What is the perihelion distance

of Halley’s Comet? The comet’s

semimajor axis is 17.8 AU.

rmin = 2aírmax

rmin = 2(17.8 AU) í 35.1 AU

rmin = 0.5 AU

What is the eccentricity of

Pluto’s orbit?

e = 0.25

12.15 - Kepler’s second law

The law of areas: An orbiting body sweeps out

equal areas in equal amounts of time.

In his second law, Kepler used a geometrical technique to show that the speed of an

orbiting planet is related to its distance from the Sun. (We use the example of a planet

and the Sun; this law applies equally well for a satellite orbiting the Earth, or for Halley’s

comet orbiting the Sun.)

Kepler used the concept of a line connecting the planet to the Sun, moving like a

second hand on a watch. As shown to the right, the line “sweeps out” slices of area over

time. His second law states that the planet sweeps out an equal area in an equal

amount of time in any part of an orbit. In an elliptical orbit, planets move slowest when

they are farthest from the Sun and move fastest when they are closest to the Sun.

Kepler established his second law nearly a century before Newton proposed his theory

of gravitation. Although Kepler did not know that gravity varied with the inverse square

of the distance, using Brahe’s data and his own keen quantitative insights he determined a key aspect of elliptical planetary motion.

Kepler’s second law

Planets in orbit sweep out equal areas

in equal times

(^234) Copyright 2000-2007 Kinetic Books Co. Chapter 12