Gravitational Constant in U.S. Customary Units

Problem: The universal gravitational constant is \(G = 66.73\times10^{-12}\,\text{m}^3/(\text{kg}\cdot\text{s}^2)\).

1. Express \(G\) in \(\text{ft}^3/(\text{slug}\cdot\text{s}^2)\).
2. Two steel spheres each weigh 500 lb at the earth's surface, and their centers are 2 ft apart. Using \(F = G\,m_1 m_2/r^2\), determine the gravitational attraction \(F\) between them in pounds.
3. Express the same force in micronewtons.

Use \(1\,\text{ft} = 0.3048\,\text{m}\), \(1\,\text{slug} = 14.59\,\text{kg}\), \(1\,\text{lb} = 4.448\,\text{N}\) and \(g = 32.2\,\text{ft/s}^2\). Very small answers can be typed in scientific notation, for example 2.5e-6.