Back-of-the-Envelope Calculations: Communication with Mars
Suppose you were living in a Mars colony, and you wanted to call home to your parents on Earth. You say, "Hello! How are you?" How long do you have to wait until you hear them say, "We're fine! How are you?"
Anywhere between about eight and a half and 45 minutes. It depends on where Mars and the Earth are relative to one another in their orbits when you make your call. If you are as close as we could be to Mars (about 79 million km) and light travels at 300,000 km/sec, it would take about 260 seconds, or 4.3 minutes, for your parents to hear your voice and another 4.3 minutes for you to finally hear their reply. If Mars and Earth are on opposite sides of the solar system, however, you and your parents would be about 380 million kilometers apart. The two-way communication time would be almost 45 minutes! Makes for a pretty slow conversation and really steep phone bills.
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.