Chapter 10.6, Problem 28ES

Use the following values, where needed:

$\begin{array}{|l|}\hline \text{radius of the Earth}=\text{4000 mi}=\text{6440 km}\hfill \\ \text{1 year }\left(\text{Earth year}\right)=\text{365 days }\left(\text{Earth days}\right)\hfill \\ \text{1 AU}=\text{92}\text{.9}\times {\text{10}}^{\text{6}}\text{mi}=\text{150}\times {\text{10}}^{\text{6}}\text{km}\hfill \\ \hline\end{array}$

The planet Jupiter is believed to have a rocky core of radius 10,000 km surrounded by two layers of hydrogen—a 40,000 km thick layer of compressed metallic-like hydrogen and a 20,000 km thick layer of ordinary molecular hydrogen. The visible features, such as the Great Red Spot, are at the outer surface of the molecular hydrogen layer. On November 6, 1997 the spacecraft Galileo was placed in a Jovian orbit to study the moon Europa. The orbit had eccentricity 0.814580 and semimajor axis 3,514,918.9 km. Find Galileo's minimum and maximum heights above the molecular hydrogen layer (see the accompanying figure).