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Kepler's second law
Beginner
The line from Sun to planet sweeps equal areas in equal times.
dA/dt = L/2mA line from the Sun to a planet sweeps equal areas in equal times, a consequence of angular momentum conservation, so planets move fastest at perihelion.
Earth moves at 30.3 km/s in January and 29.3 km/s in July.
Holds for any central force.
In more detail
Kepler's second law states that a planet sweeps out equal areas in equal times. This is equivalent to conservation of angular momentum for a central force.
Real-world uses
- Planets move fastest when closest to the Sun.
- Mission planners use the second law to time orbital manoeuvres.
- Engineers designing a satellite's orbit use equal areas in equal times to predict when it moves fastest.
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Frequently asked questions
Where does a planet move fastest?
At perihelion, its closest point to the Sun.
Is this law special to gravity?
It holds for any central force, since angular momentum is conserved.
What does Kepler's second law tell me about speed?
A planet moves faster when it is closer to the Sun, because it must sweep the same area in the same time.
Related topics in Gravitation & Orbits
Polar and low Earth orbits · Weightlessness in orbit · Kepler's first law · Kepler's third law · Elliptical orbit energy · Eccentricity