Equal areas in equal times

In the picture

1. 1The Sun: sits at one focus of the ellipse, not at its centre
2. 2Near-side wedge: short and wide, swept quickly close to the Sun
3. 3Far-side wedge: long and thin, swept slowly far from the Sun, with the same area as the near-side wedge
4. 4The planet: moves fastest at its closest point to the Sun (perihelion)

Examples

• Earth is closest to the Sun in early January and moves fastest then, which is why the northern winter half of the year is a few days shorter than the summer half.
• A figure skater spins faster when pulling their arms in, for the same reason: angular momentum is conserved.

Quiz: Equal areas in equal times (Age 17)

1. 1

   According to Kepler’s second law, what stays the same when you compare equal intervals of time along a planet’s orbit?

   • The area swept by the line joining the planet to the Sun
   • The speed of the planet
   • The distance between the planet and the Sun
2. 2

   Where in its orbit does a planet move most slowly?

   • Halfway between its closest and farthest points
   • At aphelion, its farthest point from the Sun
   • At perihelion, its closest point to the Sun
3. 3

   In the same amount of time, the Sun–planet line sweeps a short, wide wedge near the Sun and a long, thin wedge far from it. How do the areas of the two wedges compare?

   • The wedge near the Sun has the larger area
   • The two wedges have the same area
   • The wedge far from the Sun has the larger area

The answers, each with its explanation, are in the app. This lesson has left the free week, so its quiz is part of the subscription.