Why planets speed up near the Sun: Kepler's equal-areas law
30seconds
Earth moves at 30.29 km/s near 3 January and 29.29 km/s near 4 July, with nothing pushing it along. The rule behind the change is Kepler's equal-areas law: a line from the Sun to a planet sweeps out equal areas in equal times.
Stretch an orbit yourself, watch twelve equal-time wedges change shape but never size, and see why Halley's comet is about 60 times faster at its closest than at its farthest.
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