The orbital period of Halley's Comet is calculated to be 75.5 years. Many other comets have orbits that extend much farther from the sun, and hence have much longer periods. At aphelion, a typical long-period comet is about from the sun; at perihelion, it passes inside the earth's orbit.

1. Estimate the orbital period of such a comet. Give your answer in years.

2. Estimate the speed of a typical long-period comet at perihelion. (Hint: At aphelion, the comet is moving very slowly.)

3. The massive nucleus of a comet contains about of material. If the earth were struck by a long-period comet, estimate the kinetic energy the comet would have just before impact. An impact of this kind apparently occurred 65 million years ago in the Yucatan, and is implicated in the demise of the dinosaurs as well as many other ancient species. (Hint: The motion of the comet is due primarily to the gravitational attraction of the sun, not the earth.)