What percentage of Earth’s surface area could the astronauts see when Skylab 4 was at its apogee height, 437 km above the surface? To find out, model the visible surface as the surface generated by revolving the circular arc GT, shown here, about the y-axis. Then carry out these steps:

1. Use similar triangles in the figure to show that y₀/6380 = 6380/(6380 + 437). Solve for y₀.

2. To four significant digits, calculate the visible area as

3. Express the result as a percentage of Earth’s surface area.

Transcribed Image Text:

VA -6380 Yo 2πχ. 1 + dx dy 2 dy.