The problem that follow involve straight-line motion. The time t is in seconds unless othe...

The problem that follow involve straight-line motion. The time t is in seconds unless otherwise stated.

Problem

From astronomical data, Johannes Kepler deduced that the line from the sun to a planet traces out equal areas in equal times (Fig. a). Show that this result follows from the fact that the transverse component a0 of the planet's acceleration is zero. [When r changes by an amount dr and θ changes by an amount dθ (Fig. b), the resulting differential element of area is