Over any two equal times, how do the areas swept by the Sun-to-planet line compare?
Halley's comet spends decades crawling through the outer solar system, then whips around the Sun in a few months and leaves again.
This lesson uses the equal-areas rule to find where along an orbit a body runs fast and where it runs slow.
Kepler's second law again: the line from the Sun to a planet sweeps out equal areas in equal times. That rule turns into a two-step routine for any elliptical orbit.
Step 1: find the point of the orbit nearest the Sun. The body moves fastest there.
Step 2: find the point farthest from the Sun. The body moves slowest there.
An asteroid rides a stretched elliptical orbit around the Sun. Where does it move fastest?
Between the two points, the speed changes smoothly: it drops on the way out and climbs on the way back in.
A space probe coasts on a long elliptical orbit around the Sun. Where does it move slowest?
A comet's orbit runs from just inside Mercury's orbit to beyond Neptune. Where does the comet move fastest?
Find the point nearest the Sun: just inside Mercury's orbit.
By the equal-areas rule, the comet moves fastest there.
Fastest at its nearest point to the Sun, just inside Mercury's orbit.
The same comet's orbit reaches beyond Neptune. Where does the comet move slowest?
Find the point farthest from the Sun: beyond Neptune.
The Sun-to-comet line is longest there, so equal areas need the least orbit covered.
Slowest at its farthest point, beyond Neptune.
The more stretched the ellipse, the bigger the difference between fastest and slowest. That is Halley's story: months of speed near the Sun, decades of slowness far away.
A comet's speed peaks each time it crosses one particular point of its orbit. Which point?
The diagram shows a comet's current position on its orbit around the Sun. How does its speed there compare with its speed elsewhere on the orbit?
A probe's speed around the Sun is highest every March. What is true of the probe each March?
Mercury rides a mild ellipse; Halley's comet rides an extreme one. Which body shows the bigger contrast between its fastest and slowest speeds?