Back-of-the-Envelope Calculations: Orbital Distance Scale
Let's imagine a scale model of the Earth with an orbiting Space Shuttle. Suppose that the Earth is the size of a basketball. How far above the basketball does the Shuttle orbit?
About 7 mm. The Earth has a radius of about 6400 km. The Shuttle orbits about 400 km above the Earth's surface, which is a distance roughly 6% of the radius of the Earth. A basketball is about 120 mm in radius. If we find 6% of 120 mm, we should have the scale distance of the Shuttle above our basketball. If we multiply 120 mm x 0.06, we get about 7 mm. If you hold a basketball, and imagine a very teeny tiny Space Shuttle orbiting the basketball, the orbit would be 7 millimeters above the basketball! That's just a bit more than 1/4" off the surface! Surprised?? Most people visualize the Shuttle as being much farther from the Earth than that when it is in space, and many people even think that the Shuttle goes to the Moon!
References and Resources
This SERC page describes the use of Back of the Envelope Calculations
The Back of the Envelope : This page outlines one of the essays in the book "Programming Pearls" (ISBN 0-201-65788-0). The book is written for computer science faculty and students, but this portion speaks very well to back of the envelope calculations in general.