🪐 Gravitation — a planet orbiting the Sun (Kepler's laws in action)

One gravity law runs the whole chapter. Farther orbit → slower planet, longer year: T² = (4π²/GM)·a³. Spin (the planet's day) is independent of revolution (its year). This is the chapter hero: one gravitation law behind orbit, day, year and seasons.

Orbit size a 1.00 AU

Eccentricity e 0.20

Central mass M 1.00 M☉

Spin period T_day 24.0 h

Axial tilt ε 23.5°

Your latitude φ 28.6°N

Animation speed 1.0×

a = 1.00 AU · e = 0.20 · M = 1.00 M☉
Year T = √(a³/M) = 1.00 yr · r = 0.80 AU

v = √(GM(2/r−1/a)) = 29.8 km/s
F = GMm/r² = 1.00 F⊕ pulls inward (brown)

Day T_day = 24.0 h · ω = 2π/T_day = 7.27e-5 rad/s
Spins 365× per orbit · tilt ε = 23.5°

SEASONS · sin δ = sin ε·cos θ → δ = +23.5° · N summer
cos H = −tan φ·tan δ → daylight 13.9 h · noon Sun 85°