Back-of-the-Envelope Calculations: Approaching Asteroid
If asteroids careen through the solar system at 25 km/second, how far away would we have to detect one in order to have a year's notice to prepare for an impact, as was portrayed in the movie Deep Impact? How far away is that relative to the planets in our solar system?
More than 3/4 of a billion kilometers away (about 788 million kilometers, actually), which is about the distance from the Earth to somewhere between the orbits of Jupiter and Saturn. 25 km/second is 90,000 km/hour. With 8,760 hours in a year, the asteroid would travel 788 million kilometers in a year.
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.