Areala

Meet Areala, a planet who speeds up near the Sun and slows down far away, so she always sweeps out equal areas in equal times.

Kepler's second law, published in 1609, says that the line from the Sun to a planet sweeps out equal areas in equal times. Near the Sun the line is short, so the planet must move fast to sweep the same area; far away it moves slowly. Newton later showed that this law is angular-momentum conservation: gravity points straight at the Sun, so it exerts no torque, and the rate of sweeping is fixed at L/(2m).

Earth reaches perihelion in early January, about 147 million kilometres from the Sun, and aphelion in early July, about 152 million. It moves fastest in January, which is one reason northern winter is a few days shorter than northern summer.

In the sticker, the ellipse has eccentricity 0.25, and the two shaded sectors are drawn with equal area: a narrow one far away and a wider one close in.

The law holds for any central force, not only gravity, but breaks down when other bodies tug on the planet.