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Kepler's second law from L
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Equal areas in equal times follows from conserved angular momentum.
For a central force the angular momentum is constant, so the area swept per unit time, dA/dt = L/2m, is constant. Planets speed up near the Sun.
Earth moves faster in January (perihelion).
This holds for any central force, not just gravity.
In more detail
Kepler's second law, that a planet sweeps equal areas in equal times, follows from conservation of angular momentum for a central gravitational force.
Real-world uses
- Astronomers use Kepler's second law to predict planetary speeds at different points in an orbit.
- Satellite operators use the same result to plan orbital transfers.
- A planet closer to the Sun speeds up, which is required by conservation of angular momentum in its elliptical orbit.
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Frequently asked questions
Why is the planet faster near the Sun?
Because the orbit is closer, and angular momentum conservation makes the speed increase at perihelion.
Does the second law depend on the force shape?
It holds for any central force, since angular momentum is conserved.
What does equal area in equal time mean?
The line from the Sun to the planet sweeps out equal areas in equal intervals, a direct result of conserved angular momentum.
Related topics in Momentum & Collisions
Angular momentum · Conservation of angular momentum · Ice-skater spin · Collision of particles in physics labs · Compton scattering · Newton's cradle