Kepler's second lawlaw
A planet moves around the Sun: the closer, the faster. The line connecting the planet and the Sun sweeps out equal areas in equal time intervals. A figure skater pulling in their arms spins faster — the same principle applies here.
How it works
The law manifests for all bodies in orbit: planets, comets, satellites. A comet with an elongated orbit rushes swiftly near the Sun and barely crawls far away. This law helps find exoplanets: the planet's gravity makes the star wobble, and from the variation in radial velocity, which obeys Kepler's second law, the orbital parameters are calculated.
💡 If the orbit were a perfect circle, the planet's speed would remain constant. But on an ellipse, Earth is 3% faster in January than in July.
\frac{dA}{dt} = \frac{1}{2} r^2 \frac{d\theta}{dt} = \frac{L}{2m} = \text{const}
dA/dt is the time derivative of area, r is the distance from the center of force, dθ/dt is the angular velocity, L is the angular momentum of the body, m is its mass
r^2 \dot{\theta} = h = \text{const}
r is the distance, θ is the angular coordinate, \(\dot{\theta}\) = dθ/dt is the angular velocity, h is a constant equal to twice the areal velocity (h = 2 dA/dt)