radiative equilibrium

A zero-atmosphere equilibrium temperature follows from balancing absorbed starlight against thermal emission.

T_eq = [L(1−A)/(16πσd²)]^(1/4)

stellar luminosity L/L☉

distance d (AU)

Bond albedo A

—equilibrium temperature

—incident flux / Earth

—absorbed fraction

3 · Atmospheric scale height

In an isothermal ideal-gas atmosphere, pressure falls approximately exponentially with height.

H = RT/(Mg)

temperature T (K)

molar mass M (g/mol)

gravity g (m/s²)

—scale height

—P at 10 km / P₀

—P at 50 km / P₀

4 · Zero-dimensional climate balance

A global energy-balance model shows how solar input, albedo, infrared emissivity and an imposed forcing compete.

0 = S(1−A)/4 + F − εσT⁴

solar constant S (W/m²)

albedo A

effective emissivity ε

extra forcing F (W/m²)

—equilibrium T

—absorbed + forcing

teaching modelnot an Earth-system forecast

Scientific boundary: Kepler orbits and ideal atmospheres are controlled approximations. The climate panel is a zero-dimensional energy-balance model, not a forecast of Earth’s climate or a replacement for coupled atmosphere–ocean–ice models.