Kepler’s Second Law — Equal Areas: Why do planets speed up near the Sun?

Summer in the Northern Hemisphere lasts about 93 days. Winter lasts 89 days. Where does that 4-day difference come from? Doesn’t Earth orbit at a constant speed?

No. This is exactly what Kepler’s Second Law explains.

Kepler’s Second Law

The line connecting the Sun to a planet sweeps out equal areas in equal time intervals.

Why?

When a planet is closer to the Sun, gravity acts more strongly → the planet accelerates → it moves faster. When it’s farther away, gravity is weaker → it slows down. But this speed change is precisely calibrated so that the area swept per unit time stays constant. This is a direct consequence of conservation of angular momentum.

The Longer Summer

Earth is at its farthest point from the Sun in July (aphelion) — so it moves slowest. The Northern Hemisphere is in summer at this time. Because Earth is slower, summer lasts longer (93 days). In January Earth is at its closest point (perihelion) — it moves fastest — Northern winter is shorter (89 days).

References

• Halliday, Resnick & Krane — Physics, Ch. 13
• Feynman Lectures on Physics — Vol. 1, Ch. 7