Chapter 5, Problem 80RPP

Halley's Comet Edmond Halley was the first to realize that the comets observed in 1531, 1607, and 1682 were really one comet (now called Halley's Comet) that moved around the Sun in an elongated elliptical orbit (see Figure 5.5). He predicted that the peanut-shaped comet would reappear in 1757. It appeared in March 1759 (attractions to Jupiter and Saturn delayed its trip by 618 days). More recent appearances of Halley’s Comet were in 1835, 1910, and 1986. It is expected again in 2061.

The nucleus of Halley's Comet is relatively small (15 km long. 8 km wide, and 8 km thick). It has a low $\text{2}\text{.2 }\times {\text{ 10}}^{\text{14}}\text{-kg}$ mass with an average density of about ${\text{600 kg/m}}^{\text{3}}$. $\left({\text{The density of water is 1000 kg /m}}^{\text{3}}\text{.}\right)$

The nucleus rotates once every 52 h. When Halley’s Comet is closest to the Sun, temperatures on the comet can rise to about $\text{77 °C}$ and several tons of gas and dust are emitted each second, producing the long tail that we see each time it passes the Sun.

Suppose that instead of being peanut shaped, Halley’s Comet was spherical with a radius of 5.0 km (about its present volume). Which answer below is closest to what your radial acceleration would be if you were standing on the “equator" of the rotating comet?

$\begin{array}{l}\text{a}{\text{. 10}}^{\text{-5}}{\text{m/s}}^{\text{2}}\hfill \\ \text{b}{\text{. 10}}^{\text{-3}}{\text{m/s}}^{\text{2}}\hfill \\ \text{c}\text{. 0}{\text{.1 m/s}}^{\text{2}}\hfill \\ \text{d}{\text{. 10 m/s}}^{\text{2}}\hfill \\ \text{e}{\text{.1000 m/s}}^{\text{2}}\hfill \end{array}$